class: title-slide # Statistical modelling for health technology assessment and the analysis of the value of information ## Gianluca Baio ### [Department of Statistical Science](https://www.ucl.ac.uk/statistics/) | University College London .title-small[ <svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;top:.1em;fill:#00acee;height:0.8em;"> [ comment ] <path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"></path></svg> [g.baio@ucl.ac.uk](mailto:g.baio@ucl.ac.uk) <svg viewBox="0 0 512 512" 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[https://egon.stats.ucl.ac.uk/research/statistics-health-economics/](https://egon.stats.ucl.ac.uk/research/statistics-health-economics/) <svg viewBox="0 0 496 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;top:.1em;fill:black;height:0.8em;"> [ comment ] <path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"></path></svg> [https://github.com/giabaio](https://github.com/giabaio) <svg viewBox="0 0 496 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;top:.1em;fill:black;height:0.8em;"> [ comment ] <path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 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2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"></path></svg> [https://github.com/StatisticsHealthEconomics](https://github.com/StatisticsHealthEconomics) <svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;top:.1em;fill:#00acee;height:0.8em;"> [ comment ] <path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"></path></svg> [@gianlubaio](https://twitter.com/gianlubaio) ] ### 18th Armitage Lecture, MRC Biostatistics Unit, Cambridge <!-- Can also separate the various components of the extra argument 'params', eg as in ### 18th Armitage Lecture, MRC Biostatistics Unit, Cambridge, Statistical modelling for HTA and VoI --> 10 November 2021 <!-- This adds a footer (optional and with other possibilities...) --> .footer-left[ <span><a href="http://www.statistica.it/gianluca/"><img src="assets/logo.png" title="Go home" width="2.0%"></a></span> <span style="position: relative; bottom: 7px; color: #D5D5D5;"> &nbsp; &copy; Gianluca Baio (UCL)</span> ] <p style="position: absolute; top:75%; left:2.5%; font-family: Nanum Pen Script; font-size:85%; text-decoration: none; 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</svg></a>&nbsp; ] <!-- Can also add a center footer, eg to include the title of the talk --> .footer-center[ Statistical modelling for HTA and VoI ] <!-- And a right footer, to include the date --> .footer-right[ 18th Armitage Lecture, 10 Nov 2021 ] --- count: false background-image: url("img/maneskin.gif") background-size: cover --- count: false background-image: url("img/euro2020.gif") background-size: cover --- count: false background-image: url("img/olympics.gif") background-size: cover --- count: false background-image: url("img/volley-girls2.gif") background-size: cover --- count: false background-image: url("img/volley-boys.gif") background-size: cover --- count: false background-image: url("img/parisi.jpg") background-size: cover --- count: false background-image: url("img/armitage.jpg") background-size: cover --- count: false background-image: url("img/berlusconi.jpg") background-size: cover --- count: false background-image: url("img/mysite.png") background-size: cover --- exclude: true count: false # Disclaimer... <center> <blockquote class="twitter-tweet"><p lang="en" dir="ltr">Best opening sentence <a href="https://twitter.com/hashtag/ISPOREurope?src=hash&amp;ref_src=twsrc%5Etfw">#ISPOREurope</a> from Gianluca Baio: “statisticians should rule the world and Bayesian statisticians should rule all statisticians” <a href="https://t.co/GN2w7liAcR">https://t.co/GN2w7liAcR</a></p>&mdash; Manuela Joore (@ManuelaJoore) <a href="https://twitter.com/ManuelaJoore/status/1191397718930939904?ref_src=twsrc%5Etfw">November 4, 2019</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script> </center> <span style="display:block; margin-top: 40px ;"></span> ...Just so you know what you're about to get into... 😉 --- # Outline 1. Health economic evaluation - What is it? - A bit of history... - How does it work? -- 2. Make statistics great again - Uncertainty analysis - The importance of being a Bayesian... 😉 - Example: survival modelling in HTA -- 3. Value of Information - What it is and stupid examples - Relevant measures - All that glitters... -- 4. Conclusions --- # Health technology assessment (HTA) ## Objective - Combine .red[costs] and .blue[benefits] of a given intervention into a rational scheme for allocating resources > *Health technology assessment (HTA) is a method of evidence synthesis that considers evidence regarding clinical effectiveness, safety, cost-effectiveness and, when broadly applied, includes social, ethical, and legal aspects of the use of health technologies. The precise balance of these inputs depends on the purpose of each individual HTA. A major use of HTAs is in informing reimbursement and coverage decisions, in which case HTAs should include benefit-harm assessment and economic evaluation.* .alignright[<svg viewBox="0 0 384 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> <g label="icon" id="layer6" groupmode="layer"> <path id="path2" d="M 120.19265,177.73779 C 123.18778,77.35076 64.277527,63.999998 64.277527,63.999998 v 31.26245 C 40.834519,83.611374 18.32863,81.929634 18.32863,81.929634 V 337.10903 c 0,0 98.10414,-11.41744 98.10414,84.40952 0,0 36.58424,-153.37442 248.86103,26.48145 0,-61.59342 0.37757,-216.93925 0.37757,-268.28471 C 169.9561,37.131382 120.1931,177.73779 120.1931,177.73779 Z m 187.20631,173.82056 -12.37599,-97.65441 h -0.448 l -40.72819,97.65441 h -17.55994 l -38.9362,-97.65441 h -0.448 l -14.17589,97.65441 h -43.87514 l 28.8015,-169.61925 h 43.42716 l 34.43518,90.6496 36.46566,-90.6496 h 43.87513 l 25.6817,169.61925 h -44.13938 z" style="stroke-width:0.0675239"></path> </g></svg> [Luce et al, 2010](https://pubmed.ncbi.nlm.nih.gov/20579285/)] .small[(Quote stolen from a brilliant presentation by [Cynthia Iglesias](https://www.york.ac.uk/healthsciences/our-staff/cynthia-iglesias/))] <span style="display:block; margin-top: -5px ;"></span> -- ## A relatively new discipline - Basically becomes "a thing" in the 1970s - Arguably, a **historical accident**... - Economists take the lead in developing the main theory `\(\Rightarrow\)` *Health Economics* - But there's so much more to it (more on this later...) <span style="display:block; margin-top: -10px ;"></span> -- ## (Truly...) World-beating Britain - Since its establishment, the **[National Institute for Health and Care Excellence](https://www.nice.org.uk/)** (originally: National Institute for Clinical Excellence, **NICE**), has gained prominence as the global powerhouse for HTA --- # Health technology assessment (HTA) ## NICE - Established in 1999, during the first New Labour government - Health Secretary Frank Dobson on whether it will work: > *Probably not, but it's worth a bloody try!* <svg viewBox="0 0 384 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> <g label="icon" id="layer6" groupmode="layer"> <path id="path2" d="M 120.19265,177.73779 C 123.18778,77.35076 64.277527,63.999998 64.277527,63.999998 v 31.26245 C 40.834519,83.611374 18.32863,81.929634 18.32863,81.929634 V 337.10903 c 0,0 98.10414,-11.41744 98.10414,84.40952 0,0 36.58424,-153.37442 248.86103,26.48145 0,-61.59342 0.37757,-216.93925 0.37757,-268.28471 C 169.9561,37.131382 120.1931,177.73779 120.1931,177.73779 Z m 187.20631,173.82056 -12.37599,-97.65441 h -0.448 l -40.72819,97.65441 h -17.55994 l -38.9362,-97.65441 h -0.448 l -14.17589,97.65441 h -43.87514 l 28.8015,-169.61925 h 43.42716 l 34.43518,90.6496 36.46566,-90.6496 h 43.87513 l 25.6817,169.61925 h -44.13938 z" style="stroke-width:0.0675239"></path> </g></svg> [Rawlins, 2009](https://pubmed.ncbi.nlm.nih.gov/19394075/) .pull-right[ <span style="display:block; margin-top: -220px ;"></span> <center><img src=./img/dobson.jpg width='45%' title=''></center> ] -- - Main driver: tackle the inequalities and inefficiencies generated by the ".red[**postcode lottery**]" - Decisions about which drugs to fund through the NHS had historically been taken at a local level - Concerns over the fact that patients in some areas of the country could access treatments that people elsewhere, sometimes in neighbouring streets, could not `\(\Rightarrow\)` large inequalities in access to resources! <span style="display:block; margin-top: -20px ;"></span> - Ancillary objectives - Set quality standard *nationally* (although NICE is technically responsible for England & Wales only...) - De-politicise reimbursement/coverage decisions - Align with growing body of literature and experience in other countries ([PBAC](https://www.pbs.gov.au/info/industry/listing/participants/pbac) in Australia, NZHTA in New Zealand, [CADTH](https://www.cadth.ca/) in Canada, ...) --- count: false # Health technology assessment (HTA) ## NICE &ndash; *influenzing* the outcomes... .alignright[<svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;top:.1em;fill:#EA7600;height:0.8em;"> [ comment ] <path d="M503.52,241.48c-.12-1.56-.24-3.12-.24-4.68v-.12l-.36-4.68v-.12a245.86,245.86,0,0,0-7.32-41.15c0-.12,0-.12-.12-.24l-1.08-4c-.12-.24-.12-.48-.24-.6-.36-1.2-.72-2.52-1.08-3.72-.12-.24-.12-.6-.24-.84-.36-1.2-.72-2.4-1.08-3.48-.12-.36-.24-.6-.36-1-.36-1.2-.72-2.28-1.2-3.48l-.36-1.08c-.36-1.08-.84-2.28-1.2-3.36a8.27,8.27,0,0,0-.36-1c-.48-1.08-.84-2.28-1.32-3.36-.12-.24-.24-.6-.36-.84-.48-1.2-1-2.28-1.44-3.48,0-.12-.12-.24-.12-.36-1.56-3.84-3.24-7.68-5-11.4l-.36-.72c-.48-1-.84-1.8-1.32-2.64-.24-.48-.48-1.08-.72-1.56-.36-.84-.84-1.56-1.2-2.4-.36-.6-.6-1.2-1-1.8s-.84-1.44-1.2-2.28c-.36-.6-.72-1.32-1.08-1.92s-.84-1.44-1.2-2.16a18.07,18.07,0,0,0-1.2-2c-.36-.72-.84-1.32-1.2-2s-.84-1.32-1.2-2-.84-1.32-1.2-1.92-.84-1.44-1.32-2.16a15.63,15.63,0,0,0-1.2-1.8L463.2,119a15.63,15.63,0,0,0-1.2-1.8c-.48-.72-1.08-1.56-1.56-2.28-.36-.48-.72-1.08-1.08-1.56l-1.8-2.52c-.36-.48-.6-.84-1-1.32-1-1.32-1.8-2.52-2.76-3.72a248.76,248.76,0,0,0-23.51-26.64A186.82,186.82,0,0,0,412,62.46c-4-3.48-8.16-6.72-12.48-9.84a162.49,162.49,0,0,0-24.6-15.12c-2.4-1.32-4.8-2.52-7.2-3.72a254,254,0,0,0-55.43-19.56c-1.92-.36-3.84-.84-5.64-1.2h-.12c-1-.12-1.8-.36-2.76-.48a236.35,236.35,0,0,0-38-4H255.14a234.62,234.62,0,0,0-45.48,5c-33.59,7.08-63.23,21.24-82.91,39-1.08,1-1.92,1.68-2.4,2.16l-.48.48H124l-.12.12.12-.12a.12.12,0,0,0,.12-.12l-.12.12a.42.42,0,0,1,.24-.12c14.64-8.76,34.92-16,49.44-19.56l5.88-1.44c.36-.12.84-.12,1.2-.24,1.68-.36,3.36-.72,5.16-1.08.24,0,.6-.12.84-.12C250.94,20.94,319.34,40.14,367,85.61a171.49,171.49,0,0,1,26.88,32.76c30.36,49.2,27.48,111.11,3.84,147.59-34.44,53-111.35,71.27-159,24.84a84.19,84.19,0,0,1-25.56-59,74.05,74.05,0,0,1,6.24-31c1.68-3.84,13.08-25.67,18.24-24.59-13.08-2.76-37.55,2.64-54.71,28.19-15.36,22.92-14.52,58.2-5,83.28a132.85,132.85,0,0,1-12.12-39.24c-12.24-82.55,43.31-153,94.31-170.51-27.48-24-96.47-22.31-147.71,15.36-29.88,22-51.23,53.16-62.51,90.36,1.68-20.88,9.6-52.08,25.8-83.88-17.16,8.88-39,37-49.8,62.88-15.6,37.43-21,82.19-16.08,124.79.36,3.24.72,6.36,1.08,9.6,19.92,117.11,122,206.38,244.78,206.38C392.77,503.42,504,392.19,504,255,503.88,250.48,503.76,245.92,503.52,241.48Z"></path></svg> [20 years of NICE](https://indepth.nice.org.uk/20-years-of-NICE/index.html)] - The first drug appraisal was for the antiviral treatment for influenza, Relenza - Specifically, NICE said that > *there was insufficient evidence to show Relenza reduced the severity of the illness for those most at risk, the elderly and people with asthma* and so concluded that it > *was not cost effective and should not be provided on the NHS* <span style="display:block; margin-top: 50px ;"></span> -- - This didn't go down very well with the manufacturer, with the then CEO Sir Richard Sykes reportedly threatening that > *if the decision is not reversed, Glaxo Wellcome would consider leaving the UK* <span style="display:block; margin-top: 50px ;"></span> - Eventually, Relenza *was* made available on the NHS, but only with a limited basis (restricted population) --- # Health technology assessment (HTA) ## NICE &ndash; *teething problems* .alignright[<svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;top:.1em;fill:#EA7600;height:0.8em;"> [ comment ] <path d="M503.52,241.48c-.12-1.56-.24-3.12-.24-4.68v-.12l-.36-4.68v-.12a245.86,245.86,0,0,0-7.32-41.15c0-.12,0-.12-.12-.24l-1.08-4c-.12-.24-.12-.48-.24-.6-.36-1.2-.72-2.52-1.08-3.72-.12-.24-.12-.6-.24-.84-.36-1.2-.72-2.4-1.08-3.48-.12-.36-.24-.6-.36-1-.36-1.2-.72-2.28-1.2-3.48l-.36-1.08c-.36-1.08-.84-2.28-1.2-3.36a8.27,8.27,0,0,0-.36-1c-.48-1.08-.84-2.28-1.32-3.36-.12-.24-.24-.6-.36-.84-.48-1.2-1-2.28-1.44-3.48,0-.12-.12-.24-.12-.36-1.56-3.84-3.24-7.68-5-11.4l-.36-.72c-.48-1-.84-1.8-1.32-2.64-.24-.48-.48-1.08-.72-1.56-.36-.84-.84-1.56-1.2-2.4-.36-.6-.6-1.2-1-1.8s-.84-1.44-1.2-2.28c-.36-.6-.72-1.32-1.08-1.92s-.84-1.44-1.2-2.16a18.07,18.07,0,0,0-1.2-2c-.36-.72-.84-1.32-1.2-2s-.84-1.32-1.2-2-.84-1.32-1.2-1.92-.84-1.44-1.32-2.16a15.63,15.63,0,0,0-1.2-1.8L463.2,119a15.63,15.63,0,0,0-1.2-1.8c-.48-.72-1.08-1.56-1.56-2.28-.36-.48-.72-1.08-1.08-1.56l-1.8-2.52c-.36-.48-.6-.84-1-1.32-1-1.32-1.8-2.52-2.76-3.72a248.76,248.76,0,0,0-23.51-26.64A186.82,186.82,0,0,0,412,62.46c-4-3.48-8.16-6.72-12.48-9.84a162.49,162.49,0,0,0-24.6-15.12c-2.4-1.32-4.8-2.52-7.2-3.72a254,254,0,0,0-55.43-19.56c-1.92-.36-3.84-.84-5.64-1.2h-.12c-1-.12-1.8-.36-2.76-.48a236.35,236.35,0,0,0-38-4H255.14a234.62,234.62,0,0,0-45.48,5c-33.59,7.08-63.23,21.24-82.91,39-1.08,1-1.92,1.68-2.4,2.16l-.48.48H124l-.12.12.12-.12a.12.12,0,0,0,.12-.12l-.12.12a.42.42,0,0,1,.24-.12c14.64-8.76,34.92-16,49.44-19.56l5.88-1.44c.36-.12.84-.12,1.2-.24,1.68-.36,3.36-.72,5.16-1.08.24,0,.6-.12.84-.12C250.94,20.94,319.34,40.14,367,85.61a171.49,171.49,0,0,1,26.88,32.76c30.36,49.2,27.48,111.11,3.84,147.59-34.44,53-111.35,71.27-159,24.84a84.19,84.19,0,0,1-25.56-59,74.05,74.05,0,0,1,6.24-31c1.68-3.84,13.08-25.67,18.24-24.59-13.08-2.76-37.55,2.64-54.71,28.19-15.36,22.92-14.52,58.2-5,83.28a132.85,132.85,0,0,1-12.12-39.24c-12.24-82.55,43.31-153,94.31-170.51-27.48-24-96.47-22.31-147.71,15.36-29.88,22-51.23,53.16-62.51,90.36,1.68-20.88,9.6-52.08,25.8-83.88-17.16,8.88-39,37-49.8,62.88-15.6,37.43-21,82.19-16.08,124.79.36,3.24.72,6.36,1.08,9.6,19.92,117.11,122,206.38,244.78,206.38C392.77,503.42,504,392.19,504,255,503.88,250.48,503.76,245.92,503.52,241.48Z"></path></svg> [20 years of NICE](https://indepth.nice.org.uk/20-years-of-NICE/index.html)] .pull-left[ <center><img src=./img/wisdom-tooth.jpeg width='100%' title=''></center> ] .pull-right[ - The first full technology appraisal recommended that > *healthy wisdom teeth should not be removed as a precaution which was estimated might save the NHS £5m a year* - Very quickly got traction in the media as decisions would be (politically) sensitive &ndash; one way or the other... ] --- # Health technology assessment (HTA) ## NICE &ndash; Courting controversy .pull-left[ <center><img src=./img/daily-mail.png width='100%' title=''></center> ] .pull-right[ - The Evaluation consultation document says > *There were no statistically significant differences in quality of life between the ataluren and placebo groups. The company stated there was a positive trend towards improved quality of life with ataluren 40 mg/kg daily in the physical functioning subscale. The company submission also described a positive effect on school functioning and a negative trend in emotional and social subscales* - Estimated total cost per person per year of treatment with ataluren of £220,256 - This is hugely affected by the uncertainty in the evidence and assumptions enconded in the model presented for assessment! ] --- # Health technology assessment (HTA) **Objective**: Combine .red[costs] and .blue[benefits] of a given intervention into a rational scheme for allocating resources -- <center><img src=./img/hta-scheme1.png width='80%' title=''></center> --- count: false # Health technology assessment (HTA) **Objective**: Combine .red[costs] and .blue[benefits] of a given intervention into a rational scheme for allocating resources <center><img src=./img/hta-scheme2.png width='80%' title=''></center> --- count: false # Health technology assessment (HTA) **Objective**: Combine .red[costs] and .blue[benefits] of a given intervention into a rational scheme for allocating resources <center><img src=./img/hta-scheme3.png width='80%' title=''></center> --- count: false background-image: url("img/whatstheproblem.gif") background-size: cover # --- # A QALY is a QALY is a QALY(?)... - Benefits are typically measured using **Quality Adjusted Life Years** (QALYs), a measure of disease burden combining - .blue90red60[**Quantity**] of life (the amount of time spent in a given health state) - .blue60red90[**Quality**] of life (the *utility* attached to that state) <center><img src=./img/qalys.png width='65%' title='The QALYs can be computed as the area under the curve, where the x-axis represents the time spent in each health state and the y-axis represents the health value associated with a given state'></center> <span style="display:block; margin-top: -410px ;"></span> .alignright[ `\(\class{myblue}{e_i = \displaystyle\sum_{j=1}^{J} \left(u_{ij}+u_{i\hspace{.5pt}j-1}\right) \frac{\delta_{j}}{2}} \qquad \left[\style{font-family:inherit;}{\text{with: }} \class{myblue}{\delta_j = \frac{\style{font-family:inherit;}{\text{Time}}_j - \style{font-family:inherit;}{\text{Time}}_{j-1}}{\style{font-family:inherit;}{\text{Unit of time}}}}\right]\)` ] --- count: false # A QALY is a QALY is a QALY(?)... <center><img src=./img/map_opportunity_cost.png width='80%' title='This world map shows the different monetary values associated with a QALY'></center> <span style="display:block; margin-top: -10px ;"></span> .small[Stolen from <svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> [ comment ] <path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"></path></svg> [https://twitter.com/mikepaulden/status/1333467554317156353](https://twitter.com/mikepaulden/status/1333467554317156353)] --- count: false # Health technology assessment (HTA) **Objective**: Combine .red[costs] and .blue[benefits] of a given intervention into a rational scheme for allocating resources <center><img src=./img/hta-scheme4.png width='80%' title=''></center> --- # Health technology assessment (HTA) ## *To be or not to be?... (A Bayesian)* .center[ .pull-left[ ### Frequentist ("standard") <center><img src=./img/two-stage.png width='610px' title=''></center> ] .pull-right[ ### Bayesian <center><img src=./img/integrated.png width='610px' title=''></center> ] ] --- # Example ## Economic modelling for cancer drug: 3-state cancer "Markov model" - Very prevalent in HTA - Use "multistate" model to simulate progression of patients over a set of health states - Often based on time-to-event data to estimate the "transition probabilities" `\(\color{red}{\boldsymbol\lambda}\)` <span style="display:block; margin-top: 40px ;"></span> <center><img src=./img/3state-1.png width='70%' title=''></center> --- # Uncertainty analysis .small[(**P**robabilistic **S**ensitivity **A**nalysis)] .three-column[ ### Statistical model <img src="./img/unnamed-chunk-2-1.png" style="display: block; margin: auto;" width="50%"> ] .three-column[ ### Economic model <span style="display:block; margin-top: 50px ;"></span> .center[ Status quo ] .content-box-gray[ <center><img src=./img/3state-2.png width='100%' title='INCLUDE TEXT HERE'></center> ] <span style="display:block; margin-top: 80px ;"></span> .center[ New drug ] .content-box-gray[ <center><img src=./img/3state-2.png width='100%' title='INCLUDE TEXT HERE'></center> ] ] .three-column[ ### Decision analysis <table class=" lightable-classic table" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto; font-size: 12px; width: auto !important; margin-left: auto; margin-right: auto;'> <thead> <tr><th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; font-weight: bold; padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="2"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">Status quo</div></th></tr> <tr> <th style="text-align:left;background-color: white !important;text-align: center;"> Benefits </th> <th style="text-align:left;background-color: white !important;text-align: center;"> Costs </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> 741 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> 670382.1 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> 699 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> 871273.3 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> ... </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> ... </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;border-bottom: 1px solid;width: 35%; "> 726 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;border-bottom: 1px solid;width: 35%; "> 425822.2 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;font-weight: bold;width: 35%; "> 716.2 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;font-weight: bold;width: 35%; "> 790381.2 </td> </tr> </tbody> </table> <span style="display:block; margin-top: 10px ;"></span> <table class=" lightable-classic table" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto; font-size: 12px; width: auto !important; margin-left: auto; margin-right: auto;'> <thead> <tr><th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; font-weight: bold; padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="2"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">New drug</div></th></tr> <tr> <th style="text-align:left;background-color: white !important;text-align: center;"> Benefits </th> <th style="text-align:left;background-color: white !important;text-align: center;"> Costs </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> 732 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> 1131978 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> 664 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> 1325654 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> ... </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> ... </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;border-bottom: 1px solid;width: 35%; "> 811 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;border-bottom: 1px solid;width: 35%; "> 766411.4 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;font-weight: bold;width: 35%; "> 774.5 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;font-weight: bold;width: 35%; "> 1066849.8 </td> </tr> </tbody> </table> ] --- count: false # Uncertainty analysis .small[(**P**robabilistic **S**ensitivity **A**nalysis)] .three-column[ ### Statistical model <img src="./img/unnamed-chunk-6-1.png" style="display: block; margin: auto;" width="50%"> ] .three-column[ ### Economic model <span style="display:block; margin-top: 50px ;"></span> .center[ Status quo ] .content-box-gray[ <center><img src=./img/3state-2.png width='100%' title='INCLUDE TEXT HERE'></center> ] <span style="display:block; margin-top: 80px ;"></span> .center[ New drug ] .content-box-gray[ <center><img src=./img/3state-2.png width='100%' title='INCLUDE TEXT HERE'></center> ] ] .three-column[ ### Decision analysis <table class=" lightable-classic table" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto; font-size: 12px; width: auto !important; margin-left: auto; margin-right: auto;'> <thead> <tr><th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; font-weight: bold; padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="2"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">Status quo</div></th></tr> <tr> <th style="text-align:left;background-color: white !important;text-align: center;"> Benefits </th> <th style="text-align:left;background-color: white !important;text-align: center;"> Costs </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 741 </td> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 670382.1 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> 699 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> 871273.3 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> ... </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> ... </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;border-bottom: 1px solid;width: 35%; "> 726 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;border-bottom: 1px solid;width: 35%; "> 425822.2 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;font-weight: bold;width: 35%; "> 716.2 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;font-weight: bold;width: 35%; "> 790381.2 </td> </tr> </tbody> </table> <span style="display:block; margin-top: 10px ;"></span> <table class=" lightable-classic table" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto; font-size: 12px; width: auto !important; margin-left: auto; margin-right: auto;'> <thead> <tr><th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; font-weight: bold; padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="2"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">New drug</div></th></tr> <tr> <th style="text-align:left;background-color: white !important;text-align: center;"> Benefits </th> <th style="text-align:left;background-color: white !important;text-align: center;"> Costs </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 732 </td> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 1131978 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> 664 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> 1325654 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> ... </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> ... </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;border-bottom: 1px solid;width: 35%; "> 811 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;border-bottom: 1px solid;width: 35%; "> 766411.4 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;font-weight: bold;width: 35%; "> 774.5 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;font-weight: bold;width: 35%; "> 1066849.8 </td> </tr> </tbody> </table> ] .arrow1[ `\(\rightarrow\)` ] .arrow2[ `\(\rightarrow\)` ] --- count: false # Uncertainty analysis .small[(**P**robabilistic **S**ensitivity **A**nalysis)] .three-column[ ### Statistical model <img src="./img/unnamed-chunk-9-1.png" style="display: block; margin: auto;" width="50%"> ] .three-column[ ### Economic model <span style="display:block; margin-top: 50px ;"></span> .center[ Status quo ] .content-box-gray[ <center><img src=./img/3state-2.png width='100%' title='INCLUDE TEXT HERE'></center> ] <span style="display:block; margin-top: 80px ;"></span> .center[ New drug ] .content-box-gray[ <center><img src=./img/3state-2.png width='100%' title='INCLUDE TEXT HERE'></center> ] ] .three-column[ ### Decision analysis <table class=" lightable-classic table" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto; font-size: 12px; width: auto !important; margin-left: auto; margin-right: auto;'> <thead> <tr><th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; font-weight: bold; padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="2"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">Status quo</div></th></tr> <tr> <th style="text-align:left;background-color: white !important;text-align: center;"> Benefits </th> <th style="text-align:left;background-color: white !important;text-align: center;"> Costs </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 741 </td> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 670382.1 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 699 </td> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 871273.3 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> ... </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> ... </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;border-bottom: 1px solid;width: 35%; "> 726 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;border-bottom: 1px solid;width: 35%; "> 425822.2 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;font-weight: bold;width: 35%; "> 716.2 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;font-weight: bold;width: 35%; "> 790381.2 </td> </tr> </tbody> </table> <span style="display:block; margin-top: 10px ;"></span> <table class=" lightable-classic table" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto; font-size: 12px; width: auto !important; margin-left: auto; margin-right: auto;'> <thead> <tr><th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; font-weight: bold; padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="2"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">New drug</div></th></tr> <tr> <th style="text-align:left;background-color: white !important;text-align: center;"> Benefits </th> <th style="text-align:left;background-color: white !important;text-align: center;"> Costs </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 732 </td> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 1131978 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 664 </td> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 1325654 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> ... </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;width: 35%; "> ... </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;border-bottom: 1px solid;width: 35%; "> 811 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;border-bottom: 1px solid;width: 35%; "> 766411.4 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;font-weight: bold;width: 35%; "> 774.5 </td> <td style="text-align:left;background-color: white !important;text-align: center;color: white !important;font-weight: bold;width: 35%; "> 1066849.8 </td> </tr> </tbody> </table> ] .arrow1[ `\(\rightarrow\)` ] .arrow2[ `\(\rightarrow\)` ] --- count: false # Uncertainty analysis .small[(**P**robabilistic **S**ensitivity **A**nalysis)] .three-column[ ### Statistical model <img src="./img/unnamed-chunk-12-1.png" style="display: block; margin: auto;" width="50%"> ] .three-column[ ### Economic model <span style="display:block; margin-top: 50px ;"></span> .center[ Status quo ] .content-box-gray[ <center><img src=./img/3state-2.png width='100%' title='INCLUDE TEXT HERE'></center> ] <span style="display:block; margin-top: 80px ;"></span> .center[ New drug ] .content-box-gray[ <center><img src=./img/3state-2.png width='100%' title='INCLUDE TEXT HERE'></center> ] ] .three-column[ ### Decision analysis <table class=" lightable-classic table" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto; font-size: 12px; width: auto !important; margin-left: auto; margin-right: auto;'> <thead> <tr><th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; font-weight: bold; padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="2"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">Status quo</div></th></tr> <tr> <th style="text-align:left;background-color: white !important;text-align: center;"> Benefits </th> <th style="text-align:left;background-color: white !important;text-align: center;"> Costs </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 741 </td> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 670382.1 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 699 </td> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 871273.3 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> ... </td> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> ... </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;border-bottom: 1px solid;width: 35%; "> 726 </td> <td style="text-align:left;background-color: white !important;text-align: center;border-bottom: 1px solid;width: 35%; "> 425822.2 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;font-weight: bold;width: 35%; "> 716.2 </td> <td style="text-align:left;background-color: white !important;text-align: center;font-weight: bold;width: 35%; "> 790381.2 </td> </tr> </tbody> </table> <span style="display:block; margin-top: 10px ;"></span> <table class=" lightable-classic table" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto; font-size: 12px; width: auto !important; margin-left: auto; margin-right: auto;'> <thead> <tr><th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; font-weight: bold; padding-right: 4px; padding-left: 4px; background-color: white !important;" colspan="2"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">New drug</div></th></tr> <tr> <th style="text-align:left;background-color: white !important;text-align: center;"> Benefits </th> <th style="text-align:left;background-color: white !important;text-align: center;"> Costs </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 732 </td> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 1131978 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 664 </td> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> 1325654 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> ... </td> <td style="text-align:left;background-color: white !important;text-align: center;width: 35%; "> ... </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;border-bottom: 1px solid;width: 35%; "> 811 </td> <td style="text-align:left;background-color: white !important;text-align: center;border-bottom: 1px solid;width: 35%; "> 766411.4 </td> </tr> <tr> <td style="text-align:left;background-color: white !important;text-align: center;font-weight: bold;width: 35%; "> 774.5 </td> <td style="text-align:left;background-color: white !important;text-align: center;font-weight: bold;width: 35%; "> 1066849.8 </td> </tr> </tbody> </table> <span style="display:block; margin-top: -15px ;"></span> `\begin{align} \class{myblue}{\style{font-family:inherit;}{\text{ICER}}} & \class{myblue}{=} \frac{\class{myblue}{\style{font-family:inherit;}{\text{276468.6}}}}{\class{myblue}{\style{font-family:inherit;}{\text{58.3}}}}\\ & \class{myblue}{= \style{font-family:inherit;}{\text{6497.1}}} \end{align}` ] .arrow1[ `\(\rightarrow\)` ] .arrow2[ `\(\rightarrow\)` ] --- # The problem with survival analysis in HTA Time-to-event data constitute the main outcome in a large number of HTAs (e.g. for cancer drugs) .pull-left[ <span style="display:block; margin-top: 1cm ;"></span> <center><img src=./img/cake.gif width='100%' title=''></center> ] .pull-right[ ## Data 1. We may (or may not!) access **individual level data** for "our" trial, but not for the competitors' 2. The trial data have a very limited follow up, which implies large amount of censoring - This is often OK(-ish!) for "medical stats" analysis. But **HORRIBLE** for economic evaluation! `\(\Rightarrow\)` .blue[**Extrapolation**] (more on this later...) 3. Often the data are manipulated by the stats team within the sponsor and the economic modellers only get summaries/estimates - It is **ALWAYS** good to leave things to statisticians. But the modellers can (should?!) be statisticians too, so they could handle the data!... ] --- count: false # Survival analysis in HTA .alignleft[ .ubuntublue[Trial data &ndash; Kaplan-Meier curves] ] <center><img src=./img/survival_hta1.png width='60%' title='The Kaplan-Meier curves are non-parametric statistics used to estimate the survival function from lifetime data. They resemble closely the observed data'></center> <span style="display:block; margin-top: -50px ;"></span> .small[<svg viewBox="0 0 581 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> [ comment ] <path d="M581 226.6C581 119.1 450.9 32 290.5 32S0 119.1 0 226.6C0 322.4 103.3 402 239.4 418.1V480h99.1v-61.5c24.3-2.7 47.6-7.4 69.4-13.9L448 480h112l-67.4-113.7c54.5-35.4 88.4-84.9 88.4-139.7zm-466.8 14.5c0-73.5 98.9-133 220.8-133s211.9 40.7 211.9 133c0 50.1-26.5 85-70.3 106.4-2.4-1.6-4.7-2.9-6.4-3.7-10.2-5.2-27.8-10.5-27.8-10.5s86.6-6.4 86.6-92.7-90.6-87.9-90.6-87.9h-199V361c-74.1-21.5-125.2-67.1-125.2-119.9zm225.1 38.3v-55.6c57.8 0 87.8-6.8 87.8 27.3 0 36.5-38.2 28.3-87.8 28.3zm-.9 72.5H365c10.8 0 18.9 11.7 24 19.2-16.1 1.9-33 2.8-50.6 2.9v-22.1z"></path></svg> [survHE](http://www.statistica.it/gianluca/software/survhe/)] .small[<svg viewBox="0 0 496 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> [ comment ] <path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"></path></svg> [https://github.com/giabaio/survHE](https://github.com/giabaio/survHE)] --- count: false # Survival analysis in HTA .alignleft[ .ubuntublue[**Median** time:] `\(\class{ubuntublue}{t: S(t)=0.5}\)` ] <center><img src=./img/survival_hta2.png width='60%' title='The median survival time is the time (on the x-axis) in correspondence of which the estimated survival curve is equal to 0.5. That is the point in the follow up at which 50% of the population have experienced the event'></center> --- count: false # Survival analysis in HTA .alignleft[ .ubuntublue[**Mean** time:] `\(\class{ubuntublue}{\displaystyle\int_0^\infty S(t)dt}\)` ] <center><img src=./img/survival_hta3.png width='60%' title='Conversely, the mean survival time gives the point on the x-axis that balances the distribution of the times. Because the underlying time distributions is generally skewed, mean and median times tend to be different'></center> --- # Extrapolation ## A recipe for disaster?... .pull-left[ <center><img src=./img/ristorante.png width='74%' title=''></center> ] .pull-right[ <center><img src=./img/pizza.png width='185%' title=''></center> ] --- count: false # Extrapolation ## A recipe for disaster?... <img src="./img/unnamed-chunk-15-1.png" style="display: block; margin: auto;" width="60%" title=""> --- count: false # Extrapolation ## A recipe for disaster?... <img src="./img/unnamed-chunk-16-1.png" style="display: block; margin: auto;" width="60%" title=""> --- count: false # Extrapolation ## A recipe for disaster?... <img src="./img/unnamed-chunk-17-1.png" style="display: block; margin: auto;" width="60%" title=""> --- count: false # The problem with survival analysis in HTA Time-to-event data constitute the main outcome in a large number of HTAs (e.g. for cancer drugs) .pull-left[ <span style="display:block; margin-top: 1cm ;"></span> <center><img src=./img/destinyschild.gif width='100%' title=''></center> ] .pull-right[ ## Models 1. Which model is the "best fit" &ndash; how to judge that? 2. Is modelling even enough? (How to make the most of "external data") 3. Should you be Bayesians about this? - (Spoiler alert: the answer is *always* Yes!... 😉) ] --- count: false # Extrapolation ## A recipe for disaster?... .pull-left[ <img src="./img/unnamed-chunk-18-1.png" style="display: block; margin: auto;" width="100%" title=""> ] .pull-right[ <img src="./img/unnamed-chunk-19-1.png" style="display: block; margin: auto;" width="100%" title=""> ] - **NB**: Any \*IC can only tell us about model fit **for the observed data**! - Extrapolation (like missing data) is based on (virtually) untestable assumptions --- count: false # Extrapolation ## Why does this matter?... .pull-left[ - Intrinsic/pathological uncertainty in the output of the (time-to-event) statistical modelling does carry through the entire process, all the way to the decision-making <span style="display:block; margin-top: 30px ;"></span> - It is not impossible (especially in cases involving new, innovative *immuno-oncology drugs*) that the observed data be extremely sparse and subject to high censoring - In the case depicted here, the **best fitting** model responds by extrapolating a survival curve that implies .blue[Pr(alive at 15 years) > 0.75] - This may be obviously wrong/against expert or clinical opinion! ] .pull-right[ <center><img src=./img/ta174.png width='100%' title=''></center> ] --- count: false # Extrapolation ## Why does this matter?... .pull-left[ - Intrinsic/pathological uncertainty in the output of the (time-to-event) statistical modelling does carry through the entire process, all the way to the decision-making <span style="display:block; margin-top: 30px ;"></span> - It is not impossible (especially in cases involving new, innovative *immuno-oncology drugs*) that the observed data be extremely sparse and subject to high censoring - In the case depicted here, the **best fitting** model responds by extrapolating a survival curve that implies .blue[Pr(alive at 15 years) > 0.75] - This may be obviously wrong/against expert or clinical opinion! <svg viewBox="0 0 576 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;fill:red;height:1.7em;top:.45em;"> [ comment ] <path d="M569.517 440.013C587.975 472.007 564.806 512 527.94 512H48.054c-36.937 0-59.999-40.055-41.577-71.987L246.423 23.985c18.467-32.009 64.72-31.951 83.154 0l239.94 416.028zM288 354c-25.405 0-46 20.595-46 46s20.595 46 46 46 46-20.595 46-46-20.595-46-46-46zm-43.673-165.346l7.418 136c.347 6.364 5.609 11.346 11.982 11.346h48.546c6.373 0 11.635-4.982 11.982-11.346l7.418-136c.375-6.874-5.098-12.654-11.982-12.654h-63.383c-6.884 0-12.356 5.78-11.981 12.654z"></path></svg> We need to **formally** and **quantitatively** consider what the implications of this uncertainty are on the decision-making process! ] .pull-right[ <center><img src=./img/ta174.png width='100%' title=''></center> ] --- background-image: url("img/voi-scooter.jpg") background-size: cover # --- name: voi count: false # Value of Information (VoI) <style type="text/css"> .left-column30 { width: 30%; height: 92%; float: left; } .left-column30 h2, .left-column h3 { color: #035AA699; } .left-column30 h2:last-of-type, .left-column h3:last-child { color: #035AA6; } .right-column70 { width: 65%; float: right; padding-top: 0em; } </style> ## (A tale of two stupid examples) .left-column30[ <center><img src=./img/knowledge_power.jpg width='75%' title='INCLUDE TEXT HERE'></center> ] .right-columnt70[ - **Example 1**: Intervention `\(t=1\)` is more cost-effective, given current evidence - `\(\class{myblue}{\Pr(t=1 \style{font-family:inherit;}{\text{ is cost-effective}}) = \style{font-family:inherit;}{\text{0.51}}}\)` - If we get it wrong: - Increase in population average costs `\(=\)` £3 - Decrease in population average effectiveness `\(=\)` 0.000001 QALYs - .red[Large uncertainty]/.traffic-light-green[negligible consequences] `\(\Rightarrow\)` .traffic-light-green[**can afford uncertainty**!] ] --- count: false # Value of Information (VoI) ## (A tale of two stupid examples) .left-column30[ <center><img src=./img/knowledge_power.jpg width='75%' title='INCLUDE TEXT HERE'></center> ] .right-columnt70[ - **Example 1**: Intervention `\(t=1\)` is more cost-effective, given current evidence - `\(\class{myblue}{\Pr(t=1 \style{font-family:inherit;}{\text{ is cost-effective}}) = \style{font-family:inherit;}{\text{0.51}}}\)` - If we get it wrong: - Increase in population average costs `\(=\)` £3 - Decrease in population average effectiveness `\(=\)` 0.000001 QALYs - .red[Large uncertainty]/.traffic-light-green[negligible consequences] `\(\Rightarrow\)` .traffic-light-green[**can afford uncertainty**!] <span style="display:block; margin-top: 60px ;"></span> - **Example 2**: Intervention `\(t=1\)` is more cost-effective, given current evidence - `\(\class{myblue}{\Pr(t=1 \style{font-family:inherit;}{\text{ is cost-effective}}) = \style{font-family:inherit;}{\text{0.999}}}\)` - If we get it wrong: - Increase in population average costs `\(=\)` £1000000000 - Decrease in population average effectiveness `\(=\)` 999999 QALYs - .traffic-light-green[Tiny uncertainty]/.red[dire consequences] `\(\Rightarrow\)` .traffic-light-amber[**probably should think about it...**!] ] --- # Evidence based decision-making and VoI <center><img src=./img/evi_process.png width='75%' title='INCLUDE TEXT HERE'></center> -- .blue[**Process inherently Bayesian!**] <span style="display:block; margin-top: -5px ;"></span> .small[Slide stolen from [Nicky Welton](https://www.bristol.ac.uk/people/person/Nicky-Welton-9c4cd60d-0c6d-42b3-af4f-a1006a4e46ee/) &ndash; [Summer School *Bayesian methods in health economics*](http://www.statistica.it/gianluca/teaching/summer-school/)] --- # VoI: Basic ideas - A new study will provide more data - Reducing (or even eliminating?...) uncertainty in a subset of the model parameters - Update the cost-effectiveness model - If optimal decision changes, gain in monetary **.blue[net benefit]** (NB = utility) from using new optimal treatment - If optimal decision doesn't change, no gain in NB - .red[**Expected**] VoI is the average gain in NB --- count: false # VoI: Basic ideas & relevant measures - A new study will provide more data - Reducing (or even eliminating?...) uncertainty in a subset of the model parameters - Update the cost-effectiveness model - If optimal decision changes, gain in monetary net benefit (NB = utility) from using new optimal treatment - If optimal decision doesn't change, no gain in NB - .red[**Expected**] VoI is the average gain in NB <span style="display:block; margin-top: -10px ;"></span> 1. **Expected value of Perfect Information** (EVPI) - Value of completely resolving uncertainty in all input parameters to decision model - Infinite-sized, long-term follow up trial measuring everything!... - Gives an upper bound on the value of the new study &ndash; low EVPI suggests we can make our decision based on existing information --- count: false # VoI: Basic ideas & relevant measures - A new study will provide more data - Reducing (or even eliminating?...) uncertainty in a subset of the model parameters - Update the cost-effectiveness model - If optimal decision changes, gain in monetary net benefit (NB = utility) from using new optimal treatment - If optimal decision doesn't change, no gain in NB - .red[**Expected**] VoI is the average gain in NB <span style="display:block; margin-top: -10px ;"></span> 1. **Expected value of Perfect Information** (EVPI) - Value of completely resolving uncertainty in all input parameters to decision model - Infinite-sized, long-term follow up trial measuring everything!... - Gives an upper bound on the value of the new study &ndash; low EVPI suggests we can make our decision based on existing information 2. **Expected value of Partial Perfect Information** (EVPPI) - Value of eliminating uncertainty in subset of input parameters to decision model - e.g.: Infinite-sized trial measuring relative effects on 1-year survival - Useful to identify which parameters are responsible for decision uncertainty --- count: false # VoI: Basic ideas & relevant measures - A new study will provide more data - Reducing (or even eliminating?...) uncertainty in a subset of the model parameters - Update the cost-effectiveness model - If optimal decision changes, gain in monetary net benefit (NB = utility) from using new optimal treatment - If optimal decision doesn't change, no gain in NB - .red[**Expected**] VoI is the average gain in NB <span style="display:block; margin-top: -10px ;"></span> 1. **Expected value of Perfect Information** (EVPI) - Value of completely resolving uncertainty in all input parameters to decision model - Infinite-sized, long-term follow up trial measuring everything!... - Gives an upper bound on the value of the new study &ndash; low EVPI suggests we can make our decision based on existing information 2. **Expected value of Partial Perfect Information** (EVPPI) - Value of eliminating uncertainty in subset of input parameters to decision model - e.g.: Infinite-sized trial measuring relative effects on 1-year survival - Useful to identify which parameters are responsible for decision uncertainty 3. **Expected value of Sample Information** (EVSI) - Value of reducing uncertainty by conducting a specific study of a given design - Can compare the benefits and costs of a study with given design - Is the proposed study likely to be a good use of resource? What is the optimal design? --- count: false # VoI: Basic ideas & relevant measures <svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="position:relative;display:inline-block;fill:#035AA6;height:1.7em;top:.45em;"> [ comment ] <path d="M256 8C119.043 8 8 119.083 8 256c0 136.997 111.043 248 248 248s248-111.003 248-248C504 119.083 392.957 8 256 8zm0 110c23.196 0 42 18.804 42 42s-18.804 42-42 42-42-18.804-42-42 18.804-42 42-42zm56 254c0 6.627-5.373 12-12 12h-88c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 12-12h12v-64h-12c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 12-12h64c6.627 0 12 5.373 12 12v100h12c6.627 0 12 5.373 12 12v24z"></path></svg> In general, VoI measures are always expressed as something like <span style="display:block; margin-top: 40px ;"></span> .center[ .content-box-gray[ .olive[**VoI measure**] `\(=\)` .blue[**Some idealised decision-making process**] `\(-\)` .magenta[**current decision-making process**] ] ] -- <span style="display:block; margin-top: 40px ;"></span> ## Complexity - There's no natural upper bound - Voi measures are positive, but *how low is low?*... - Need to account for other factors - How much would it cost to get to the point when we can make the idealised decision-making process? - Who would that affect? - For how long? - ... - Computational & modelling issues - You need to know what you're doing (again, modelling **fundamentally** Bayesian) - And use suitable tools (basically, never use spreadsheets...) --- exclude: false # Summarising uncertainty analysis (PSA) ## Expected Value of Perfect Information .alignleft[ <table class=" lightable-classic table" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto; margin-left: auto; margin-right: auto;'> <thead> <tr> <th style="empty-cells: hide;" colspan="1"></th> <th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="4"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">Parameter simulations</div></th> </tr> <tr> <th style="text-align:center;"> Iteration </th> <th style="text-align:center;"> \(\pi_0\) </th> <th style="text-align:center;"> \(\rho\) </th> <th style="text-align:center;"> \(\ldots\) </th> <th style="text-align:center;"> \(\gamma\) </th> </tr> </thead> <tbody> <tr> <td style="text-align:center;width: 2cm; "> 1 </td> <td style="text-align:center;width: 2cm; "> 0.585 </td> <td style="text-align:center;width: 2cm; "> 0.3814 </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> 0.4194 </td> </tr> <tr> <td style="text-align:center;width: 2cm; "> 2 </td> <td style="text-align:center;width: 2cm; "> 0.515 </td> <td style="text-align:center;width: 2cm; "> 0.0166 </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> 0.0768 </td> </tr> <tr> <td style="text-align:center;width: 2cm; "> 3 </td> <td style="text-align:center;width: 2cm; "> 0.611 </td> <td style="text-align:center;width: 2cm; "> 0.1373 </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> 0.0592 </td> </tr> <tr> <td style="text-align:center;width: 2cm; "> 4 </td> <td style="text-align:center;width: 2cm; "> 0.195 </td> <td style="text-align:center;width: 2cm; "> 0.7282 </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> 0.7314 </td> </tr> <tr> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> </tr> <tr> <td style="text-align:center;width: 2cm; border-bottom: 2px solid;"> 1000 </td> <td style="text-align:center;width: 2cm; border-bottom: 2px solid;"> 0.0305 </td> <td style="text-align:center;width: 2cm; border-bottom: 2px solid;"> 0.204 </td> <td style="text-align:center;width: 2cm; border-bottom: 2px solid;"> \(\ldots\) </td> <td style="text-align:center;width: 2cm; border-bottom: 2px solid;"> 0.558 </td> </tr> </tbody> </table> ] <span style="display:block; margin-top: 9.5cm ;"></span> - Characterise uncertainty in the model parameters - In a full Bayesian setting, these are drawings from the posterior distribution of `\(\boldsymbol\theta\)` - In a frequentist setting, these are typically bootstrap draws from a set of univariate ditributions that describe some level of uncertainty around the MLEs --- exclude: false count: false # Summarising uncertainty analysis (PSA) ## Expected Value of Perfect Information .alignleft[ <table class=" lightable-classic table" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto; margin-left: auto; margin-right: auto;'> <thead> <tr> <th style="empty-cells: hide;" colspan="1"></th> <th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="4"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">Parameter simulations</div></th> <th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="2"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">Expected utility</div></th> </tr> <tr> <th style="text-align:center;"> Iteration </th> <th style="text-align:center;"> \(\pi_0\) </th> <th style="text-align:center;"> \(\rho\) </th> <th style="text-align:center;"> \(\ldots\) </th> <th style="text-align:center;"> \(\gamma\) </th> <th style="text-align:center;"> \(\nb_0(\boldsymbol\theta)\) </th> <th style="text-align:center;"> \(\nb_1(\boldsymbol\theta)\) </th> </tr> </thead> <tbody> <tr> <td style="text-align:center;width: 2cm; "> 1 </td> <td style="text-align:center;width: 2cm; "> 0.585 </td> <td style="text-align:center;width: 2cm; "> 0.3814 </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> 0.4194 </td> <td style="text-align:center;width: 2cm; font-style: italic;"> 77480.00 </td> <td style="text-align:center;width: 2cm; color: black !important;"> 67795.00 </td> </tr> <tr> <td style="text-align:center;width: 2cm; "> 2 </td> <td style="text-align:center;width: 2cm; "> 0.515 </td> <td style="text-align:center;width: 2cm; "> 0.0166 </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> 0.0768 </td> <td style="text-align:center;width: 2cm; "> 87165.00 </td> <td style="text-align:center;width: 2cm; font-style: italic;color: black !important;"> 106535.00 </td> </tr> <tr> <td style="text-align:center;width: 2cm; "> 3 </td> <td style="text-align:center;width: 2cm; "> 0.611 </td> <td style="text-align:center;width: 2cm; "> 0.1373 </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> 0.0592 </td> <td style="text-align:center;width: 2cm; font-style: italic;"> 58110.00 </td> <td style="text-align:center;width: 2cm; color: black !important;"> 38740.00 </td> </tr> <tr> <td style="text-align:center;width: 2cm; "> 4 </td> <td style="text-align:center;width: 2cm; "> 0.195 </td> <td style="text-align:center;width: 2cm; "> 0.7282 </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> 0.7314 </td> <td style="text-align:center;width: 2cm; "> 77480.00 </td> <td style="text-align:center;width: 2cm; font-style: italic;color: black !important;"> 87165.00 </td> </tr> <tr> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; color: black !important;"> \(\ldots\) </td> </tr> <tr> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> 1000 </td> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> 0.0305 </td> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> 0.204 </td> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> \(\ldots\) </td> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> 0.558 </td> <td style="text-align:center;border-bottom: 2px black solid;width: 2cm; "> 48425.00 </td> <td style="text-align:center;border-bottom: 2px black solid;width: 2cm; font-style: italic;color: black !important;"> 87165.00 </td> </tr> <tr> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> </td> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> </td> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> </td> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> </td> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> Average </td> <td style="text-align:center;border-bottom: 2px black solid;width: 2cm; "> 72365.35 </td> <td style="text-align:center;border-bottom: 2px black solid;width: 2cm; font-style: italic;color: magenta !important;"> 77403.49 </td> </tr> </tbody> </table> ] <span style="display:block; margin-top: 9.5cm ;"></span> - Uncertainty in the parameters induces a distribution of decisions - Typically based on the **net benefits**: `\(\class{myblue}{\nb_t(\boldsymbol\theta)=k\mu_{et}-\mu_{ct}}\)` - In each parameter configuration can identify the *optimal strategy* - Averaging over the uncertainty in `\(\boldsymbol\theta\)` provides `\(t^*\)`, the overall optimal decision *given current uncertainty* (= choose the intervention associated with .magenta[*highest* **expected utility**]) --- exclude: false count: false # Summarising uncertainty analysis (PSA) ## Expected Value of Perfect Information .alignleft[ <table class=" lightable-classic table" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto; margin-left: auto; margin-right: auto;'> <thead> <tr> <th style="empty-cells: hide;" colspan="1"></th> <th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="4"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">Parameter simulations</div></th> <th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="2"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">Expected utility</div></th> <th style="empty-cells: hide;" colspan="2"></th> </tr> <tr> <th style="text-align:center;"> Iteration </th> <th style="text-align:center;"> \(\pi_0\) </th> <th style="text-align:center;"> \(\rho\) </th> <th style="text-align:center;"> \(\ldots\) </th> <th style="text-align:center;"> \(\gamma\) </th> <th style="text-align:center;"> \(\nb_0(\boldsymbol\theta)\) </th> <th style="text-align:center;"> \(\nb_1(\boldsymbol\theta)\) </th> <th style="text-align:center;"> Maximum net benefit </th> <th style="text-align:center;"> Opportunity loss </th> </tr> </thead> <tbody> <tr> <td style="text-align:center;width: 2cm; "> 1 </td> <td style="text-align:center;width: 2cm; "> 0.585 </td> <td style="text-align:center;width: 2cm; "> 0.3814 </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> 0.4194 </td> <td style="text-align:center;width: 2cm; font-style: italic;"> 77480.00 </td> <td style="text-align:center;width: 2cm; color: black !important;"> 67795.00 </td> <td style="text-align:center;color: black !important;"> 77480.00 </td> <td style="text-align:center;color: black !important;"> 9685.00 </td> </tr> <tr> <td style="text-align:center;width: 2cm; "> 2 </td> <td style="text-align:center;width: 2cm; "> 0.515 </td> <td style="text-align:center;width: 2cm; "> 0.0166 </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> 0.0768 </td> <td style="text-align:center;width: 2cm; "> 87165.00 </td> <td style="text-align:center;width: 2cm; font-style: italic;color: black !important;"> 106535.00 </td> <td style="text-align:center;color: black !important;"> 106535.00 </td> <td style="text-align:center;color: black !important;"> 0.00 </td> </tr> <tr> <td style="text-align:center;width: 2cm; "> 3 </td> <td style="text-align:center;width: 2cm; "> 0.611 </td> <td style="text-align:center;width: 2cm; "> 0.1373 </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> 0.0592 </td> <td style="text-align:center;width: 2cm; font-style: italic;"> 58110.00 </td> <td style="text-align:center;width: 2cm; color: black !important;"> 38740.00 </td> <td style="text-align:center;color: black !important;"> 58110.00 </td> <td style="text-align:center;color: black !important;"> 19370.00 </td> </tr> <tr> <td style="text-align:center;width: 2cm; "> 4 </td> <td style="text-align:center;width: 2cm; "> 0.195 </td> <td style="text-align:center;width: 2cm; "> 0.7282 </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> 0.7314 </td> <td style="text-align:center;width: 2cm; "> 77480.00 </td> <td style="text-align:center;width: 2cm; font-style: italic;color: black !important;"> 87165.00 </td> <td style="text-align:center;color: black !important;"> 87165.00 </td> <td style="text-align:center;color: black !important;"> 0.00 </td> </tr> <tr> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2cm; color: black !important;"> \(\ldots\) </td> <td style="text-align:center;color: black !important;"> \(\ldots\) </td> <td style="text-align:center;color: black !important;"> \(\ldots\) </td> </tr> <tr> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> 1000 </td> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> 0.0305 </td> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> 0.204 </td> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> \(\ldots\) </td> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> 0.558 </td> <td style="text-align:center;border-bottom: 2px black solid;width: 2cm; "> 48425.00 </td> <td style="text-align:center;border-bottom: 2px black solid;width: 2cm; font-style: italic;color: black !important;"> 87165.00 </td> <td style="text-align:center;border-bottom: 2px black solid;color: black !important;"> 87165.00 </td> <td style="text-align:center;border-bottom: 2px black solid;color: black !important;"> 0.00 </td> </tr> <tr> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> </td> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> </td> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> </td> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> </td> <td style="text-align:center;width: 2cm; border-bottom: 2px black solid;"> Average </td> <td style="text-align:center;border-bottom: 2px black solid;width: 2cm; "> 72365.35 </td> <td style="text-align:center;border-bottom: 2px black solid;width: 2cm; font-style: italic;color: magenta !important;"> 77403.49 </td> <td style="text-align:center;border-bottom: 2px black solid;font-weight: bold;color: blue !important;"> 91192.02 </td> <td style="text-align:center;border-bottom: 2px black solid;font-weight: bold;color: olive !important;"> 13788.53 </td> </tr> </tbody> </table> ] <span style="display:block; margin-top: 9.5cm ;"></span> - **Expected value of "Perfect" Information** (EVPI) summarises uncertainty in the decision - Defined as the .olive[**average Opportunity Loss**], or .blue[**average maximum expected utility under "perfect" information**] `\(-\)` .magenta[**maximum expected utility overall**]: <span style="display:block; margin-top: -20px ;"></span> `$$\class{olive}{\evpi} = \class{blue}{\E_\boldsymbol{\theta}\left[\max_t \nb_t(\boldsymbol\theta) \right]} - \class{magenta}{\max_t \E_\boldsymbol\theta \left[\nb_t(\boldsymbol\theta)\right]}$$` --- exclude: true count: false # Summarising PSA <img src="./img/unnamed-chunk-24-1.png" style="display: block; margin: auto;" width="53%"> --- # Summarising PSA + Research priority <style type="text/css"> <!-- https://www.garrickadenbuie.com/blog/better-progressive-xaringan/?panelset=r-markdown --> .shading > li { color: gray; } .shading > li:last-of-type { color: #24568c; font-weight: normal; } </style> ## Expected Value of Partial Perfect Information - `\(\class{blue}{\bm\theta} =\)` all the model parameters; can be split into two subsets - The ".myblue[**parameters of interest**]", `\(\class{myblue}{\bm\phi}\)`, e.g. prevalence of a disease, HRQL measures, length of stay in hospital, ... - The ".olive[**remaining parameters**], `\(\class{olive}{\bm\psi}\)`, e.g. cost of treatment with other established medications, ... - We are interested in quantifying the value of gaining more information on `\(\class{myblue}{\bm\phi}\)`, while leaving current level of uncertainty on `\(\class{olive}{\bm\psi}\)` unchanged -- <ul class="shading"> <li>First, consider the expected utility (EU) <b>if</b> we were able to learn \(\class{myblue}{\bm\phi}\) but not \(\class{myblue}{\bm\psi}\)</li> </ul> <span style="display:block; margin-top: 3cm ;"></span> `$$\class{myblue}{\E_{\bm\psi\mid\bm\phi}[\nb_t(\bm\theta)]}$$` --- count: false # Summarising PSA + Research priority ## Expected Value of Partial Perfect Information - `\(\class{blue}{\bm\theta} =\)` all the model parameters; can be split into two subsets - The ".myblue[**parameters of interest**]", `\(\class{myblue}{\bm\phi}\)`, e.g. prevalence of a disease, HRQL measures, length of stay in hospital, ... - The ".olive[**remaining parameters**], `\(\class{olive}{\bm\psi}\)`, e.g. cost of treatment with other established medications, ... - We are interested in quantifying the value of gaining more information on `\(\class{myblue}{\bm\phi}\)`, while leaving current level of uncertainty on `\(\class{olive}{\bm\psi}\)` unchanged <ul class="shading"> <li>First, consider the expected utility (EU) <b>if</b> we were able to learn \(\class{gray}{\bm\phi}\) but not \(\class{gray}{\bm\psi}\)</li> <li><b>If</b> we knew \(\class{myblue}{\bm\phi}\) perfectly, best decision = the maximum of this EU</li> </ul> <span style="display:block; margin-top: 2.25cm ;"></span> `$$\class{myblue}{\max_t}\class{gray}{\E_{\bm\psi\mid\bm\phi}[\nb_t(\bm\theta)]}$$` --- count: false # Summarising PSA + Research priority ## Expected Value of Partial Perfect Information - `\(\class{blue}{\bm\theta} =\)` all the model parameters; can be split into two subsets - The ".myblue[**parameters of interest**]", `\(\class{myblue}{\bm\phi}\)`, e.g. prevalence of a disease, HRQL measures, length of stay in hospital, ... - The ".olive[**remaining parameters**], `\(\class{olive}{\bm\psi}\)`, e.g. cost of treatment with other established medications, ... - We are interested in quantifying the value of gaining more information on `\(\class{myblue}{\bm\phi}\)`, while leaving current level of uncertainty on `\(\class{olive}{\bm\psi}\)` unchanged <ul class="shading"> <li>First, consider the expected utility (EU) <b>if</b> we were able to learn \(\class{gray}{\bm\phi}\) but not \(\class{gray}{\bm\psi}\)</li> <li><b>If</b> we knew \(\class{gray}{\bm\phi}\) perfectly, best decision = the maximum of this EU</li> <li>Of course, we cannot know \(\class{myblue}{\bm\phi}\) <b>perfectly</b>, so take the expected value</li> </ul> <span style="display:block; margin-top: 1.1cm ;"></span> `$$\class{myblue}{\E_{\bm\phi}}\class{myblue}{\left [\class{gray}{\max_t\E_{\bm\psi\mid\bm\phi}[\nb_t(\bm\theta)]}\right]}$$` --- count: false # Summarising PSA + Research priority ## Expected Value of Partial Perfect Information - `\(\class{blue}{\bm\theta} =\)` all the model parameters; can be split into two subsets - The ".myblue[**parameters of interest**]", `\(\class{myblue}{\bm\phi}\)`, e.g. prevalence of a disease, HRQL measures, length of stay in hospital, ... - The ".olive[**remaining parameters**], `\(\class{olive}{\bm\psi}\)`, e.g. cost of treatment with other established medications, ... - We are interested in quantifying the value of gaining more information on `\(\class{myblue}{\bm\phi}\)`, while leaving current level of uncertainty on `\(\class{olive}{\bm\psi}\)` unchanged <ul class="shading"> <li>First, consider the expected utility (EU) <b>if</b> we were able to learn \(\class{gray}{\bm\phi}\) but not \(\class{gray}{\bm\psi}\)</li> <li><b>If</b> we knew \(\class{gray}{\bm\phi}\) perfectly, best decision = the maximum of this EU</li> <li>Of course, we cannot know \(\class{gray}{\bm\phi}\) <b>perfectly</b>, so take the expected value</li> <li>And compare this with the <b>maximum expected utility overall</b></li> </ul> <span style="display:block; margin-top: .5cm ;"></span> `$$\class{gray}{\E_{\bm\phi}\left[\max_t\E_{\bm\psi\mid\bm\phi}[\nb_t(\bm\theta)]\right]}\class{myblue}{-\max_t \E_{\bm\theta}[\nb_t(\bm\theta)]}$$` --- count: false # Summarising PSA + Research priority ## Expected Value of Partial Perfect Information - `\(\class{blue}{\bm\theta} =\)` all the model parameters; can be split into two subsets - The ".myblue[**parameters of interest**]", `\(\class{myblue}{\bm\phi}\)`, e.g. prevalence of a disease, HRQL measures, length of stay in hospital, ... - The ".olive[**remaining parameters**], `\(\class{olive}{\bm\psi}\)`, e.g. cost of treatment with other established medications, ... - We are interested in quantifying the value of gaining more information on `\(\class{myblue}{\bm\phi}\)`, while leaving current level of uncertainty on `\(\class{olive}{\bm\psi}\)` unchanged <ul class="shading"> <li>First, consider the expected utility (EU) <b>if</b> we were able to learn \(\class{gray}{\bm\phi}\) but not \(\class{gray}{\bm\psi}\)</li> <li><b>If</b> we knew \(\class{gray}{\bm\phi}\) perfectly, best decision = the maximum of this EU</li> <li>Of course, we cannot know \(\class{gray}{\bm\phi}\) <b>perfectly</b>, so take the expected value</li> <li>And compare this with the <b>maximum expected utility overall</b></li> <li>This is the EVPPI</li> </ul> <span style="display:block; margin-top: -.55cm ;"></span> `$$\class{myblue}{\evppi = \E_{\bm\phi}\left[\max_t\E_{\bm\psi\mid\bm\phi}[\nb_t(\bm\theta)]\right]-\max_t \E_{\bm\theta}[\nb_t(\bm\theta)]}$$` --- count: false # Summarising PSA + Research priority ## Expected Value of Partial Perfect Information - `\(\class{blue}{\bm\theta} =\)` all the model parameters; can be split into two subsets - The ".myblue[**parameters of interest**]", `\(\class{myblue}{\bm\phi}\)`, e.g. prevalence of a disease, HRQL measures, length of stay in hospital, ... - The ".olive[**remaining parameters**], `\(\class{olive}{\bm\psi}\)`, e.g. cost of treatment with other established medications, ... - We are interested in quantifying the value of gaining more information on `\(\class{myblue}{\bm\phi}\)`, while leaving current level of uncertainty on `\(\class{olive}{\bm\psi}\)` unchanged <ul class="shading"> <li>First, consider the expected utility (EU) <b>if</b> we were able to learn \(\class{gray}{\bm\phi}\) but not \(\class{gray}{\bm\psi}\)</li> <li><b>If</b> we knew \(\class{gray}{\bm\phi}\) perfectly, best decision = the maximum of this EU</li> <li>Of course, we cannot know \(\class{gray}{\bm\phi}\) <b>perfectly</b>, so take the expected value</li> <li>And compare this with the <b>maximum expected utility overall</b></li> <li>This is the EVPPI</li> </ul> <span style="display:block; margin-top: -.55cm ;"></span> `$$\class{myblue}{\evppi = \E_{\bm\phi}\left[\class{red}{\max_t\E_{\bm\psi\mid\bm\phi}[\nb_t(\bm\theta)]}\right]-\max_t \E_{\bm\theta}[\nb_t(\bm\theta)]}$$` - .red[**That**] is the difficult part! - Can do nested Monte Carlo, but takes for ever to get accurate results - .orange[**Recent methods**] based on **GAMs**/**Gaussian Process regression**/**spatial modelling** very efficient and quick! <span style="display:block; margin-top: -17px ;"></span> .alignright[.small[<svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> <g groupmode="layer" 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Strong](https://www.sheffield.ac.uk/scharr/people/staff/mark-strong) &ndash; [Summer School *Bayesian methods in health economics*](http://www.statistica.it/gianluca/teaching/summer-school/)] --- exclude: true count: false # EVPPI &ndash; Brute force/nested MC Assuming there are only two interventions, can consider `\(\class{myblue}{\inb(\bm\theta)=\nb_1(\bm\theta)-\nb_0(\bm\theta)}\)` <center><img src=./img/brute-force-2_26.png width='44%' title='INCLUDE TEXT HERE'></center> --- exclude: true count: false # EVPPI &ndash; model as a regression problem... Can model as a **regression** problem `\begin{align} \nb_t(\bm\theta) =& \E_{\bm\psi\mid\bm\theta}[\nb_t(\bm\theta)] + \varepsilon, \qquad \style{font-family:inherit;}{\text{ with }} \varepsilon \sim \dnorm(0,\sigma^2_\varepsilon) \\ =& \class{olive}{g(\bm\phi)} + \class{myblue}{\varepsilon} \end{align}` <span style="display:block; margin-top: -20px ;"></span> "Data" - **Simulations** for `\(\nb_t(\bm\theta)\)` as ".myblue[response]" - **Simulations** for `\(\bm\phi\)` as ".olive[covariates]" - **NB**: Only need `\(S\)` data points (=PSA simulations), instead of `\(S_\bm\phi \times S_\bm\psi\)`! .center[ <table class=" lightable-classic table" style='font-family: "Arial Narrow", "Source Sans Pro", sans-serif; margin-left: auto; margin-right: auto; font-size: 18px; width: auto !important; margin-left: auto; margin-right: auto;'> <thead> <tr> <th style="empty-cells: hide;" colspan="1"></th> <th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="4"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">Parameter simulations ('covariates')</div></th> <th style="padding-bottom:0; padding-left:3px;padding-right:3px;text-align: center; " colspan="2"><div style="border-bottom: 1px solid #111111; margin-bottom: -1px; ">'Responses'</div></th> </tr> <tr> <th style="text-align:center;"> Iteration </th> <th style="text-align:center;"> \(\pi_0\) </th> <th style="text-align:center;"> \(\rho\) </th> <th style="text-align:center;"> \(\ldots\) </th> <th style="text-align:center;"> \(\gamma\) </th> <th style="text-align:center;"> \(\nb_0(\boldsymbol\theta)\) </th> <th style="text-align:center;"> \(\nb_1(\boldsymbol\theta)\) </th> </tr> </thead> <tbody> <tr> <td style="text-align:center;width: 2.5cm; "> 1 </td> <td style="text-align:center;width: 2.5cm; "> 0.585 </td> <td style="text-align:center;width: 2.5cm; "> 0.3814 </td> <td style="text-align:center;width: 2.5cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2.5cm; "> 0.4194 </td> <td style="text-align:center;width: 2.5cm; "> 77480 </td> <td style="text-align:center;width: 2.5cm; "> 67795 </td> </tr> <tr> <td style="text-align:center;width: 2.5cm; "> 2 </td> <td style="text-align:center;width: 2.5cm; "> 0.515 </td> <td style="text-align:center;width: 2.5cm; "> 0.0166 </td> <td style="text-align:center;width: 2.5cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2.5cm; "> 0.0768 </td> <td style="text-align:center;width: 2.5cm; "> 87165 </td> <td style="text-align:center;width: 2.5cm; "> 106535 </td> </tr> <tr> <td style="text-align:center;width: 2.5cm; "> 3 </td> <td style="text-align:center;width: 2.5cm; "> 0.611 </td> <td style="text-align:center;width: 2.5cm; "> 0.1373 </td> <td style="text-align:center;width: 2.5cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2.5cm; "> 0.0592 </td> <td style="text-align:center;width: 2.5cm; "> 58110 </td> <td style="text-align:center;width: 2.5cm; "> 38740 </td> </tr> <tr> <td style="text-align:center;width: 2.5cm; "> 4 </td> <td style="text-align:center;width: 2.5cm; "> 0.195 </td> <td style="text-align:center;width: 2.5cm; "> 0.7282 </td> <td style="text-align:center;width: 2.5cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2.5cm; "> 0.7314 </td> <td style="text-align:center;width: 2.5cm; "> 77480 </td> <td style="text-align:center;width: 2.5cm; "> 87165 </td> </tr> <tr> <td style="text-align:center;width: 2.5cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2.5cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2.5cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2.5cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2.5cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2.5cm; "> \(\ldots\) </td> <td style="text-align:center;width: 2.5cm; "> \(\ldots\) </td> </tr> <tr> <td style="text-align:center;width: 2.5cm; border-bottom: 2px solid;"> \(S\) </td> <td style="text-align:center;width: 2.5cm; border-bottom: 2px solid;"> 0.0305 </td> <td style="text-align:center;width: 2.5cm; border-bottom: 2px solid;"> 0.204 </td> <td style="text-align:center;width: 2.5cm; border-bottom: 2px solid;"> \(\ldots\) </td> <td style="text-align:center;width: 2.5cm; border-bottom: 2px solid;"> 0.558 </td> <td style="text-align:center;width: 2.5cm; border-bottom: 2px solid;"> 48425 </td> <td style="text-align:center;width: 2.5cm; border-bottom: 2px solid;"> 87165 </td> </tr> </tbody> </table> ] --- exclude: true count: false # EVPPI &ndash; model as a regression problem... <center><img src=./img/brute-force-3_28.png width='48%' title='INCLUDE TEXT HERE'></center> --- exclude: true count: false # EVPPI &ndash; model as a regression problem... <center><img src=./img/brute-force-4_29.png width='48%' title='INCLUDE TEXT HERE'></center> --- exclude: true count: false # EVPPI &ndash; model as a regression problem... <center><img src=./img/brute-force-5_30.png width='51%' title='INCLUDE TEXT HERE'></center> --- exclude: true count: false # EVPPI &ndash; model as a regression problem... - Once the functions `\(\class{olive}{g_t(\bm\phi)}\)` are estimated, can approximate `\begin{align} \evppi&=\E_\bm\phi \left[ \max_t \E_{\bm\psi\mid\bm\phi} [\nb_t(\bm\theta)] \right] - \max_t \E_\bm\theta [\nb_t(\bm\theta)] \\ &\approx\frac{1}{S}\sum_{s=1}^S \max_t \hat{g}_t(\bm\phi_s) - \max_t \frac{1}{S}\sum_{s=1}^S \hat{g}_t(\bm\phi_s) \end{align}` -- exclude: true - **NB**: `\(\class{olive}{g_t(\bm\phi)}\)` can be complex, so need to use .orange[**flexible**] regression methods - **GAMs**: `\(\displaystyle g_t(\bm\phi)=\sum_{q=1}^{Q_\bm\phi} h_t(\phi_{sq})\)` with `\(h_t(\cdot)=\)` smooth functions (cubic polynomials) - very fast, but only if number of important parameters `\(Q_\bm\phi\leq 5\)` (interactions increase model size exponentially) - If `\(Q_\bm\phi >5\)` then use .blue[**Gaussian Process**] regression (GPR) - [Strong et al](https://journals.sagepub.com/doi/full/10.1177/0272989x13505910): original GPR method - [Heath et al](https://onlinelibrary.wiley.com/doi/full/10.1002/sim.6983): based on spatial modelling; can be more computationally efficient - Other methods based on alternative approaches - Most are implemented in the <svg viewBox="0 0 581 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> [ comment ] <path d="M581 226.6C581 119.1 450.9 32 290.5 32S0 119.1 0 226.6C0 322.4 103.3 402 239.4 418.1V480h99.1v-61.5c24.3-2.7 47.6-7.4 69.4-13.9L448 480h112l-67.4-113.7c54.5-35.4 88.4-84.9 88.4-139.7zm-466.8 14.5c0-73.5 98.9-133 220.8-133s211.9 40.7 211.9 133c0 50.1-26.5 85-70.3 106.4-2.4-1.6-4.7-2.9-6.4-3.7-10.2-5.2-27.8-10.5-27.8-10.5s86.6-6.4 86.6-92.7-90.6-87.9-90.6-87.9h-199V361c-74.1-21.5-125.2-67.1-125.2-119.9zm225.1 38.3v-55.6c57.8 0 87.8-6.8 87.8 27.3 0 36.5-38.2 28.3-87.8 28.3zm-.9 72.5H365c10.8 0 18.9 11.7 24 19.2-16.1 1.9-33 2.8-50.6 2.9v-22.1z"></path></svg> package [BCEA](http://www.statistica.it/gianluca/software/bcea/) (see also: <svg viewBox="0 0 496 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> [ comment ] <path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"></path></svg> [https://github.com/giabaio/BCEA](https://github.com/giabaio/BCEA/tree/dev)) --- count: false # Summarising PSA + Research priority .pull-left[ <center><img src=./img/evppi-plot-1.png width='100%' title=''></center> ] .pull-right[ <center><img src=./img/info-rank-1.png width='100%' title=''></center> ] <span style="display:block; margin-top: -20px ;"></span> .small[<svg viewBox="0 0 581 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> [ comment ] <path d="M581 226.6C581 119.1 450.9 32 290.5 32S0 119.1 0 226.6C0 322.4 103.3 402 239.4 418.1V480h99.1v-61.5c24.3-2.7 47.6-7.4 69.4-13.9L448 480h112l-67.4-113.7c54.5-35.4 88.4-84.9 88.4-139.7zm-466.8 14.5c0-73.5 98.9-133 220.8-133s211.9 40.7 211.9 133c0 50.1-26.5 85-70.3 106.4-2.4-1.6-4.7-2.9-6.4-3.7-10.2-5.2-27.8-10.5-27.8-10.5s86.6-6.4 86.6-92.7-90.6-87.9-90.6-87.9h-199V361c-74.1-21.5-125.2-67.1-125.2-119.9zm225.1 38.3v-55.6c57.8 0 87.8-6.8 87.8 27.3 0 36.5-38.2 28.3-87.8 28.3zm-.9 72.5H365c10.8 0 18.9 11.7 24 19.2-16.1 1.9-33 2.8-50.6 2.9v-22.1z"></path></svg> package [BCEA](http://www.statistica.it/gianluca/software/bcea/)] .small[<svg viewBox="0 0 496 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> [ comment ] <path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"></path></svg> [https://github.com/giabaio/BCEA](https://github.com/giabaio/BCEA/tree/dev)] .small[<svg viewBox="0 0 640 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> [ comment ] <path d="M624 416H381.54c-.74 19.81-14.71 32-32.74 32H288c-18.69 0-33.02-17.47-32.77-32H16c-8.8 0-16 7.2-16 16v16c0 35.2 28.8 64 64 64h512c35.2 0 64-28.8 64-64v-16c0-8.8-7.2-16-16-16zM576 48c0-26.4-21.6-48-48-48H112C85.6 0 64 21.6 64 48v336h512V48zm-64 272H128V64h384v256z"></path></svg> [https://egon.stats.ucl.ac.uk/projects/BCEAweb](https://egon.stats.ucl.ac.uk/projects/BCEAweb/)] --- # "*Can **we** do it?...*" ### [https://savi.shef.ac.uk/SAVI/](http://savi.shef.ac.uk/SAVI/) <iframe frameborder="no" src="https://savi.shef.ac.uk/SAVI/" style=" position: fixed; top: -15px; bottom: 0px; right: 0px; left: -200px; width: 100%; border: none; margin: 0; padding: 0; overflow: hidden; z-index: 999999; height: 120%; ms-transform: scale(0.45); -moz-transform: scale(0.45); -o-transform: scale(0.45); -webkit-transform: scale(0.45); transform: scale(0.65); "></iframe> .right25[ <span style="display:block; margin-top: 70px ;"></span> <center><img src=./img/bob-the-builder.jpg width='90%' title=''></center> ] --- # Research priority ## Expected value of **sample** information <span style="display:block; margin-top: -15px ;"></span> <center><img src=./img/voi_scheme1.png width='65%' title='INCLUDE TEXT HERE'></center> --- count: false # Research priority ## Expected value of **sample** information <span style="display:block; margin-top: -15px ;"></span> <center><img src=./img/voi_scheme2.png width='65%' title='INCLUDE TEXT HERE'></center> <span style="display:block; margin-top: 10px ;"></span> .small[Stolen from various presentations by [Anna Heath](https://sites.google.com/site/annaheathstats/)] --- count: false # Research priority ## Expected value of **sample** information .alignright[.small[<svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> <g groupmode="layer" id="layer6" label="icon"> <path style="stroke-width:0.07717" d="m 115.59247,222.50738 c -9.72601,0 -18.734334,7.07397 -24.986084,14.41694 -5.061076,5.95394 -7.591049,15.13238 -7.591049,22.77486 0,7.6402 2.870733,16.13879 7.931808,22.09274 6.152292,7.34297 12.778135,12.37522 22.603045,12.37522 8.83314,0 19.33786,-3.70766 25.389,-9.76105 6.1523,-6.05338 11.26931,-16.21737 11.26931,-25.04826 0,-8.73142 -2.39548,-19.18696 -8.54776,-25.24039 -6.15229,-6.15455 -17.33741,-11.61061 -26.06883,-11.61061 z m 174.6438,2.39944 c -10.12046,0 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7.88829,-19.35029 z m 43.91029,220.24265 H 388.24626 V 185.84118 h 48.82277 z" id="path2"></path> </g></svg> [Jackson et al (2021)](https://www.annualreviews.org/doi/pdf/10.1146/annurev-statistics-040120-010730)]] - EVSI measures the value of reducing uncertainty by running a study of **a given design** `$$\evsi = \E_{\boldsymbol{X}} \left[ \max_t\ \color{blue}{\E_{\boldsymbol\theta \mid \boldsymbol{X}} \left[ \nb_t(\boldsymbol\theta) \right]} \right] - \max_{t}\color{magenta}{\E_{\boldsymbol\theta}\left[\nb_{t}(\boldsymbol\theta)\right]}$$` .box-left[ ↑ Value of decision based on **sample** information (for a given study design) ] .box-right[ ↑ Value of decision based on **current** information ] <span style="display:block; margin-top: 70px ;"></span> - Can compare the benefits and costs of a study with given design - To see if a proposed study likely to be a good use of resources - To find the optimal study design --- count: false # Research priority ## Expected value of **sample** information .alignright[.small[<svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> <g groupmode="layer" id="layer6" label="icon"> <path style="stroke-width:0.07717" d="m 115.59247,222.50738 c -9.72601,0 -18.734334,7.07397 -24.986084,14.41694 -5.061076,5.95394 -7.591049,15.13238 -7.591049,22.77486 0,7.6402 2.870733,16.13879 7.931808,22.09274 6.152292,7.34297 12.778135,12.37522 22.603045,12.37522 8.83314,0 19.33786,-3.70766 25.389,-9.76105 6.1523,-6.05338 11.26931,-16.21737 11.26931,-25.04826 0,-8.73142 -2.39548,-19.18696 -8.54776,-25.24039 -6.15229,-6.15455 -17.33741,-11.61061 -26.06883,-11.61061 z m 174.6438,2.39944 c -10.12046,0 -18.35798,3.98058 -24.70919,11.93724 -5.15827,6.38628 -7.73967,13.66255 -7.73967,21.82831 0,8.27088 2.5814,15.59914 7.73967,21.98538 6.35064,7.95667 14.58873,11.93729 24.70919,11.93729 9.03149,0 16.67002,-3.25109 22.9212,-9.74241 6.25399,-6.59703 9.37846,-14.65259 9.37846,-24.18026 0,-9.422 -3.17646,-17.37639 -9.52708,-23.86775 -6.2495,-6.59477 -13.8428,-9.89721 -22.77258,-9.89721 z M 255.99998,7.9999981 C 119.03396,7.9999981 7.9999985,119.03394 7.9999985,255.99998 7.9999985,392.96602 119.03396,504 255.99998,504 392.96606,504 504,392.96602 504,255.99998 504,119.03394 392.96606,7.9999981 255.99998,7.9999981 Z M 197.17431,331.79065 h -45.93563 v -18.69931 c -4.66437,5.85506 -15.63869,11.82369 -20.40025,14.50172 -8.33473,4.66267 -19.65377,7.70067 -30.27265,7.70067 -17.167865,0 -32.44885,-5.425 -45.844653,-17.23173 -15.977193,-14.0903 -23.483472,-35.63322 -23.483472,-58.85447 0,-23.61798 8.186103,-42.47212 24.559999,-56.56242 12.999092,-11.21393 28.896046,-20.18949 45.766106,-20.18949 9.82264,0 21.93961,0.88269 30.57214,5.04865 4.96218,2.38076 13.84449,7.98548 19.10448,13.44381 v -98.50164 h 45.93564 v 229.34421 z m 157.21544,-21.13999 c -15.28099,17.58718 -36.66682,26.38303 -64.15348,26.38303 -27.58613,0 -49.01942,-8.79585 -64.30436,-26.38303 -12.60069,-14.44803 -18.90387,-32.19228 -18.90387,-53.23507 0,-18.94908 6.35065,-35.75132 19.0525,-50.4079 15.37988,-17.69285 37.26185,-26.54011 65.64139,-26.54011 26.09766,0 46.93585,8.84558 62.51694,26.54011 12.70185,14.44806 19.05247,31.66734 19.05247,51.66468 0.003,20.20586 -6.29921,37.53085 -18.90159,51.97886 z m 38.76899,-199.21794 c 5.35888,-5.35888 11.85868,-8.03746 19.49892,-8.03746 7.64024,0 14.14005,2.67858 19.49893,8.03746 5.35888,5.25945 8.03746,11.70955 8.03746,19.35034 0,7.73965 -2.67858,14.28864 -8.03746,19.64753 -5.25944,5.25944 -11.75925,7.8883 -19.49893,7.8883 -7.64247,0 -14.14227,-2.67861 -19.49892,-8.0375 -5.2594,-5.35885 -7.88829,-11.85871 -7.88829,-19.49892 -0.003,-7.6402 2.62889,-14.0903 7.88829,-19.35029 z m 43.91029,220.24265 H 388.24626 V 185.84118 h 48.82277 z" id="path2"></path> </g></svg> [Jackson et al (2021)](https://www.annualreviews.org/doi/pdf/10.1146/annurev-statistics-040120-010730)]] - EVSI measures the value of reducing uncertainty by running a study of **a given design** `$$\evsi = \E_{\boldsymbol{X}} \left[ \max_t\ \color{blue}{\E_{\boldsymbol\theta \mid \boldsymbol{X}} \left[ \nb_t(\boldsymbol\theta) \right]} \right] - \max_{t}\color{magenta}{\E_{\boldsymbol\theta}\left[\nb_{t}(\boldsymbol\theta)\right]}$$` .box-left[ ↑ Value of decision based on **sample** information (for a given study design) ] .box-right[ ↑ Value of decision based on **current** information ] <span style="display:block; margin-top: 70px ;"></span> - Can compare the benefits and costs of a study with given design - To see if a proposed study likely to be a good use of resources - To find the optimal study design - Computationally complex - Requires specific knowledge of the model for (future/hypothetical) data collection - Again, recent methods have improved efficiency .alignright[.small[<svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> <g groupmode="layer" id="layer6" label="icon"> <path style="stroke-width:0.07717" d="m 115.59247,222.50738 c -9.72601,0 -18.734334,7.07397 -24.986084,14.41694 -5.061076,5.95394 -7.591049,15.13238 -7.591049,22.77486 0,7.6402 2.870733,16.13879 7.931808,22.09274 6.152292,7.34297 12.778135,12.37522 22.603045,12.37522 8.83314,0 19.33786,-3.70766 25.389,-9.76105 6.1523,-6.05338 11.26931,-16.21737 11.26931,-25.04826 0,-8.73142 -2.39548,-19.18696 -8.54776,-25.24039 -6.15229,-6.15455 -17.33741,-11.61061 -26.06883,-11.61061 z m 174.6438,2.39944 c -10.12046,0 -18.35798,3.98058 -24.70919,11.93724 -5.15827,6.38628 -7.73967,13.66255 -7.73967,21.82831 0,8.27088 2.5814,15.59914 7.73967,21.98538 6.35064,7.95667 14.58873,11.93729 24.70919,11.93729 9.03149,0 16.67002,-3.25109 22.9212,-9.74241 6.25399,-6.59703 9.37846,-14.65259 9.37846,-24.18026 0,-9.422 -3.17646,-17.37639 -9.52708,-23.86775 -6.2495,-6.59477 -13.8428,-9.89721 -22.77258,-9.89721 z M 255.99998,7.9999981 C 119.03396,7.9999981 7.9999985,119.03394 7.9999985,255.99998 7.9999985,392.96602 119.03396,504 255.99998,504 392.96606,504 504,392.96602 504,255.99998 504,119.03394 392.96606,7.9999981 255.99998,7.9999981 Z M 197.17431,331.79065 h -45.93563 v -18.69931 c -4.66437,5.85506 -15.63869,11.82369 -20.40025,14.50172 -8.33473,4.66267 -19.65377,7.70067 -30.27265,7.70067 -17.167865,0 -32.44885,-5.425 -45.844653,-17.23173 -15.977193,-14.0903 -23.483472,-35.63322 -23.483472,-58.85447 0,-23.61798 8.186103,-42.47212 24.559999,-56.56242 12.999092,-11.21393 28.896046,-20.18949 45.766106,-20.18949 9.82264,0 21.93961,0.88269 30.57214,5.04865 4.96218,2.38076 13.84449,7.98548 19.10448,13.44381 v -98.50164 h 45.93564 v 229.34421 z m 157.21544,-21.13999 c -15.28099,17.58718 -36.66682,26.38303 -64.15348,26.38303 -27.58613,0 -49.01942,-8.79585 -64.30436,-26.38303 -12.60069,-14.44803 -18.90387,-32.19228 -18.90387,-53.23507 0,-18.94908 6.35065,-35.75132 19.0525,-50.4079 15.37988,-17.69285 37.26185,-26.54011 65.64139,-26.54011 26.09766,0 46.93585,8.84558 62.51694,26.54011 12.70185,14.44806 19.05247,31.66734 19.05247,51.66468 0.003,20.20586 -6.29921,37.53085 -18.90159,51.97886 z m 38.76899,-199.21794 c 5.35888,-5.35888 11.85868,-8.03746 19.49892,-8.03746 7.64024,0 14.14005,2.67858 19.49893,8.03746 5.35888,5.25945 8.03746,11.70955 8.03746,19.35034 0,7.73965 -2.67858,14.28864 -8.03746,19.64753 -5.25944,5.25944 -11.75925,7.8883 -19.49893,7.8883 -7.64247,0 -14.14227,-2.67861 -19.49892,-8.0375 -5.2594,-5.35885 -7.88829,-11.85871 -7.88829,-19.49892 -0.003,-7.6402 2.62889,-14.0903 7.88829,-19.35029 z m 43.91029,220.24265 H 388.24626 V 185.84118 h 48.82277 z" id="path2"></path> </g></svg> [Heath et al (2021)](https://doi.org/10.1177/0272989X20912402)]] - Regression-based .small[(<svg viewBox="0 0 384 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> <g label="icon" id="layer6" groupmode="layer"> <path id="path2" d="M 120.19265,177.73779 C 123.18778,77.35076 64.277527,63.999998 64.277527,63.999998 v 31.26245 C 40.834519,83.611374 18.32863,81.929634 18.32863,81.929634 V 337.10903 c 0,0 98.10414,-11.41744 98.10414,84.40952 0,0 36.58424,-153.37442 248.86103,26.48145 0,-61.59342 0.37757,-216.93925 0.37757,-268.28471 C 169.9561,37.131382 120.1931,177.73779 120.1931,177.73779 Z m 187.20631,173.82056 -12.37599,-97.65441 h -0.448 l -40.72819,97.65441 h -17.55994 l -38.9362,-97.65441 h -0.448 l -14.17589,97.65441 h -43.87514 l 28.8015,-169.61925 h 43.42716 l 34.43518,90.6496 36.46566,-90.6496 h 43.87513 l 25.6817,169.61925 h -44.13938 z" style="stroke-width:0.0675239"></path> </g></svg> [Strong et al, 2015](https://pubmed.ncbi.nlm.nih.gov/25810269/))] - Importance Sampling .small[(<svg viewBox="0 0 384 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> <g label="icon" id="layer6" groupmode="layer"> <path id="path2" d="M 120.19265,177.73779 C 123.18778,77.35076 64.277527,63.999998 64.277527,63.999998 v 31.26245 C 40.834519,83.611374 18.32863,81.929634 18.32863,81.929634 V 337.10903 c 0,0 98.10414,-11.41744 98.10414,84.40952 0,0 36.58424,-153.37442 248.86103,26.48145 0,-61.59342 0.37757,-216.93925 0.37757,-268.28471 C 169.9561,37.131382 120.1931,177.73779 120.1931,177.73779 Z m 187.20631,173.82056 -12.37599,-97.65441 h -0.448 l -40.72819,97.65441 h -17.55994 l -38.9362,-97.65441 h -0.448 l -14.17589,97.65441 h -43.87514 l 28.8015,-169.61925 h 43.42716 l 34.43518,90.6496 36.46566,-90.6496 h 43.87513 l 25.6817,169.61925 h -44.13938 z" style="stroke-width:0.0675239"></path> </g></svg> [Menzies et al, 2016](https://pubmed.ncbi.nlm.nih.gov/25911600/))] - Gaussian approximation .small[(<svg viewBox="0 0 384 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> <g label="icon" id="layer6" groupmode="layer"> <path id="path2" d="M 120.19265,177.73779 C 123.18778,77.35076 64.277527,63.999998 64.277527,63.999998 v 31.26245 C 40.834519,83.611374 18.32863,81.929634 18.32863,81.929634 V 337.10903 c 0,0 98.10414,-11.41744 98.10414,84.40952 0,0 36.58424,-153.37442 248.86103,26.48145 0,-61.59342 0.37757,-216.93925 0.37757,-268.28471 C 169.9561,37.131382 120.1931,177.73779 120.1931,177.73779 Z m 187.20631,173.82056 -12.37599,-97.65441 h -0.448 l -40.72819,97.65441 h -17.55994 l -38.9362,-97.65441 h -0.448 l -14.17589,97.65441 h -43.87514 l 28.8015,-169.61925 h 43.42716 l 34.43518,90.6496 36.46566,-90.6496 h 43.87513 l 25.6817,169.61925 h -44.13938 z" style="stroke-width:0.0675239"></path> </g></svg> [Jalal et al, 2015](https://pubmed.ncbi.nlm.nih.gov/25840900/); <svg viewBox="0 0 384 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> <g label="icon" id="layer6" groupmode="layer"> <path id="path2" d="M 120.19265,177.73779 C 123.18778,77.35076 64.277527,63.999998 64.277527,63.999998 v 31.26245 C 40.834519,83.611374 18.32863,81.929634 18.32863,81.929634 V 337.10903 c 0,0 98.10414,-11.41744 98.10414,84.40952 0,0 36.58424,-153.37442 248.86103,26.48145 0,-61.59342 0.37757,-216.93925 0.37757,-268.28471 C 169.9561,37.131382 120.1931,177.73779 120.1931,177.73779 Z m 187.20631,173.82056 -12.37599,-97.65441 h -0.448 l -40.72819,97.65441 h -17.55994 l -38.9362,-97.65441 h -0.448 l -14.17589,97.65441 h -43.87514 l 28.8015,-169.61925 h 43.42716 l 34.43518,90.6496 36.46566,-90.6496 h 43.87513 l 25.6817,169.61925 h -44.13938 z" style="stroke-width:0.0675239"></path> </g></svg> [Jalal and Alarid-Escudero, 2018](https://pubmed.ncbi.nlm.nih.gov/28735563/))] - Moment matching .small[(<svg viewBox="0 0 384 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> <g label="icon" id="layer6" groupmode="layer"> <path id="path2" d="M 120.19265,177.73779 C 123.18778,77.35076 64.277527,63.999998 64.277527,63.999998 v 31.26245 C 40.834519,83.611374 18.32863,81.929634 18.32863,81.929634 V 337.10903 c 0,0 98.10414,-11.41744 98.10414,84.40952 0,0 36.58424,-153.37442 248.86103,26.48145 0,-61.59342 0.37757,-216.93925 0.37757,-268.28471 C 169.9561,37.131382 120.1931,177.73779 120.1931,177.73779 Z m 187.20631,173.82056 -12.37599,-97.65441 h -0.448 l -40.72819,97.65441 h -17.55994 l -38.9362,-97.65441 h -0.448 l -14.17589,97.65441 h -43.87514 l 28.8015,-169.61925 h 43.42716 l 34.43518,90.6496 36.46566,-90.6496 h 43.87513 l 25.6817,169.61925 h -44.13938 z" style="stroke-width:0.0675239"></path> </g></svg> [Heath et al, 2018](https://pubmed.ncbi.nlm.nih.gov/29126364/))] - Can be used to drive design of new study (eg sample size calculations) --- count: false # Research priority ## Expected value of **sample** information <span style="display:block; margin-top: -35px ;"></span> .pull-left[ <center><img src=./img/voi1.png width='85%' title='INCLUDE TEXT HERE'></center> ] .pull-right[ <center><img src=./img/voi2.png width='85%' title='INCLUDE TEXT HERE'></center> ] <span style="display:block; margin-top: -25px ;"></span> .small[ <svg viewBox="0 0 496 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> [ comment ] <path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"></path></svg> [https://github.com/giabaio/EVSI](https://github.com/giabaio/EVSI) and [https://github.com/chjackson/voi](https://github.com/chjackson/voi) <svg viewBox="0 0 640 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> [ comment ] <path d="M624 416H381.54c-.74 19.81-14.71 32-32.74 32H288c-18.69 0-33.02-17.47-32.77-32H16c-8.8 0-16 7.2-16 16v16c0 35.2 28.8 64 64 64h512c35.2 0 64-28.8 64-64v-16c0-8.8-7.2-16-16-16zM576 48c0-26.4-21.6-48-48-48H112C85.6 0 64 21.6 64 48v336h512V48zm-64 272H128V64h384v256z"></path></svg> [https://egon.stats.ucl.ac.uk/projects/EVSI](https://egon.stats.ucl.ac.uk/projects/EVSI) <span style="display:block; margin-top: 10px ;"></span> <svg viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg" style="height:1em;fill:currentColor;position:relative;display:inline-block;top:.1em;"> <g groupmode="layer" id="layer6" label="icon"> <path style="stroke-width:0.07717" d="m 115.59247,222.50738 c -9.72601,0 -18.734334,7.07397 -24.986084,14.41694 -5.061076,5.95394 -7.591049,15.13238 -7.591049,22.77486 0,7.6402 2.870733,16.13879 7.931808,22.09274 6.152292,7.34297 12.778135,12.37522 22.603045,12.37522 8.83314,0 19.33786,-3.70766 25.389,-9.76105 6.1523,-6.05338 11.26931,-16.21737 11.26931,-25.04826 0,-8.73142 -2.39548,-19.18696 -8.54776,-25.24039 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-5.2594,-5.35885 -7.88829,-11.85871 -7.88829,-19.49892 -0.003,-7.6402 2.62889,-14.0903 7.88829,-19.35029 z m 43.91029,220.24265 H 388.24626 V 185.84118 h 48.82277 z" id="path2"></path> </g></svg> [Heath et al (2019)](https://doi.org/10.1177/0272989X19837983) ] --- count: false # Research priority ## Expected value of **sample** information <center><img src=./img/voi3.png width='63%' title='INCLUDE TEXT HERE'></center> --- # *"Tell me a sad story in just one slide..."* ### [NICE HTA evaluation methods update](https://www.nice.org.uk/about/what-we-do/our-programmes/nice-guidance/nice-technology-appraisal-guidance/changes-to-health-technology-evaluation) (2021) .medium[ > *2.16. The use of Expected Value of Perfect Information (EVPI) will .red[**not**] be adopted into the NICE methods. Stakeholders raised concerns about this proposal and the majority disagreed with it. It was noted that the added value of EVPI and how it would be used in decision-making was unclear as experiences from other countries suggested that its added value to decision making is minimal. There were concerns that it would add complexity to decision making, and the additional burden for analysts and reviewers may not be worth it. On the other hand, .blue[some stakeholders argued that the proposal did not go far enough and should include expected value of partially perfect information (EVPPI) and expected value of sample information (EVSI)].* ] --- count: false # *"Tell me a sad story in just one slide..."* ### [NICE HTA evaluation methods update](https://www.nice.org.uk/about/what-we-do/our-programmes/nice-guidance/nice-technology-appraisal-guidance/changes-to-health-technology-evaluation) (2021) .medium[ > *2.16. The use of Expected Value of Perfect Information (EVPI) will .red[**not**] be adopted into the NICE methods. Stakeholders raised concerns about this proposal and the majority disagreed with it. It was noted that the added value of EVPI and how it would be used in decision-making was unclear as experiences from other countries suggested that its added value to decision making is minimal. There were concerns that it would add complexity to decision making, and the additional burden for analysts and reviewers may not be worth it. On the other hand, .blue[some stakeholders argued that the proposal did not go far enough and should include expected value of partially perfect information (EVPPI) and expected value of sample information (EVSI)].* ] <span style="display:block; margin-top: 40px ;"></span> .pull-left[ <center><img width="580!important;" src="img/careless-whisper.gif" title=""></center> ] .pull-right[ .medium[ - Push from industrial representatives, despite attempts at clarifying/simplyfing concepts/guidelines - CADHT actually say > *When the decision problem includes consideration of further research to inform future decisions, .blue[a value-of-information analysis should be undertaken as part of the reference case]. [...] To identify these critical values and correctly quantify the impact of a parameter taking a specific value (on both the probability of an intervention being cost-effective and the expected net benefit), .blue[recent methodological work suggests that a two-stage expected value of perfect parameter information analysis may be useful]* ] ] --- # Conclusions - HTA is fundamentally based on statistical modelling &ndash; and statisticians should be much more heavily involved in the whole process - More modellers with stronger statistical background &ndash; often (**though not always!**) use of suboptimal tools is a red flag for lack of necessary sophistication in statistical modelling - More statisticians developing methods, sitting on panels and creating critical mass --- count: false # Conclusions - HTA is fundamentally based on statistical modelling &ndash; and statisticians should be much more heavily involved in the whole process - More modellers with stronger statistical background &ndash; often (**though not always!**) use of suboptimal tools is a red flag for lack of necessary sophistication in statistical modelling - More statisticians developing methods, sitting on panels and creating critical mass <span style="display:block; margin-top: 40px ;"></span> .pull-left[ - VoI methods can be very helpful - The can address multiple questions, including research prioritisation - Vital in issues such as managed entry/conditional reimbursment - Still a battle - But: ... ] .pull-right[ <center><img src=./img/over-till-its-over.gif width='25%' title=''></center> ] --- # "*Where can I look for more, you ask?...*" [https://r-hta.org/](https://r-hta.org/) <iframe frameborder="no" src="https://r-hta.org/" style=" position: fixed; top: 30px; bottom: 0px; right: 0px; width: 200%; border: none; margin: 0; padding: 0; overflow: hidden; z-index: 999999; height: 100%; ms-transform: scale(0.45); -moz-transform: scale(0.45); -o-transform: scale(0.45); -webkit-transform: translate(+50%, -50%); transform: translate(+50%, -50%); <!-- -webkit-transform: scale(0.45); transform: scale(0.70); --> "> </iframe> --- count: false # "*Where can I look for more, you ask?...*" [https://www.convoi-group.org/](https://www.convoi-group.org/) <iframe frameborder="no" src="https://www.convoi-group.org/" style=" position: fixed; top: 30px; bottom: 0px; right: 0px; width: 140%; border: none; margin: 0; padding: 0; overflow: hidden; z-index: 999999; height: 100%; ms-transform: scale(0.45); -moz-transform: scale(0.45); -o-transform: scale(0.45); -webkit-transform: scale(0.45); transform: scale(0.70); "> </iframe> --- class: scroll-up count: false .huge[SPECIAL THANKS]<br> Anna Heath (Sick Kids Hospital, Toronto, Canada) &bull; Mark Strong (University of Sheffield, UK) &bull; Nicky Welton (University of Bristol, UK) &bull; Chris Jackson (MRC Biostatistics Unit, Cambridge, UK) &bull; Howard Thom (University of Bristol, UK) &bull; the ConVOI Consortium &bull; the R-HTA Consortium &bull; Cynthia Iglesias (University of York, UK) &bull; Andrea Manca (University of York, UK) &bull; Manuela Joore (Maastricht University, Netherlands) &bull; Mike Paulden (University of Alberta, Canada) <br><br><br><br><br> .large[**Soundtrack**]<br> "Zitti e buoni" (Performed by Måneskin) &bull; "We are the champions" (Performed by Queen) &bull; "I will survive" (Performed by Cake) &bull; "Survivor" (Performed by Desiny's Child) &bull; "Careless whispers" (Performed by George Michael) <br><br><br><br><br><br><br> .small[No non-statistician and no non-Bayesian statistician have been willingly harmed during the making of these slides] --- class: thankyou-michelle