Leveraging real-world evidence for health technology assessment – Using big data to enable patient access

# Leveraging real-world evidence for health technology assessment – Using big data to enable patient access

## Gianluca Baio

### [Department of Statistical Science](https://www.ucl.ac.uk/statistics/) | University College London    
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### ISPOR Europe 2022, Vienna (Austria)

7 November 2022

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Blended survival curves  &nbsp; | &nbsp; ISPOR Europe 2022  &nbsp; | &nbsp;  7 Nov 2022
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# What are we talking about?...

]

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## 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! `$\Rightarrow$` Extrapolation    
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](https://twitter.com/manuelajoore/status/1329413099678539785). But the modellers can (should?!) be statisticians too, so they could handle the data!...

]

---

## Data

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!...)

]

---

## A couple of examples

exclude: true
1. ICD & Cardiac death
   
   - Relatively old-ish work
   - Combination of RCT and observational/registry data

exclude: true
<ol style="counter-reset: my-counter 1;">
<li> "Blending" 
</li>
<ul> 
<li> Newer method </li>
<li> <b><i>Similar</i></b> to mixture cure models &ndash; but not quite the same...</li>
</ul>
</ol>

---

## Basic idea/modelling
.alignright[<svg viewBox="0 0 384 512" style="height:1em;position:relative;display:inline-block;top:.1em;" xmlns="http://www.w3.org/2000/svg">  <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> [Benaglia et al (2015)](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4847642/)]

Use UK population data (matched by age/sex) to "**anchor**" the ICD population at risk

- Perhaps the easiest way to do this is to relate the hazard between the two populations &ndash; eg **proportional hazard** (PH) model
<span style="display:block; margin-top: -20px ;"></span>
   `$$\class{myblue}{h_{\rm{ICD}}(t) = e^{\beta}h_{\rm{UK}}(t) \qquad \Leftrightarrow \qquad \HR = \frac{h_{\rm{ICD}}(t)}{h_{\rm{UK}}(t)} = e^{\beta} = \style{font-family:inherit;}{\text{Constant}}}$$`
   
<span style="display:block; margin-top: -20px ;"></span>
   
- Relatively easy to model &ndash; but probably very unrealistic!

- ICD patients are at (much?) greater risk of arrhythmia death 
   - If the proportion of deaths caused by arrythmia changes over time, we would induce bias, because we would be extrapolate a constant HR for all causes mortality
   
--

exclude: true
- Formally account for multiple mortality causes (.blue[**Poly-Weibull**] model <svg viewBox="0 0 384 512" style="height:1em;position:relative;display:inline-block;top:.1em;" xmlns="http://www.w3.org/2000/svg">  <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> [Demiris et al, 2015](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4456429/)):
`\begin{align}
\class{myblue}{h_{\rm{ICD}}(t)} &\class{myblue}{= h}_{\rm{\class{red}{ICD}}}^{\rm{\class{myblue}{arr}}}\class{myblue}{(t) + h}_{\rm{\class{red}{ICD}}}^{\rm{\class{myblue}{oth}}}\class{myblue}{(t)} \\
&\class{myblue}{=} \class{orange}{e^\beta} \class{myblue}{h^{\rm{arr}}}_{\rm{\class{blue}{UK}}}\class{myblue}{(t)} + \class{myblue}{h^{\rm{oth}}}_{\rm{\class{blue}{UK}}}\class{myblue}{(t)} \\
&\class{myblue}{=} \class{orange}{e^\beta}\class{myblue}{\alpha_1 \mu_1 t^{\alpha_1-1} + \alpha_2 \mu_2 t^{\alpha_2-1}}
\end{align}`

<span style="display:block; margin-top: -20px ;"></span>
- This assumes that
   -  Arrhythmia hazard is .orange[**proportional**] to matched UK population
   - Other causes hazard is **identical** to matched UK population

---

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# Example &ndash; ICD & Cardiac death

## Turning prior *information* into a prior *distribution*

- In the ICD case, age at entry is around 60 &ndash; we **know** that people won't survive more than 60 more years
   - Setting a prior for the scale `$\mu_i \sim \dunif(0,100)$` implies that the prior mean survival of the resulting Weibull distribution is 
   `$$\class{myblue}{\style{font-family:inherit;}{\text{expected survival time}}=\mu_i\Gamma\left(1+\frac{1}{\alpha}\right) < 60}$$`
   
- Can also include some knowledge on the shape `$\alpha$` and the coefficient `$\beta$` to limit their variations in reasonable ranges...

exclude: true
.pull-left-nospace[
<center><img src=./img/friends-gif.gif width='100%' title=''></center>
]
.pull-right-nospace[
- This isn't necessarily easy! 
   - You need to be friends with a statistician...

- Don't be lost in translation...
   - *Elicit* the actual .blue[**information**] and then map it onto a possible and reasonable .red[**distribution**]
   - Mapping changes with the mathematical properties of the underlying sampling distribution selected...
]

---

- Ignoring cause-specific mortality (simple .red[Weibull model]) results in larger bias, especially for females, mostly because the arrhythmia proportion of deaths does vary over time in that subgroup

---

# Example

### Observed data ([NICE TA 174](https://www.nice.org.uk/guidance/ta174))
<center><img src=./img/surv1-1.png width='72%' title=''></center>

---

### Parametric fitting/extrapolation
<center><img src=./img/surv2-1.png width='72%' title=''></center>

---

## What do we see?

- The data are **sparse** (lots of censoring) and the follow up is limited in comparison to the relevant time horizon

- The **best fitting** model (Gompertz) responds by extrapolating a survival curves that implies `$\Pr(\style{font-family:inherit;}{\text{Still alive after 15 years}})>$` 0.5

- This is most likely a ridiculous finding!

exclude: true
<span style="display:block; margin-top: 40px ;"></span>
## What do we know?

- Perhaps we may think a bit more carefully and figure out some kind of "constraint" or upper limit for the survival probability at a given time point in the future...

- Maybe, it's not so controversial to assume that, **before observing any data**, `$\Pr(\style{font-family:inherit;}{\text{Still alive after about 6 years}})$` should not exceed, say, 0.20

- We can use this information in our prior specification and let it be modified by the observed data
   - This is a relatively strong prior, so you would need a **really** strong signal to modify it significantly...

---

## "Blended" survival curves

<span style="display:block; margin-top: -50px ;"></span>
### .alignright[<svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;" xmlns="http://www.w3.org/2000/svg">  <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> [Che et al (2022)](https://doi.org/10.1177/0272989X221134545)]

### Consider two separate process

1. Driven *exclusively* by the .red[**observed data**]

- Similar to a "standard" HTA analysis &ndash; use this to estimate `$S_{obs}(t\mid\bm\theta_{obs})$`
   - Main objective: produce the **best** fit possible to the *observed* information 
   - **NB**: Unlike in a "standard" modelling exercise where the issue of overfitting is potentially critical, achieving a very close approximation to the observed dynamics has much less important implications in the case of blending

<ol style="counter-reset: my-counter 1;">
<li><p style="color:blue;"><b>"External" process</b></p>
   <ul>
   <li>Used to derive a separate survival curve, ${S_{ext}(t\mid\bm\theta_{ext})}$ to describe the <b><i>long-term</i></b> estimate for the survival probabilities</li>
   <li>Could use "hard" evidence (eg RWE/registries/cohort studies/etc)...</li>
   <li>...Or, purely subjective knwoledge elicited from experts (or both!)</li>
   </ul>
</li>
</ol>

.footnote[
<svg viewBox="0 0 496 512" style="height:1em;position:relative;display:inline-block;top:.1em;" xmlns="http://www.w3.org/2000/svg">  <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> [`R` Code (for the paper)](https://github.com/StatisticsHealthEconomics/blendR-paper)
.alignright[<svg viewBox="0 0 496 512" style="height:1em;position:relative;display:inline-block;top:.1em;" xmlns="http://www.w3.org/2000/svg">  <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> [`R` package `blendR`](https://github.com/StatisticsHealthEconomics/blendR)]
]

---

count: false
# Example &ndash; Blended survival curves
.panelset[
.panel[.panel-name[Stats]
Combine the two processes to obtain
`\begin{align}
\class{myblue}{S_{ble}(t\mid\bm\theta) = S_{obs}(t\mid\bm\theta_{obs})^{1-\pi(t; \alpha, \beta, a, b)}\times S_{ext}(t\mid\bm\theta_{ext})^{\pi(t;\alpha, \beta, a, b)}}
\end{align}`
<span style="display:block; margin-top: -20px ;"></span>
where:
<span style="display:block; margin-top: 30px ;"></span>

- `$\bm \theta = \{\bm \theta_{obs}, \bm \theta_{ext}, \alpha, \beta, a, b\}$` is the vector of .red[**model parameters**] 
<span style="display:block; margin-top: 30px ;"></span>

- `$\displaystyle \class{myblue}{\pi(t;\alpha,\beta,a,b) = \Pr\left(T\leq \frac{t-a}{b-a}\mid \alpha,  \beta\right) = F_{\text{Beta}}\left (\frac{t-a}{b-a}\mid \alpha, \beta \right)}$` is a .blue[**weight** function] controlling the extent to which `$S_{obs}(\cdot)$` and `$S_{ext}(\cdot)$` are blended together 
<span style="display:block; margin-top: 30px ;"></span>

- `$t \in [0,T^*]$`, is the .orange[**interval of times**] over which we want to perform our evaluation

<span style="display:block; margin-top: 50px ;"></span>
.content-box-beamer[
### 
**NB**: This is *not* the same as a "mixture cure model"!

- In MCM, one mixed survival curve (cured vs non cured individuals)
- In BSC, short- vs long-term processed modelled explicitly
]
]

<span style="display:block; margin-top: -10px ;"></span>
<center><img src=./img/blending_process-1.png width='75%' title=''></center>
]

<span style="display:block; margin-top: -10px ;"></span>
<center><img src=./img/betacdf_weight-1.png width='75%' title=''></center>
]

<span style="display:block; margin-top: -10px ;"></span>
<center><img src=./img/blending_weights-1.png width='75%' title=''></center>
]

]

---

---

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background-image: url("img/limitations.gif")
background-size: cover

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# Comments

- The main point of the "blending" procedure is to recognise that, sometimes (often...), the observed data are just not good enough to simultaneously
   
   1. Provide the best fit to the observed data
   2. Provide a reasonable extrapolation for the long-term survival

- Instead, we let the observed data tell us about the short-term survival **and** some external information tell us something about the long-term survival

- When external data/RWE are available, they should be leveraged

- BSCs allow to do this in a relatively straightforward way
   
   - The "heavy-lifting" is done by the weight function that determines how the sources are blended together
   
   - This is based on (possibly untestable, but certainly open/upfront!) assumptions

- This combination of difference sources of evidence is naturally Bayesian

- Ultimately, we don't really care about the two components &ndash; rather we want to fully characterise the uncertainty in the blended curve
   
   - ... But to get that is simple algebra to combine the posterior distributions for `$S_{obs}(t\mid\bm\theta_{obs})$` and `$S_{ext}(t\mid\bm\theta_{ext})$`

---

NULL

---