What if there’s no censoring?…

Philip Cooney has alerted me to a slight inconsistency in survHE. Basically, he was trying to work in a setting where the data contain no censoring, using the HMC/rstan models generated by survHE. All works OK when using some of the models implemented, but failed when trying to fit the Gamma, Generalised Gamma and Generalised F.

The reason for this is that, for simplicity (and actually, our empirical tests show that computational run-time is much reduced) these models construct the log-likelihood by separating the set of individuals who are fully observed from the one of individuals who are censored. Basically, the model splits the data into \(\boldsymbol{y}=(y^{\rm{obs}},y^{\rm{cens}})\), when \(y^{\rm{cens}}\) is a latent parameter and then considers \[y^{\rm{obs}}_i \sim p(y^{\rm{obs}}\mid \mu_i,\alpha) \qquad {\sf and} \qquad g(\mu_i) = \boldsymbol{X}^{\rm{obs}}_i \boldsymbol\beta\] and \[y^{\rm{cens}}_i \sim p(y^{\rm{cens}}\mid \mu_i,\alpha) \qquad {\sf and} \qquad g(\mu_i) = \boldsymbol{X}^{\rm{obs}}_i \boldsymbol\beta + \log(d_i),\] where \(d_i\) is the censored time (so the point at which the individuals have exited from the study without experiencing the event).

Because the two variables share the parameters, effectively the estimates account for censoring in this formulation. But, for these three models, survHE couldn’t handle in its default implementation, the case in which the number of censored data was 0.

Philip and I have fixed the code and I’ve now updated the GitHub devel version — I’ve upped the version number to 1.1.3 and included Philip as a contributor.