Assessing survival models by interval testing with Poisson-binomial distributions

Selecting appropriate parametric survival models is often a pivotal part of a regulatory submission for new pharmaceutical products.

With recent developments in complex survival approaches, the number of suitable models is increasing, making model selection more challenging.

Common approaches to model selection include AIC, BIC, and expert opinion on survival extrapolation.

However, these approaches primarily assess relative goodness-of-fit, providing limited insight into where, and to what extent, a fitted model is incompatible with the observed data.

We propose evaluating survival models using Poisson-binomial distributions across specified time intervals.

Two interval selection approaches, censor-defined intervals and 10 evenly-spaced intervals, are presented with worked examples.

A simulation exercise, targeting two proposed test statistics across 12 standard scenarios (with different data maturity and patient numbers), demonstrated that for every scenario the empirical Type I error did not exceed the nominal 5% level.

Our proposed model selection technique goes beyond classical approaches by highlighting time intervals where models perform poorly.