Predictive Assessment and Comparison of Bayesian Survival Models for Cancer Recurrence

TL;DR

The paper addresses challenges in predictive checking and predictive comparison for Bayesian survival analyses when censored times and time-dependent effects complicate model evaluation. It introduces targeted, scenario-based recommendations for parametric survival, Bernoulli, and cross-model comparisons, including handling censoring, left-truncation, and time discretization with PSIS-LOO CV. Through a simulation-based case study mimicking gastrointestinal stromal tumour data, it demonstrates when different models excel (e.g., Bernoulli for time-dependent treatments) and provides practical guidance on diagnostics and interpretation. The work advances the Bayesian survival analysis workflow by systematizing checks and comparisons and linking them to open-source tools, while also outlining limitations and avenues for future development and real-data applications.

Abstract

Complex data features, such as unmodelled censored event times and variables with time-dependent effects, are common in cancer recurrence studies and pose challenges for Bayesian survival modelling. Current methodologies for predictive model checking and comparison often fail to adequately address these features. This paper bridges that gap by introducing new, targeted recommendations for predictive assessment and comparison of Bayesian survival models. Our recommendations cover a variety of different scenarios and models. Accompanying code together with our implementations to open source software help in replicating the results and applying our recommendations in practice.

Figures (23)

• Figure 1: An example of a Bernoulli model applied in cancer recurrence prediction. The model predicts the probability of recurrence for a patient for each year after surgery conditional on the fact that it has not happened in the previous years. The model allows the inclusion of variables with time-dependent effects. The patient in the example receives adjuvant treatment for three years after surgery, and the time-dependent effect of treatment on the predicted probability can be clearly seen in the figure. The figure shows that the predicted probability of event jumps high immediately after the adjuvant treatment ends.
• Figure 2: The intervals plot displays observations with dark points, medians of predictive draws with lighter points, and central intervals for predictive draws with vertical bars. When the model fits well, most observations should fall within the corresponding predictive intervals.
• Figure 3: The PIT-ECDF plot visualises the empirical cumulative distribution function (ECDF) of the probability integral transformation (PIT) of observations with respect to the corresponding predictive draws. The plot also displays central simultaneous confidence bands that can be used to assess whether observations and predictive draws come from the same distribution. PIT-ECDF that exceeds the confidence bands indicates a lack of fit.
• Figure 4: The Kaplan-Meier overlay plot shows the Kaplan-Meier survival curve kaplan1958 of the observations with a dark colour and the empirical CCDF estimates of the predictive draws with a lighter colour. If the survival curve deviates from the empirical CCDF estimates of the predictive draws, there is probably some lack of fit.
• Figure 5: Two different Kaplan-Meier overlay plots for the same data set where some data points are left-truncated. a) Left-truncation is not taken into account. b) Left-truncation is taken into account.