Practical survival analysis tools for heterogeneous cohorts and informative censoring

In heterogeneous cohorts and those where censoring by non-primary risks is informative many conventional survival analysis methods are not applicable; the proportional hazards assumption is usually violated at population level and the observed crude hazard rates are no longer estimators of what they would have been in the absence of other risks. In this paper, we develop a fully Bayesian survival analysis to determine the probabilistically optimal description of a heterogeneous cohort and we propose a novel means of recovering hazard rates and survival functions `decontaminated' of the effects of any competing risks. Most competing risks studies implicitly assume that risk correlations are induced by cohort or disease heterogeneity that is not captured by covariates. We additionally assume that proportional hazards hold at the level of individuals, for all risks, leading to a generic statistical description that allows us to decontaminate the effects of informative censoring, and from which Cox regression, frailty and random effects models, and latent class models can all be recovered as special cases. Synthetic data confirm that our approach can map a cohort's substructure, and remove heterogeneity-induced false protectivity and false aetiology effects. Application to survival data from the ULSAM cohort leads to plausible alternative explanations for previous counter-intuitive inferences to prostate cancer. The importance of managing cardiovascular disease as a comorbidity in women diagnosed with breast cancer is suggested on application to survival data from the AMORIS study.