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

Practical survival analysis tools for heterogeneous cohorts and informative censoring