  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.
