Clustering method for censored and collinear survival data

In this paper we propose a Dirichlet process mixture model for censored survival data with covariates. This model is suitable in two scenarios. First, this method can be used to identify clusters determined by both the censored survival data and the predictors. Second, this method is suitable for highly correlated predictors, in cases when the usual survival models cannot be implemented because they would be unstable due to multicollinearity. The Dirichlet process mixture model links a response vector to covariate data through cluster membership and in this paper this model is extended for mixtures of Weibull distributions, which can be used to model survival times and also allow for censoring. We propose two variants of this model, one with a shape parameter common to all clusters (referred to as a global parameter) for the Weibull distributions and one with a cluster-specific shape parameter. The first satisfies the proportional hazard assumption, while the latter is very flexible, as it has the advantage of allowing estimation of the survival curve whether or not the proportional hazards assumption is satisfied. We present a simulation study and, to demonstrate the applicability of the method in practice, a real application to sleep surveys in older women from The Australian Longitudinal Study on Women’s Health. The method developed in the paper is available in the R package PReMiuM.