Addressing missing covariates for the regression analysis of competing risks: Prognostic modelling for triaging patients diagnosed with prostate cancer.

Competing risks arise in medical research when subjects are exposed to various types or causes of death. Data from large cohort studies usually exhibit subsets of regressors that are missing for some study subjects. Furthermore, such studies often give rise to censored data. In this article, a carefully formulated likelihood-based technique for the regression analysis of right-censored competing risks data when two of the covariates are discrete and partially missing is developed. The approach envisaged here comprises two models: one describes the covariate effects on both long-term incidence and conditional latencies for each cause of death, whilst the other deals with the observation process by which the covariates are missing. The former is formulated with a well-established mixture model and the latter is characterised by copula-based bivariate probability functions for both the missing covariates and the missing data mechanism. The resulting formulation lends itself to the empirical assessment of non-ignorability by performing sensitivity analyses using models with and without a non-ignorable component. The methods are illustrated on a 20-year follow-up involving a prostate cancer cohort from the National Cancer Institutes Surveillance, Epidemiology, and End Results program.