Dependent masking and system life data analysis: Bayesian inference for two-component systems

A Bayesian approach to competing risks analysis with masked cause of death

Cause-specific analyses under a competing risks framework have received considerable attention in the statistical literature. Such analyses are useful for comparing mortality patterns across racial and/or age groups. Earlier work in the statistical literature focused on the situation when the cause of death is known. A challenging twist to the problem arises when the cause of death is not known exactly, but can be narrowed down to a set of potential causes that do not necessarily act independently. This phenomenon, referred to as masking, is often the result of incomplete or partial information on death certificates and/or lack of routine autopsy on every patient. In this article we propose a semiparametric Bayesian approach for analyzing competing risks survival data with masked cause of death. The models proposed do not assume independence among the causes, and are valid for an arbitrary number of causes. Further, the Bayesian approach is flexible in allowing a general pattern of missingness for the cause of death. We illustrate our methodology using breast cancer data from the Detroit Surveillance, Epidemiology, and End Results registry.

Inference for the dependent competing risks model with masked causes of failure

The competing risks model is useful in settings in which individuals/units may die/fail for different reasons. The cause specific hazard rates are taken to be piecewise constant functions. A complication arises when some of the failures are masked within a group of possible causes. Traditionally, statistical inference is performed under the assumption that the failure causes act independently on each item. In this paper we propose an EM-based approach which allows for dependent competing risks and produces estimators for the sub-distribution functions. We also discuss identifiability of parameters if none of the masked items have their cause of failure clarified in a second stage analysis (e.g. autopsy). The procedures proposed are illustrated with two datasets.