Bayesian sensitivity analysis to the non-ignorable missing cause of failure for hybrid censored competing risks data

Abstract

ABSTRACT Competing risks arise when an individual is exposed to the several causes of failure. In this case, the recorded data includes two components, the failure times and the cause of failure indicators. Such data may suffer from censoring in the former part and missingness in the latter part. Prior researches have ignored the missing mechanism when analysing such data which might lead to invalid statistical inferences. Since the ignorability assumption is unverifiable from the available data, the sensitivity analysis is recommended. In this paper, the Bayesian index of local sensitivity to non-ignorability (ISNI) is derived to quantify the sensitivity of Bayesian estimators to the ignorability assumption for hybrid censored incomplete competing risks data when the lifetimes follow exponential, Weibull, and generalized exponential distributions. Also, some simulation studies are conducted to evaluate the performance of the proposed Bayesian ISNI in different missing and competing risks scenarios. Finally, a real-world example is analysed for illustrative purposes.