Robust estimation with variational Bayes in presence of competing risks

Variational Bayes, a method from machine learning, can provide a good approximation to the intractable posterior density function. It converges fast and works efficiently for large data sets. In this paper, we employ this method for robust Bayesian estimation of cause-specific quantities using competing risk data with missing causes. We consider the contamination class of prior distributions for the concerned parameter and discuss the implementation of ML-II procedure of Good (Good thinking: the foundations of probability and its applications, University of Minnesota Press, Minnesota , 1983) through variational Bayes approach in order to select a prior in a data-dependent fashion leading to a robust posterior. We perform sensitivity analysis to observe the influence of prior on some posterior quantities of interest. We analyze a real data set of computer hard-drives having three competing causes of failure and illustrate that the considered method provides robust Bayes estimates of concerned parameters, cause-specific hazard, and cumulative incidence function.