Analysis of masked competing risks data with cause and time dependent masking mechanism

Abstract

In this paper, we discuss the estimation problem of the competing risks model when the exact cause of failure for some units may not be completely observed. The failure times of the components are assumed to follow Weibull distributions with different shape and scale parameters according to each competing risk. In the applied competing risks analysis, it is common to have failed units during life testing which do not have a certain cause of failure. Actually, the cause is not completely missed but is only known to belong to a certain subset of all possible causes. This case is known as masking. We propose to analyse these data assuming an underling masking mechanism as apart of data model, to allow the potential dependency of the masking probability on the unknown cause of failure and/or the observed failure time, applying an appropriate Generalized Linear Model. The parameters of the joint competing risks and masking mechanism model are estimated using the maximum likelihood approach. Also, several simulation studies are conducted to access the effect of different masking rates, mechanisms and sample sizes on the parameter estimation of Weibull competing risks data with different sets of shape and scale parameters. Finally, a real data example is analysed to illustrate the application of the proposed methods.