The effects of misclassification of the actual cause of death in competing risks analysis

The problem of competing risks analysis arises often in public health, demography, actuarial science, industrial reliability applications, and experiments in medical therapeutics. In the classical competing risks scenario one models the risks with a vector (T = (T1, ..., Tk) of non-negative random variables that represents the potential times to death of k risks. One cannot see T directly but sees instead Y = min (T1, ..., Tk) and the actual cause of death. The major difficulty with this analysis is the requirement for the expert to specify the single cause of death that, in fact, may not be the actual cause. This paper addresses competing risks analysis for the situations where one observes Y and the set of several possible causes of death specified by the expert. Many times there are several causes that act together and realistically it is impossible for the expert to assign a death to a single cause. In particular, I provide a likelihood for parametric competing risks analysis when the actual cause of death is possibly misclassified. The data include time to death, Y, and a set of possible causes of death. If misclassification probabilities are unknown, I propose a Baysian analysis based on a prior distribution for the parameters of interest and for the misclassification probabilities.