Bayesian Analysis of Bivariate Competing Risks Models

Absolutely continuous bivariate exponential (ACBVE) models have been widely used in the analysis of competing risks data involving two risk components. For such an analysis, frequentist approach often runs into difficulty due to a likelihood containing some nonidentifiable parameters. With an end to overcome this nonindentifiability, we consider Bayesian procedures. Utilization of informative priors in the Bayesian analysis is attractive in the presence of historical data. However, systematic prior elicitation becomes difficult when no such data is available. The present study focuses instead on Bayesian analysis with noninformative priors. The ACBVE model structure often leads to a likelihood function with a nonregular Fisher information matrix impeding thereby the calculation of standard noninformative priors such as Jeffreys’s prior and its variants. As a remedy, a stagewise noninformative prior elicitation strategy is proposed. A variety of noninformative priors are developed, and are used for data analysis. These priors are evaluated according to the frequentist probability matching criterion for identifiable parameters. In addition, this paper examines the asymptotic property of nonidentifiable parameters under certain informative setting.