A Mixture Modeling of Recall-Based Current Status Competing Risks Data

In this article, we consider the analysis of current status competing risks data with recall information. It is observed that memory fades with passes of time. The chance of recalling an event depends on the difference between time to event and monitoring time. This available information is utilized in modeling current status data. We consider two causes competing for risks with the current status data scenario when the lifetimes of the event of interest follow two different distributions, Exponential and Rayleigh distribution for cause $1$ and cause $2$ respectively. New estimation methods for such data are developed in classical and Bayesian frameworks. In the classical approach, to obtain the maximum likelihood estimates, an equivalent quantity approach based on the Expectation-Maximization algorithm is proposed. For asymptotic confidence intervals, the observed Fisher information matrix is calculated using the principle of missing information. Under the Bayesian framework, conjugate priors are considered for unknown parameters, and estimates are obtained under the square error loss function. Three-stage Gibbs Sampling is proposed for drawing samples from conditional posteriors. Bayesian Credible and Highest Posterior Density intervals are constructed based on the Markov Chain Monte Carlo samples generated from full conditionals. For illustration purposes, simulation and real data study are established.