Analysis of left truncated and right censored competing risks data

In this article, the analysis of left truncated and right censored competing risks data is carried out, under the assumption of the latent failure times model. It is assumed that there are two competing causes of failures, although most of the results can be extended for more than two causes of failures. The lifetimes corresponding to the competing causes of failures are assumed to follow Weibull distributions with the same shape parameter but different scale parameters. The maximum likelihood estimation procedure of the model parameters is discussed, and confidence intervals are provided using the bootstrap approach. When the common shape parameter is known, the maximum likelihood estimators of the scale parameters can be obtained in explicit forms, and when it is unknown we provide a simple iterative procedure to compute the maximum likelihood estimator of the shape parameter. The Bayes estimates and the associated credible intervals of unknown parameters are also addressed under a very flexible set of priors on the shape and scale parameters. Extensive Monte Carlo simulations are performed to compare the performances of the different methods. A numerical example is provided for illustrative purposes. Finally the results have been extended when the two competing causes of failures are assumed to be independent Weibull distributions with different shape parameters.