Analysis of Left Truncated and Right Censored Competing Risks Data

TL;DR

This paper develops statistical methods for analyzing complex failure time data with left truncation and right censoring, focusing on Weibull models with competing risks, and compares frequentist and Bayesian approaches through simulations and a real example.

Contribution

It introduces explicit maximum likelihood estimators and Bayesian estimates for Weibull competing risks models under complex censoring and truncation.

Findings

MLEs have explicit forms when shape parameter is known

Iterative procedure for unknown shape parameter

Bayesian estimates with flexible priors outperform frequentist methods in simulations

Abstract

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.