Statistical inference for competing risks model under progressive interval censored Weibull data

This is the authors' abstract. We don't add key points for this paper.

In this paper, we discussed the estimation problem for the competing risks model when the data are progressive interval censored and follow Weibull distribution with an unknown common shape parameter. The parameters were estimated using both maximum likelihood and Bayesian methods and the Fisher information matrix was derived. The importance sampling method was employed to obtain the Bayes estimates. In the presence of competing risks, it is possible that the causes of failure for some units are not observed and the problem of missing causes of failure arises. In this situation, discussing the consequences of departures from the ignorability assumption on the Bayes estimates of the model parameters is crucial. Therefore, we studied the impact of missing causes of failure on inference in the proposed competing risks model using the Bayesian “index of local sensitivity to non-ignorability”. A simulation study was conducted to compare Bayes estimates under both informative and less informative priors with the corresponding maximum likelihood estimates, and also to assess the sensitivity of the parameter estimation to the non-ignorable missing data in a Bayesian setup. An illustrative example based on the real data is given.