In this article, interval-censored competing risks data are analyzed when some of the causes of failure are missing. The vertical modeling approach has been proposed here. This approach utilizes the data to extract information to the maximum possible extent especially when some causes of failure are missing. The maximum likelihood estimates of the model parameters are obtained. The asymptotic confidence intervals for the model parameters are constructed using approaches based on observed Fisher information matrix, and parametric bootstrap. A simulation study is considered in detail to assess the performance of the point and interval estimators. It is observed that the proposed analysis performs better than the complete case analysis. This establishes the fact that the our methodology is an extremely useful technique for interval-censored competing risks data when some of the causes of failure are missing. Such analysis seems to be quite useful for smaller sample sizes where complete case analysis may have a significant impact on the inferential procedures. Through Monte Carlo simulations, the effect of a possible model misspecification is also assessed on the basis of the cumulative incidence function. For illustration purposes, three datasets are analyzed and in all cases the conclusion appears to be quite realistic.
Keywords: Gompertz model; Interval censoring; competing risks; confidence intervals; cumulative incidence function; maximum likelihood estimates.
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