Competing-Risks Time-to-Event Modeling Using the Generalized Gamma Distribution Under Progressive Type-II Censoring

Modeling time-to-event data without accounting for risk factors may lead to biased conclusions. Therefore, researchers sometimes assume the existence of competing risks to accurately model life data. Furthermore, since medical research can be time-consuming and costly, experimenters may consider optimizing their use of resources by employing a censoring plan, such as a progressive Type-II censoring scheme. This study investigates statistical inference for a competing-risks model based on Stacy’s generalized gamma distribution under the latter censoring scheme. A couple of frequentist estimation methods—namely, maximum likelihood estimation and maximum product-of-spacings estimation—are used to obtain point estimates of the model parameters. Using the point estimators, asymptotic confidence intervals are constructed alongside two bootstrapping confidence intervals—namely, the percentile and Studentized bootstrap confidence intervals. Monte Carlo simulations are used to numerically examine the performance of both point and interval estimation using appropriate criteria. Overall, the simulations indicate that maximum product-of-spacings estimation outperforms maximum likelihood estimation, particularly in estimating the shape parameter under heavier censoring. The practical illustration of Stacy’s competing-risks model is achieved by analyzing two real medical datasets concerning pneumonia in intensive care and leukemia stem cell transplantation. Overall, the information criteria confirm that Stacy’s competing-risks model provides a robust fit relative to its submodels, offering a highly flexible framework for complex survival data.