Comparison of some methods to estimate the Cox proportional hazards model for interval-censored data

Abstract

Interval censored data is common in several areas of knowledge, such as: epidemiology, finance, demo- graphy, medicine, among others. They occur when the event of interest, the failure time, is not observed exactly, but is within some interval of the observation time. Often in this situation an imputation is made of the data that is not exactly known. Some methods of multiple imputation proposed in the literature are the PMDA (Poor Man’s Data Augmentation) algorithm and the ANDA (Asymptotic Normal Data Augmen- tation) algorithm, which allow estimating the parameters of the Cox proportional hazards model using classical estimation methods. There are also alternative methods to make these estimations such as the ICM (Iterative Convex Minorant) algorithm and a Bayesian approach, which do not impute the data with interval censoring.

In this work, a comparison was made via simulation of the performance of the estimators of the Cox model parameters produced by each of the aforementioned methods. The results showed that in general terms the ICM methods and the Bayesian approach present higher coverage probability values and lower mean square errors, in addition when increasing the sample size these values significantly improve compared to the PMDA and ANDA multiple imputation methods. In the latter, there were no significant differences between the results. Finally, an application was made with real data associated with a study of mastitis in milk cattle.