Expectation-Maximization Algorithm for the Weibull Proportional Hazard Model under Current Status Data

Abstract

Due to the flexibility of the Weibull distribution and the proportional hazard (PH) model, Weibull PH is widely used in survival analysis under right censored data and interval censored data but it is seldom investigated under current status data, partially because there is less information in current status data than in right censored data and interval censored data. This paper considers the Weibull PH model under the current status data and introduces the Poisson latent variables to augment the data, then uses the expectation-maximization (EM) algorithm to obtain the maximum likelihood estimators of the model parameters. The EM algorithm is compared with the Newton–Raphson (NR) algorithm from several perspectives in the simulation studies, and the results show that the proposed method has several highlights, such as computational simplicity, improved convergence stability, and overall estimator results that are either comparable or slightly better in terms of bias. Furthermore, the performance of the Weibull PH model and the semi-parametric PH model is compared under two simulation scenarios, and two standard model selection criteria are used for model selection. The results indicate that the Weibull PH model has significant advantages when failure time follows a Weibull distribution. Lastly, the Weibull PH model along with EM algorithm is applied to lung tumor data and intraocular lens (IOL) calcification data with the aim of assessing the impact of covariates, including environmental factors and gender, on event timing and risk.