Semiparametric Probit Regression Model with General Interval-Censored Failure Time Data

Abstract

Interval-censored data frequently arise in various biomedical areas involving periodical follow-ups where the failure or event time of interest cannot be observed exactly but is only known to fall into a time interval. This article considers a semiparametric probit regression model, a valuable alternative to other commonly used semiparametric models in survival analysis, to investigate potential risk factors for the interval-censored failure time of interest. We develop an expectation-maximization (EM) algorithm to conduct the pseudo maximum likelihood estimation (MLE) using the working independence strategy for general or mixed-case interval-censored data. The resulting estimators of regression parameters are shown to be consistent and asymptotically normal with the empirical process techniques. In addition, we propose a novel penalized EM algorithm for simultaneously achieving variable selection and parameter estimation in the case of high-dimensional covariates. The proposed variable selection method can be readily implemented with some existing software and considerably reduces the estimation error of the proposed pseudo-MLE approach. Simulation studies demonstrate the satisfactory performance of the proposed methods. An application to a set of interval-censored data on prostate cancer further confirms the utility of the methodology. Supplementary materials for this article are available online.

Keywords:

• EM algorithm
• Interval censoring
• Pseudo-likelihood
• Semiparametric probit model
• Variable selection

Data Availability Statement

The data supporting this study’s findings are not publicly available due to privacy restrictions but can be requested from https://cdas.cancer.gov/plco/.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Shuwei Li’s research was partially supported by the National Statistical Science Research Project (Grant No. 2022LY041) and Nature Science Foundation of Guangdong Province of China (Grant No. 2022A1515011901). Liuquan Sun’s research was partially supported by the National Natural Science Foundation of China (Grant No. 12171463). Xinyuan Song’ research was partially supported by the GRF grant (Grant No. 14302220) from the Research Grant Council of the Hong Kong Special Administrative Region.