Abstract
Partly interval-censored data, comprising exact and interval-censored observations, are prevalent in biomedical, clinical, and epidemiological studies. This paper studies a flexible class of the semiparametric Cox-Aalen transformation models for regression analysis of such data. These models offer a versatile framework by accommodating both multiplicative and additive covariate effects and both constant and time-varying effects within a transformation, while also allowing for potentially time-dependent covariates. Moreover, this class of models includes many popular models such as the semiparametric transformation model, the Cox-Aalen model, the stratified Cox model, and the stratified proportional odds model as special cases. To facilitate efficient computation, we formulate a set of estimating equations and propose an Expectation-Solving (ES) algorithm that guarantees stability and rapid convergence. Under mild regularity assumptions, the resulting estimator is shown to be consistent and asymptotically normal. The validity of the weighted bootstrap is also established. A supremum test is proposed to test the time-varying covariate effects. Finally, the proposed method is evaluated through comprehensive simulations and applied to analyze data from a randomized HIV/AIDS trial.
Funding Statement
This research was partially supported by the National Institutes of Health, National Institute of Allergy and Infectious Diseases [grant numbers UM1 AI68635 and R37 AI054165]. The research of Xi Ning was supported, in part, by the 2022 Graduate School Summer Fellowship Program from the University of North Carolina at Charlotte (UNC Charlotte). The research of Yanqing Sun was partially supported by the National Science Foundation [grant number DMS-1915829] and the Reassignment of Duties fund provided by UNC Charlotte. Yinghao Pan’s work was partially supported by the National Science Foundation [grant number DMS-2316868] and funds provided by UNC Charlotte.
Acknowledgments
The authors thank the editor for handling the paper and the associate editor and two referees for their comments that greatly improved this article.
Citation
Xi Ning. Yanqing Sun. Yinghao Pan. Peter B. Gilbert. "Regression analysis of semiparametric Cox-Aalen transformation models with partly interval-censored data." Electron. J. Statist. 19 (1) 240 - 290, 2025. https://doi.org/10.1214/24-EJS2341
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