A Semiparametric Cox–Aalen Transformation Model with Censored Data

Author:

Ning Xi1ORCID,Pan Yinghao1ORCID,Sun Yanqing1ORCID,Gilbert Peter B.23

Affiliation:

1. Department of Mathematics and Statistics, University of North Carolina at Charlotte , Charlotte, North Carolina , USA

2. Department of Biostatistics, University of Washington , Seattle, Washington , USA

3. Vaccine and Infectious Disease and Public Health Sciences Divisions, Fred Hutchinson Cancer Center , Seattle, Washington , USA

Abstract

Abstract We propose a broad class of so-called Cox–Aalen transformation models that incorporate both multiplicative and additive covariate effects on the baseline hazard function within a transformation. The proposed models provide a highly flexible and versatile class of semiparametric models that include the transformation models and the Cox–Aalen model as special cases. Specifically, it extends the transformation models by allowing potentially time-dependent covariates to work additively on the baseline hazard and extends the Cox–Aalen model through a predetermined transformation function. We propose an estimating equation approach and devise an expectation-solving (ES) algorithm that involves fast and robust calculations. The resulting estimator is shown to be consistent and asymptotically normal via modern empirical process techniques. The ES algorithm yields a computationally simple method for estimating the variance of both parametric and nonparametric estimators. Finally, we demonstrate the performance of our procedures through extensive simulation studies and applications in two randomized, placebo-controlled human immunodeficiency virus (HIV) prevention efficacy trials. The data example shows the utility of the proposed Cox–Aalen transformation models in enhancing statistical power for discovering covariate effects.

Funder

National Institute of Allergy and Infectious Diseases

National Institutes of Health

National Science Foundation

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,General Agricultural and Biological Sciences,General Immunology and Microbiology,General Biochemistry, Genetics and Molecular Biology,General Medicine,Statistics and Probability

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