Seminar by Prof. Yangjianchen Xu, Department of Statistics and Actuarial Science, University of Waterloo

The Cox regression model is widely used to study the effects of potentially time-dependent covariates on a possibly censored event time. However, statistical inference can be invalid and misleading if the model is mis-specified. It is highly challenging to check the adequacy of the Cox regression model with interval-censored data because the event times are known only to lie in random time intervals, and none of the event times are directly observed. In this talk, I will describe a novel solution to this problem. Specifically, we construct certain stochastic processes that are informative about various components of the model (i.e., proportional hazards assumption, exponential link function, and functional forms of covariates). We show that these stochastic processes can be viewed as the score statistics for testing zero regression parameters under some extended models. We establish their weak convergence to Gaussian processes through modern empirical process theory. We then approximate the limiting distributions by Monte Carlo simulation and develop graphical and numerical procedures to check model assumptions and improve goodness-of-fit. We evaluate the performance of the proposed methods through extensive simulation studies and provide an application to the Atherosclerosis Risk in Communities Study.

Prof. Yangjianchen Xu is an Assistant Professor in the Department of Statistics and Actuarial Science at the University of Waterloo. He obtained his Ph.D. in Biostatistics from the University of North Carolina at Chapel Hill. His research focuses on survival analysis, semiparametric models, robust inference, data privacy, and infectious diseases. Prof. Xu’s work has been published in top-tier journals such as Biometrika, Biometrics, New England Journal of Medicine, JAMA, and The Lancet Infectious Diseases. For more details, please visit his homepage at https://yangjc-xu.github.io/.