Date of Award


Document Type

Open Access Thesis




Norman J. Arnold School of Public Health

First Advisor

Jiajia Zhang


The proportional hazards (PH) model, proposed by Cox (1972), is one of the most popular survival models for analyzing time-to-event data. To use the PH model properly, one must examine whether the data satisfy the PH assumption. An alternative model should be suggested if the PH assumption is invalid. The main purpose of this thesis is to examine the performance of five existing methods for assessing the PH assumption. Through extensive simulations, the powers of five different existing methods are compared; these methods include the likelihood ratio test, the Schoenfeld residuals test, the scaled Schoenfeld residuals test, Lin et al. (2006) score test, and the martingale-based residuals test. Results from SAS and R show that the power will vary depending on the form of hazard. For the hazard considered here with a clear jump point at which the PH assumption is violated, the power depends on the time to the violation of proportional hazards, the direction and magnitude of the hazard’s change, and the censoring rate of the data. Leukemia remission and Stanford heart transplant data were used to illustrate testing of the five methods.

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