Statistical Power to Detect Simultaneous Violation of Proportionality in Hazards and Additive Assumption in Cox Regression Model

Author

Lawrence Mensah Agbota, The University of Texas Rio Grande Valley

Date of Award

7-2025

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Applied Statistics and Data Science

First Advisor

Kristina Vatcheva

Second Advisor

Santanu Chakraborty

Third Advisor

Mrinal Kanti Roychowdhury

Abstract

The Cox proportional hazards regression model is a widely employed semi-parametric tool in epidemiological and medical research for analyzing time-to-event data and assessing the relationship between patient survival times and one or more predictors. This method involves regression analyses necessitating a meticulous approach to careful examination of the covariates and the relationship among covariates included in the model through a series of critical decisions and steps. Violation of the additivity of the effects and the proportionality in hazards (PH) assumption can lead to biased results and misleading scientific findings. We conducted a Monte Carlo simulation study to assess the performance and adequacy of statistical tests for identifying significant interaction effects and non-PH in Cox regression. We generated right-censored survival datasets varying the magnitude of regression coefficients and event r ates. The analysis of the simulated data demonstrated that in the incorrectly specified Cox regression model due to non-PH in a covariate, the identification of a significant statistical interaction effect with the same covariate was underpowered. Grambsch and Therneau’s PH test performed better before the inclusion of the interaction term in the model, while the cumulative martingale residuals-based test had greater power to detect violations in the PH assumption regardless of the inclusion of the interaction term in the model. We recommend that during the Cox regression modeling process, statistical testing for interaction effect needs to be performed before and after testing and correcting for non-PH. Likewise, testing for PH, especially using the Grambsch and Therneau test, should be conducted before and after the inclusion of the interaction term in the model. Finally, we recommend the cumulative martingale residuals-based test PH test, which showed greater power to detect non-PH.

Comments

Copyright 2025 Lawrence Mensah Agbota. All Rights Reserved. https://proquest.com/docview/3253954791

Recommended Citation

Agbota, L. M. (2025). Statistical power to detect simultaneous violation of proportionality in hazards and additive assumption in cox regression model [Master's thesis, The University of Texas Rio Grande Valley]. ScholarWorks @ UTRGV. https://scholarworks.utrgv.edu/etd/1769