Estimating Confidence Intervals for Hazard Ratio with Composite Covariates in the Cox Models

Abstract

Hazard ratio (HR) estimation is fundamental in survival analysis, particularly in Cox proportional hazards models, where covariates influence time-to-event outcomes. When covariates are combined into composite variables, constructing confidence intervals (CIs) for the resulting HRs becomes challenging due to potential multicollinearity, interaction effects, and violations of the proportional hazards assumption. This paper presents a systematic approach for constructing confidence intervals for HRs associated with composite covariates, comparing standard methods such as the Wald, likelihood ratio, and bootstrap-based intervals. Through simulation studies for different scenarios of Cox regression models, we evaluate the performance of these methods in terms of bias, coverage probability, and robustness under various data conditions. The findings of this study provide practical recommendations for researchers dealing with composite covariates in survival analysis, ensuring reliable inference in epidemiological and clinical studies.