Robust Cox Regression as an Alternative Method to Estimate Adjusted Relative Risk in Prospective Studies with Common Outcomes

Objective: To demonstrate the use of robust Cox regression in estimating adjusted relative risks (and confidence intervals) when all participants with an identical follow-up time and when a common outcome is investigated. Methods: In this paper, we propose an alternative statistical method, robust Cox regression, to estimate adjusted relative risks in prospective studies. We use simulated cohort data to examine the suitability of robust Cox regression. Results: Robust Cox regression provides estimates that are equivalent to those of modified Poisson regression: regression coefficients, relative risks, 95% confidence intervals, P values. It also yields reasonable probabilities (bounded by 0 and 1). Unlike modified Poisson regression, robust Cox regression allows for four automatic variable selection methods, it directly computes adjusted relative risks for continuous variables, and is able to incorporate time-dependent covariates. Conclusion: Given the popularity of Cox regression in the medical and epidemiological literature, we believe that robust Cox regression may gain wider acceptance and application in the future. We recommend robust Cox regression as an alternative analytical tool to modified Poisson regression. In this study we demonstrated its utility to estimate adjusted relative risks for common outcomes in prospective studies with two or three waves of data collection (spaced similarly).