Incorporating sampling weights into robust estimation of Cox proportional hazards regression model, with illustration in the Multi-Ethnic Study of Atherosclerosis

Background Cox proportional hazards regression models are used to evaluate associations between exposures of interest and time-to-event outcomes in observational data. When exposures are measured on only a sample of participants, as they are in a case-cohort design, the sampling weights must be incorporated into the regression model to obtain unbiased estimating equations. Methods Robust Cox methods have been developed to better estimate associations when there are influential outliers in the exposure of interest, but these robust methods do not incorporate sampling weights. In this paper, we extend these robust methods, which already incorporate influence weights, so that they also accommodate sampling weights. Results Simulations illustrate that in the presence of influential outliers, the association estimate from the weighted robust method is closer to the true value than the estimate from traditional weighted Cox regression. As expected, in the absence of outliers, the use of robust methods yields a small loss of efficiency. Using data from a case-cohort study that is nested within the Multi-Ethnic Study of Atherosclerosis (MESA) longitudinal cohort study, we illustrate differences between traditional and robust weighted Cox association estimates for the relationships between immune cell traits and risk of stroke. Conclusions Robust weighted Cox regression methods are a new tool to analyze time-to-event data with sampling, e.g. case-cohort data, when exposures of interest contain outliers.