Abstract
BackgroundCox 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.MethodsRobust 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.ResultsSimulations 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.ConclusionsRobust 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.
Highlights
Cox proportional hazards regression models are used to evaluate associations between exposures of interest and time-to-event outcomes in observational data
In the “Application” section we evaluate the association between the immune cell traits and stroke in the Multi-Ethnic Study of Atherosclerosis (MESA) case-cohort sample to illustrate practical differences between traditional and robust weighted Cox regressions
Sampling weights are implemented in one robust method that focuses on robustness to variation in proportional hazards (PH) over time [5, 7], but not in another that is more robust to influential outliers [3, 8, 9]
Summary
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. 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. Cox proportional hazards regression models [1] are widely mates can be weighted by the inverse sampling probability used for analysis of time-to-event data. Accounting for the sampling scheme is crucial in obtaining unbiased estimates that reflect population-level associations between exposure and outcome
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