Incorporating sampling weights into robust estimation of Cox proportional hazards regression model, with illustration in
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(2020) 20:62
RESEARCH ARTICLE
Open Access
Incorporating sampling weights into robust estimation of Cox proportional hazards regression model, with illustration in the Multi-Ethnic Study of Atherosclerosis Colleen M. Sitlani1* , Thomas Lumley2 , Barbara McKnight3 , Kenneth M. Rice3 , Nels C. Olson4 , Margaret F. Doyle4 , Sally A. Huber4 , Russell P. Tracy4,5 , Bruce M. Psaty1,6,7,8 and Joseph A. C. Delaney6,9
Abstract 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. Keywords: Cox regression, Sampling weights, Case-cohort design, Robust regression, Immune cell traits
Background Cox proportional hazards regression models [1] are widely used for analysis of time-to-event data. Modifications of traditional Cox models have been developed to accommodate several important scenarios, including data sampled from a bigger population of interest and data containing *Correspondence: [email protected] Department of Medicine, Cardiovascular Health Research Unit, University of Washington, 1730 Minor Ave, Suite 1360, 98101 Seattle, WA, USA Full list of author information is available at the end of the article 1
influential outliers. In the context of data sampling, estimates can be weighted by the inverse sampling probability [2]. To reduce the impact of violation of model assumptions, several robust methods have been proposed [3–6]. One robust method focuses on robustness to variation in proportional hazards over time [5, 7], and incorporates sampling weights. However, a related robust method that focuses on robustness to influential outliers [3, 8, 9] does not incorporate samplin
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