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

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.

First-Passage Time Analysis Based on GPS Data Offers a New Approach to Estimate Restricted Zones for the Management of Infectious Diseases in Wildlife: A Case Study Using the Example of African Swine Fever

“…In the wild boar example, the results of the different CPH models were qualitatively similar, which allowed us to use the fixed-effects CPH models for approximate predictions of the individual's risk of leaving an area and to demonstrate the strength of our results. We applied a weighted model to deal with proportional hazard violation and to account for unbalanced sample sizes between individuals [44,45], but this model ran very slowly (∼24 hr vs. a few minutes for the other two CPH models). Therefore, it may be even less suitable if more data or covariates are included in the model.…”

Can Cardiopulmonary Rehabilitation Facilitate Weaning of Extracorporeal Membrane Oxygenation (CaRe-ECMO)? Study Protocol for a Prospective Multidisciplinary Randomized Controlled Trial

“…Categorical variables will be compared with the chi-square or Fisher's exact tests and continuous variables will be compared with the Student's ttest or the Wilcoxon signed-rank test, as appropriate. The time effect of day the time-to-event outcomes identified (e.g., rate of ready for ECMO weaning, rate of ECMO weaning, rate of mechanical ventilation weaning, all-cause mortality, and rate of major post-ECMO complications) between the groups will be estimated with the Cox proportional hazards regression analysis and graphically illustrated using the Kaplan-Meier methods until CaRe-ECMO days 7, 14, 30, and 90, respectively (40). Variables, including total length of ready for ECMO weaning, total length of ECMO weaning, total length of mechanical ventilation, ECMO unit LOS, and total hospital LOS, will be treated with timeto-event data and will be analyzed with mixed-effects ordered logistic regression (41).…”