Testing the proportional hazards assumption in case-cohort analysis

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Abstract
Case-cohort studies have become common in epidemiological studies of rare disease, with Cox regression models the principal method used in their analysis. However, no appropriate procedures to assess the assumption of proportional hazards of case-cohort Cox models have been proposed. We extended the correlation test based on Schoenfeld residuals, an approach used to evaluate the proportionality of hazards in standard Cox models. Specifically, pseudolikelihood functions were used to define “case-cohort Schoenfeld residuals”, and then the correlation of these residuals with each of three functions of event time (i.e., the event time itself, rank order, Kaplan-Meier estimates) was determined. The performances of the proposed tests were examined using simulation studies. We then applied these methods to data from a previously published case-cohort investigation of the insulin/IGF-axis and colorectal cancer. Simulation studies showed that each of the three correlation tests accurately detected non-proportionality. Application of the proposed tests to the example case-cohort investigation dataset showed that the Cox proportional hazards assumption was not satisfied for certain exposure variables in that study, an issue we addressed through use of available, alternative analytical approaches. The proposed correlation tests provide a simple and accurate approach for testing the proportional hazards assumption of Cox models in case-cohort analysis. Evaluation of the proportional hazards assumption is essential since its violation raises questions regarding the validity of Cox model results which, if unrecognized, could result in the publication of erroneous scientific findings.

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