Using cumulative sums of martingale residuals for model checking in nested case-control studies

Standard use of Cox regression requires collection of covariate information for all individuals in a cohort even when only a small fraction of them experiences the event of interest (fail). This may be very expensive for large cohorts. Further in biomarker studies, it will imply a waste of valuable biological material that one may want to save for future studies. A nested case-control study offers a useful alternative. For this design, covariate information is only needed for the failing individuals (cases) and a sample of controls selected from the cases' at-risk sets. Methods based on martingale residuals are useful for checking the fit of Cox's regression model for cohort data. But similar methods have so far not been developed for nested case-control data. In this article, it is described how one may define martingale residuals for nested case-control data, and it is shown how plots and tests based on cumulative sums of martingale residuals may be used to check model fit. The plots and tests may be obtained using available software.