Kernel machine testing for risk prediction with stratified case cohort studies

Large assembled cohorts with banked biospecimens offer valuable opportunities to identify novel markers for risk prediction. When the outcome of interest is rare, an effective strategy to conserve limited biological resources while maintaining reasonable statistical power is the case cohort (CCH) sampling design, in which expensive markers are measured on a subset of cases and controls. However, the CCH design introduces significant analytical complexity due to outcome-dependent, finite-population sampling. Current methods for analyzing CCH studies focus primarily on the estimation of simple survival models with linear effects; testing and estimation procedures that can efficiently capture complex non-linear marker effects for CCH data remain elusive. In this article, we propose inverse probability weighted (IPW) variance component type tests for identifying important marker sets through a Cox proportional hazards kernel machine (CoxKM) regression framework previously considered for full cohort studies (Cai et al., 2011). The optimal choice of kernel, while vitally important to attain high power, is typically unknown for a given dataset. Thus, we also develop robust testing procedures that adaptively combine information from multiple kernels. The proposed IPW test statistics have complex null distributions that cannot easily be approximated explicitly. Furthermore, due to the correlation induced by CCH sampling, standard resampling methods such as the bootstrap fail to approximate the distribution correctly. We, therefore, propose a novel perturbation resampling scheme that can effectively recover the induced correlation structure. Results from extensive simulation studies suggest that the proposed IPW CoxKM testing procedures work well in finite samples. The proposed methods are further illustrated by application to a Danish CCH study of Apolipoprotein C-III markers on the risk of coronary heart disease.