Robust genomic control and robust delta centralization tests for case-control association studies

The population-based case-control design is a powerful approach for detecting susceptibility markers of a complex disease. However, this approach may lead to spurious association when there is population substructure: population stratification (PS) or cryptic relatedness (CR). Two simple approaches to correct for the population substructure are genomic control (GC) and delta centralization (DC). GC uses the variance inflation factor to correct for the variance distortion of a test statistic, and the DC centralizes the non-central chi-square distribution of the test statistic. Both GC and DC have been studied for case-control association studies mainly under a specific genetic model (e.g. recessive, additive or dominant), under which an optimal trend test is available. The genetic model is usually unknown for many complex diseases. In this situation, we study the performance of three robust tests based on the GC and DC corrections in the presence of the population substructure. Our results show that, when the genetic model is unknown, the DC- (or GC-) corrected maximum and Pearson's association test are robust and have good control of Type I error and high power relative to the optimal trend tests in the presence of PS (or CR).