A Kinship-Based Modification of the Armitage Trend Test to Address Hidden Population Structure and Small Differential Genotyping Errors

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Abstract
We propose a modification of the well-known Armitage trend test to address the problems associated with hidden population structure and hidden relatedness in genome-wide case-control association studies. The new test adopts beneficial traits from three existing testing strategies: the principal components, mixed model, and genomic control while avoiding some of their disadvantageous characteristics, such as the tendency of the principal components method to over-correct in certain situations or the failure of the genomic control approach to reorder the adjusted tests based on their degree of alignment with the underlying hidden structure. The new procedure is based on Gauss-Markov estimators derived from a straightforward linear model with an imposed variance structure proportional to an empirical relatedness matrix. Lastly, conceptual and analytical similarities to and distinctions from other approaches are emphasized throughout. Our simulations show that the power performance of the proposed test is quite promising compared to the considered competing strategies. The power gains are especially large when small differential differences between cases and controls are present; a likely scenario when public controls are used in multiple studies. The proposed modified approach attains high power more consistently than that of the existing commonly implemented tests. Its performance improvement is most apparent when small but detectable systematic differences between cases and controls exist.