In this paper, our goals are (1) to characterize the effect of cryptic relatedness on testing in case-control samples, particularly from an isolated population, (2) to estimate cryptic relatedness with such samples, and (3) to develop an approach for testing for association with a correction for cryptic relatedness. To test for association between markers and disease and to simultaneously account for unknown relatedness among individuals, we propose to modify the corrected χ2 test by using estimated, rather than assigned, coefficients of relatedness. We focus on the corrected χ2 test because of its desirable statistical behavior, ease of computation, and applicability to a variety of marker and data types. We perform simulations to evaluate the statistical properties of the corrected χ2 test for use in the context of case-control data, and we illustrate the advantage of the proposed method by application to two samples from genetic isolates.
