Power and Effective Study Size in Heritability Studies.

Correlation between study units in quantitative genetics studies often makes it difficult to compare important inferential aspects of studies. Describing the relatedness between study units is critical to capture features of pedigree studies involving heritability, including power and precision of heritability estimates. Blangero et al (2012) showed that in pedigree studies the power to detect heritability is a function of the true heritability and the eigenvalues of the kinship matrix. We extend this to a more general setting which allows statements about expected precision of heritability estimates. Using two different Taylor series approximations, we summarize the relatedness in a study design by one or two parameters. These relatedness summary parameters (RSPs) are functions of the eigenvalues or log-eigenvalues of the kinship matrix. Using the RSPs based on the log-eigenvalues, we accurately approximate the expectation of the likelihood ratio test and expected confidence interval widths. We define an effective sample size of a target study as one which has the equivalent power and precision to a reference design. Using unrelated sibpairs as the reference design provides very accurate assessments of power. RSPs and effective sample sizes provide new tools for comparing studies and communicating information about relatedness in heritability studies.