Estimating uncertainty in family-based GWAS

Standard genome-wide association studies (GWASs) are vulnerable to confounding factors, including stratification, assortative mating, and dynastic effects. Family studies such as sibling-based GWAS (sib-GWAS) mitigate such confounding and are becoming the tool of choice for teasing apart direct genetic effects---causal effects of one's genotype on one's own phenotype---from other factors. However, due in part to their smaller sample sizes, sib-GWAS allelic effect estimates are much noisier than standard (i.e., population-based) GWAS estimates. The quantification of this estimation uncertainty is essential for many uses of sib-GWAS, including polygenic scoring, causal inference (e.g., Mendelian randomization), disentangling direct from indirect familial effects, and measuring assortative mating. Here, we investigate sources of uncertainty in sib-GWAS allelic effect estimators. We study their impacts on the biases of three uncertainty measurement methods, including two that are commonly used and a new resampling-based approach we propose. We find that heterogeneity in allelic effects or heteroskedasticity across families (e.g., due to variation in genetic backgrounds or environments) can bias existing methods, and that this bias is more severe for small samples and rare variants. In contrast, the resampling-based approach we propose is approximately unbiased under all scenarios we considered. We validate our theoretical predictions, as well as the importance of effect heterogeneity and heteroskedasticity, using simulations and empirical analysis in the UK Biobank. In sum, this study helps understand the sources of uncertainty in family-based genotype-phenotype association studies and provides a robust method to estimate uncertainty.