Technical Note: Efficient and accurate estimation of genotype odds ratios in biobank-based unbalanced case-control studies

Abstract

In genome-wide association studies (GWASs), genotype log-odds ratios (LORs) quantify the effects of the variants on the binary phenotypes, and calculating the genotype LORs for all of the markers is required for several downstream analyses. Calculating genotype LORs at a genome-wide scale is computationally challenging, especially when analyzing large-scale biobank data, which involves performing thousands of GWASs phenome-wide. Since most of the binary phenotypes in biobank-based studies have unbalanced (case : control = 1 : 10) or often extremely unbalanced (case : control = 1 : 100) case-control ratios, the existing methods cannot provide a scalable and accurate way to estimate the genotype LORs. The traditional logistic regression provides biased LOR estimates in such situations. Although the Firth bias correction method can provide unbiased LOR estimates, it is not scalable for genome-wide or phenome-wide scale association analyses typically used in biobank-based studies, especially when the number of non-genetic covariates is large. On the other hand, the saddlepoint approximation-based test (fastSPA), which can provide accurate p values and is scalable to analyse large-scale biobank data, does not provide the genotype LOR estimates as it is a score-based test. Here, we propose a scalable method based on score statistics, to accurately estimate the genotype LORs, adjusting for non-genetic covariates. Comparing to the Firth method, our proposed method reduces the computational complexity from O(nK2 + K3) to O(n), where n is the sample-size, and K is the number of non-genetic covariates. Our method is ~ 10x faster than the Firth method when 15 covariates are being adjusted for. Through extensive numerical simulations, we show that the proposed method is both scalable and accurate in estimating the genotype ORs in genome-wide or phenome-wide scale.