A Fast and Accurate Algorithm to Test for Binary Phenotypes and Its Application to PheWAS

The availability of electronic health record (EHR)-based phenotypes allows for genome-wide association analyses in thousands of traits and has great potential to enable identification of genetic variants associated with clinical phenotypes. We can interpret the phenome-wide association study (PheWAS) result for a single genetic variant by observing its association across a landscape of phenotypes. Because a PheWAS can test thousands of binary phenotypes, and most of them have unbalanced or often extremely unbalanced case-control ratios (1: 10 or 1: 600, respectively), existing methods cannot provide an accurate and scalable way to test for associations. Here, we propose a computationally fast score-test-based method that estimates the distribution of the test statistic by using the saddlepoint approximation. Our method is much (similar to 100 times) faster than the state-of-the-art Firth's test. It can also adjust for covariates and control type I error rates even when the case-control ratio is extremely unbalanced. Through application to PheWAS data from the Michigan Genomics Initiative, we show that the proposed method can control type I error rates while replicating previously known association signals even for traits with a very small number of cases and a large number of controls.