Abstract
We investigate saddlepoint approximations of tail probabilities of the score test statistic in logistic regression for genome-wide association studies. The inaccuracy in the normal approximation of the score test statistic increases with increasing imbalance in the response and with decreasing minor allele counts. Applying saddlepoint approximation methods greatly improve the accuracy, even far out in the tails of the distribution. By using exact results for a simple logistic regression model, as well as simulations for models with nuisance parameters, we compare double saddlepoint methods for computing two-sided -values and mid--values. These methods are also compared to a recent single saddlepoint procedure. We investigate the methods further on data from UK Biobank with skin and soft tissue infections as phenotype, using both common and rare variants.