Fast score test with global null estimation regardless of missing genotypes.

In genome-wide association studies (GWASs) for binary traits (or case-control samples) in the presence of covariates to be adjusted for, researchers often use a logistic regression model to test variants for disease association. Popular tests include Wald, likelihood ratio, and score tests. For likelihood ratio test and Wald test, maximum likelihood estimation (MLE), which requires iterative procedure, must be computed for each single nucleotide polymorphism (SNP). In contrast, the score test only requires MLE under the null model, being lower in computational cost than other tests. Usually, genotype data include missing genotypes because of assay failures. It loses computational efficiency in the conventional score test (CST), which requires null estimation by excluding individuals with missing genotype for each SNP. In this study, we propose two new score tests, called PM1 and PM2, that use a single global null estimator for all SNPs regardless of missing genotypes, thereby enabling faster computation than CST. We prove that PM2 and CST have an equivalent asymptotic power and that the power of PM1 is asymptotically lower than that of PM2. We evaluate the performance of the proposed methods in terms of type I error rates and power by simulation studies and application to real GWAS data provided by the Alzheimer's Disease Neuroimaging Initiative (ADNI), confirming our theoretical results. ADNI-GWAS application demonstrated that the proposed score tests improve computational speed about 6-18 times faster than the existing tests, CST, Wald tests and likelihood ratio tests. Our score tests are general and applicable to other regression models.