<p>Sample relatedness is a major confounder in genome-wide association studies (GWAS), potentially leading to inflated type I error rates if not appropriately controlled. A common strategy is to incorporate a random effect related to genetic relatedness matrix (GRM) into regression models. However, this approach is challenging for large-scale GWAS of complex traits, such as longitudinal traits. Here we propose a scalable and accurate analysis framework, SPA_GRM, which controls for sample relatedness via a precise approximation of the joint distribution of genotypes. SPA_GRM can utilize GRM-free models and thus is applicable to various trait types and statistical methods, including linear mixed models and generalized estimation equations for longitudinal traits. A hybrid strategy incorporating saddlepoint approximation greatly increases the accuracy to analyze low-frequency and rare genetic variants, especially in unbalanced phenotypic distributions. We also introduce SPA_GRM(CCT) to aggregate the results following different models via Cauchy combination test. Extensive simulations and real data analyses demonstrated that SPA_GRM maintains well-controlled type I error rates and SPA_GRM(CCT) can serve as a broadly effective method. Applying SPA_GRM to 79 longitudinal traits extracted from UK Biobank primary care data, we identified 7,463 genetic loci, making a pioneering attempt to conduct GWAS for these traits as longitudinal traits.</p>