Genetic association studies have successfully identified numerous genetic variants associated with complex diseases and gene expression levels, providing unprecedented opportunities to discover new biology through downstream analyses. Examples of such analyses include multivariate methods, which can enhance the power to detect signals by borrowing information across similar or correlated conditions; fine-mapping analysis, which aims to identify potentially causal loci among many highly correlated genetic variants; and Mendelian randomization, which estimates the causal effect of one trait on another using genetic variants as instruments. In this dissertation, we focus on improving methods for downstream analysis, with the goal of enhancing the power of statistical inference. In Chapter 2, we improve the fitting algorithm of a widely used multivariate method, the multivariate adaptive shrinkage (MASH) by Urbut et al. [2019]. In Chapter 3, we develop a new method for fine-mapping time-to-event outcomes, building on the existing "Sum of Single Effects" (SuSiE) fine-mapping approach by Wang et al. [2020]. In Chapter 4, we address the challenges associated with the small sample sizes of within-family genotype data. Specifically, we develop methods to improve the efficiency of estimates derived from within-family data, which also lead to variance reduction in Mendelian randomization.