We developed a likelihood-based approach for analyzing summary-level statistics and external linkage disequilibrium information to estimate effect-size distributions of common variants, characterized by the proportion of underlying susceptibility SNPs and a flexible normal-mixture model for their effects. Analysis of results available across 32 genome-wide association studies showed that, while all traits are highly polygenic, there is wide diversity in the degree and nature of polygenicity. Psychiatric diseases and traits related to mental health and ability appear to be most polygenic, involving a continuum of small effects. Most other traits, including major chronic diseases, involve clusters of SNPs that have distinct magnitudes of effects. We predict that the sample sizes needed to identify SNPs that explain most heritability found in genome-wide association studies will range from a few hundred thousand to multiple millions, depending on the underlying effect-size distributions of the traits. Accordingly, we project the risk-prediction ability of polygenic risk scores across a wide variety of diseases.

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Mendelian randomization (MR) has emerged as a major tool for the investigation of causal relationship among traits, utilizing results from large-scale genome-wide association studies. Bias due to horizontal pleiotropy, however, remains a major concern. We propose a novel approach for robust and efficient MR analysis using large number of genetic instruments, based on a novel spike-detection algorithm under a normal-mixture model for underlying effect-size distributions. Simulations show that the new method, MRMix, provides nearly unbiased or/and less biased estimates of causal effects compared to alternative methods and can achieve higher efficiency than comparably robust estimators. Application of MRMix to publicly available datasets leads to notable observations, including identification of causal effects of BMI and age-at-menarche on the risk of breast cancer; no causal effect of HDL and triglycerides on the risk of coronary artery disease; a strong detrimental effect of BMI on the risk of major depressive disorder.