We approach the problem of combining top-ranking association statistics or P-values from a new perspective which leads to a remarkably simple and powerful method. Statistical methods, such as the rank truncated product (RTP), have been developed for combining top-ranking associations, and this general strategy proved to be useful in applications for detecting combined effects of multiple disease components. To increase power, these methods aggregate signals across top ranking single nucleotide polymorphisms (SNPs), while adjusting for their total number assessed in a study. Analytic expressions for combined top statistics or P-values tend to be unwieldy, which complicates interpretation and practical implementation and hinders further developments. Here, we propose the augmented rank truncation (ART) method that retains main characteristics of the RTP but is substantially simpler to implement. ART leads to an efficient form of the adaptive algorithm, an approach where the number of top ranking SNPs is varied to optimize power. We illustrate our methods by strengthening previously reported associations of μ-opioid receptor variants with sensitivity to pain.

Historically, the majority of statistical association methods have been designed assuming availability of SNP-level information. However, modern genetic and sequencing data present new challenges to access and sharing of genotype-phenotype datasets, including cost management, difficulties in consolidation of records across research groups, etc. These issues make methods based on SNP-level summary statistics particularly appealing. The most common form of combining statistics is a sum of SNP-level squared scores, possibly weighted, as in burden tests for rare variants. The overall significance of the resulting statistic is evaluated using its distribution under the null hypothesis.Here, we demonstrate that this basic approach can be substantially improved by decorrelating scores prior to their addition, resulting in remarkable power gains in situations that are most commonly encountered in practice; namely, under heterogeneity of effect sizes and diversity between pairwise LD. In these situations, the power of the traditional test, based on the added squared scores, quickly reaches a ceiling, as the number of variants increases. Thus, the traditional approach does not benefit from information potentially contained in any additional SNPs, while our decorrelation by orthogonal transformation (DOT) method yields steady gain in power. We present theoretical and computational analyses of both approaches, and reveal causes behind sometimes dramatic difference in their respective powers. We showcase DOT by analyzing breast cancer data, in which our method strengthened levels of previously reported associations and implied the possibility of multiple new alleles that jointly confer breast cancer risk.

Meta-analysis of genome-wide association studies (GWAS) has become a useful tool to identify genetic variants that are associated with complex human diseases. To control spurious associations between genetic variants and disease that are caused by population stratification, double genomic control (GC) correction for population stratification in meta-analysis for GWAS has been implemented in the software METAL and GWAMA and is widely used by investigators. In this research, we conducted extensive simulation studies to evaluate the double GC correction method in meta-analysis and compared the performance of the double GC correction with that of a principal components analysis (PCA) correction method in meta-analysis. Results show that when the data consist of population stratification, using double GC correction method can have inflated type I error rates at a marker with significant allele frequency differentiation in the subpopulations (such as caused by recent strong selection). On the other hand, the PCA correction method can control type I error rates well and has much higher power in meta-analysis compared to the double GC correction method, even though in the situation that the casual marker does not have significant allele frequency difference between the subpopulations. We applied the double GC correction and PCA correction to meta-analysis of GWAS for two real datasets from the Atherosclerosis Risk in Communities (ARIC) project and the Multi-Ethnic Study of Atherosclerosis (MESA) project. The results also suggest that PCA correction is more effective than the double GC correction in meta-analysis.