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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 of 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 and cleft lip data, in which our method strengthened levels of previously reported associations and implied the possibility of multiple new alleles that jointly confer disease risk. Author summary: Joint analysis of association between the outcome and a group of SNPs within a genetic region is increasingly recognized to complement single-SNP analysis and shed light on the underlying molecular mechanisms. However, the correlation among GWAS association results calls for specifically tailored statistical methods. Here we propose DOT (Decorrelation by Orthogonal Transformation) method that can efficiently combine evidence of association over different SNPs and genes within a pathway without access to the original genotypic data. DOT is fast, does not rely on a permutation algorithm, and is often dramatically more powerful than other popular methods, such as VEGAS and the recently proposed ACAT. We believe that DOT will become a useful addition to the toolbox of methods based on the summary statistics for the GWAS community. [ABSTRACT FROM AUTHOR]