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Multi-marker association tests can be more powerful than single-locus analyses because they aggregate the variant information within a gene/region. However, combining the association signals of multiple markers within a gene/region may cause noise due to the inclusion of neutral variants, which usually compromises the power of a test. To reduce noise, the “adaptive combination of  P -values” (ADA) method removes variants with larger  P -values. However, when both rare and common variants are considered, it is not optimal to truncate variants according to their  P -values. An alternative summary measure, the Bayes factor (BF), is defined as the ratio of the probability of the data under the alternative hypothesis to that under the null hypothesis. The BF quantifies the “relative” evidence supporting the alternative hypothesis. Here, we propose an “adaptive combination of Bayes factors” (ADABF) method that can be directly applied to variants with a wide spectrum of minor allele frequencies. The simulations show that ADABF is more powerful than single-nucleotide polymorphism (SNP)-set kernel association tests and burden tests. We also analyzed 1,109 case-parent trios from the Schizophrenia Trio Genomic Research in Taiwan. Three genes on chromosome 19p13.2 were found to be associated with schizophrenia at the suggestive significance level of 5 × 10 −5 .

Adaptive combination of Bayes factors as a powerful method for the joint analysis of rare and common variants