Background: Rare variants association analyses with binary outcomes that use likelihood-based tests such as the Score and Wald tests, suffer from inflated type 1 error. The problem is exacerbated when pooling together individual-level data from diverse parent studies, with potentially different proportions of affected individuals and different frequencies of genetic variants. For example, the analysis of short sleep (< 6 hours/night) considers ~22,000 individuals from TOPMed of European, African, Hispanic, and Asian descent, and the proportion of short sleepers is highest among African Americans. Here, the Score test detected many spurious associations
 
Methods: We propose a class of semi-parametric tests for association of rare variants with binary traits. Given a vector of probabilities of affection status among a set of (possibly correlated) carriers of a rare variants, we test whether the number of affected individuals among these carriers is consistent with their probability vector. Our carriers-only tests use the Poisson-Binomial (BinomiRare test) or Conway-Maxwell-Poisson (CMP test) distributions.
 
Results: We performed genetic analysis of short sleep in TOPMed. The Score test did not control the type 1 error. The SAIGE test improved upon the Score test, but had also high inflation when there were less than 30 carriers of the rare variant, and was slower than the carriers-only approach. When there are at least 30 carriers, the SAIGE and carriers-only tests had similar performance (correlation between p-value = 0.96), with SAIGE being often slightly more powerful. Still, in the single region that passed the genome-wide significance threshold, the most significant associations were detected by BinomiRare. A variant chr2: 33765596:A:G (chr2 p22.3; 65 carriers; CADD score=15.3) had BinomiRare p-value 7.4x10-9, SAIGE p-value=2.6x10-8.

Conclusions: carriers-only tests offer a computationally efficient (in terms of both time and memory) alternative to other tests of rare variant associations. They protect the type 1 error for arbitrary number of carriers of the rare variant.