Most regression-based tests of the association between a low-count variant and a binary outcome do not protect type 1 error, especially when tests are rejected based on a very low significance threshold. Noted exception is the Firth test. However, it was recently shown that in meta-analyzing multiple studies all asymptotic, regression-based tests, including the Firth, may not control type 1 error in some settings, and the Firth test may suffer a substantial loss of power. The problem is exacerbated when the case-control proportions differ between studies. I propose the BinomiRare exact test that circumvents the calibration problems of regression-based estimators. It quantifies the strength of association between the variant and the disease outcome based on the departure of the number of diseased individuals carrying the variant from the expected distribution of disease probability, under the null hypothesis of no association between the disease outcome and the rare variant. I provide a meta-analytic strategy to combine tests across multiple cohorts, which requires that each cohort provides the disease probabilities of all carriers of the variant in question, and the number of diseased individuals among the carriers. I show that BinomiRare controls type 1 error in meta-analysis even when the case-control proportions differ between the studies, and does not lose power compared to pooled analysis. I demonstrate the test in studying the association of rare variants with asthma in the Hispanic Community Health Study/Study of Latinos.
Keywords: Poisson-binomial distribution; exact test; mid P-value.
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