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Sparse data bias, where there is a lack of sufficient cases, is a common problem in data analysis, particularly when studying rare binary outcomes. Although a two‐step meta‐analysis approach may be used to lessen the bias by combining the summary statistics to increase the number of cases from multiple studies, this method does not completely eliminate bias in effect estimation. In this paper, we propose a one‐shot distributed algorithm for estimating relative risk using a modified Poisson regression for binary data, named ODAP‐B. We evaluate the performance of our method through both simulation studies and real‐world case analyses of postacute sequelae of SARS‐CoV‐2 infection in children using data from 184 501 children across eight national academic medical centers. Compared with the meta‐analysis method, our method provides closer estimates of the relative risk for all outcomes considered including syndromic and systemic outcomes. Our method is communication‐efficient and privacy‐preserving, requiring only aggregated data to obtain relatively unbiased effect estimates compared with two‐step meta‐analysis methods. Overall, ODAP‐B is an effective distributed learning algorithm for Poisson regression to study rare binary outcomes. The method provides inference on adjusted relative risk with a robust variance estimator. [ABSTRACT FROM AUTHOR] more...