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Next generation sequencing technologies have made it possible to investigate the role of rare variants (RVs) in disease etiology. Because RVs associated with disease susceptibility tend to be enriched in families with affected individuals, study designs based on affected sib pairs (ASP) can be more powerful than case-control studies. We construct tests of RV-set association in ASPs for single genomic regions as well as for multiple regions. Single-region tests can efficiently detect a gene region harboring susceptibility variants, while multiple-region extensions are meant to capture signals dispersed across a biological pathway, potentially as a result of locus heterogeneity. Within ascertained ASPs, the test statistics contrast the frequencies of duplicate rare alleles (usually appearing on a shared haplotype) against frequencies of a single rare allele copy (appearing on a nonshared haplotype); we call these allelic parity tests. Incorporation of minor allele frequency estimates from reference populations can markedly improve test efficiency. Under various genetic penetrance models, application of the tests in simulated ASP data sets demonstrates good type I error properties as well as power gains over approaches that regress ASP rare allele counts on sharing state, especially in small samples. We discuss robustness of the allelic parity methods to the presence of genetic linkage, misspecification of reference population allele frequencies, sequencing error and de novo mutations, and population stratification. As proof of principle, we apply single- and multiple-region tests in a motivating study data set consisting of whole exome sequencing of sisters ascertained with early onset breast cancer., (© 2020 The Authors. Genetic Epidemiology published by Wiley Periodicals Inc.)