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We show the effective sample size for the unified estimator applied to n 0 = 20,000 sibling pairs and n 1 singletons, relative to the effective sample size of using the sibling pairs alone with imputation. The parental genotypes in the sibling sample are imputed 3 using unphased data. The parental genotypes for the singletons are imputed linearly. When imputing using unphased data, the gain depends upon the minor allele frequency 3 , which we show for a fixed correlation between siblings residuals of 0.3. We confirmed the theoretical results using simulations (Supplementary Note 2.1 ).

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