Power to detect an association after imputation by IBD. The maximal power to detect an association is shown, with and without imputation by IBD and with sequenced individuals selected either randomly or according to their total sharing. The parameters we used were *N* = 10,000, *L* = 278 cM (one chromosome), *m* = 1 cM, cohort size of 500 cases and 500 controls, a total sequencing budget of *n*_{s} = 100 individuals, and a threshold *P*-value of *Q* = 0.01. For each carrier frequency *β*, we computed the power for each pair of *n*_{c}_{,}_{s} and *n*_{t}_{,}_{s} (number of sequenced cases and controls, respectively), such that *n*_{c}_{,}_{s} + *n*_{t}_{,}_{s} = *n*_{s}, and recorded and plotted the maximal power. The power was calculated using Equations 35 and 36, where in Equation 35, *p*_{c} was set to zero for the case of no imputation, or calculated using Equations 32 and 34 (random selection and selection by total sharing, respectively, and adjusted for diploid individuals). For the studied parameter set, imputation by IBD leads to a major increase in power. Proper selection of individuals for sequencing also contributes to the power but only slightly.

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