Supplemental Material for Ziyatdinov et al., 2021

Supplementary Material contains sections that describe propositions used to derive the effective size multiplier (Section S1.1); detailed analytical derivations for the multipliers in the case of family-based designs (Section S1.2); general forms and examples of relationship matrices necessary to compute the multiplier (Section S1.3); detailed description of simulation settings (Section S1.4) and some additional simulation results (Section S1.5). Table S1 presents the criteria used for inference of pairwise relationships in the UK Biobank dataset. Table S2 gives numerical results for the multiplier in the UK Biobank dataset. Figures S1-5 show simulation results that confirm the accuracy of the proposed multiplier. Figures S7-8 present the multiplier for different study designs based on related pairs. Figures S9-16 show additional results from simulations and real data analyses.