Type I error rates.

Notes: A total number of 50,000 quantitatively phenotyped individuals were simulated, of which 500, 1,000, and 2,000 individuals with equally numbers of highest and lowest phenotypes were selected as case and control subjects. The gene length varied from 500 to 2,000 nucleotides. Type I error rates were estimated on 1,000 replicates at the significance level 0.05. For each replicate, 10,000 permutations were performed. Abbreviation: Collapsing, the collapsing method proposed by Li and Leal [15]; SCollapsing, the collapsing method with selective grouping strategy; AOC, the approximately optimal collapsing; GWWS, the group-wise weighted sum method proposed by Madsen and Browning [17]; SGWWS, the GWWS method with selective grouping strategy.