PMC:4572492 / 35568-39728 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/4572492","sourcedb":"PMC","sourceid":"4572492","source_url":"https://www.ncbi.nlm.nih.gov/pmc/4572492","text":"Simulation Models\nThe following three models, as previously considered by Aschard et al.,16 were used to simulate the data:Model1:E[Y]=βGG+βE1E1+βGE1G⋅E1Model2:E[Y]=βE1E1+βE2E2+βGE1G⋅E1+βGE2G⋅E2Model3:E[Y]=βGE1G⋅E1\nFor all three models, the observed genetic variant (G) was coded additively with minor allele frequency (MAF) of 0.3. Y was simulated from models with varying effects (βs) and residual variation (ε) following a standard normal distribution (mean = 0, standard deviation = 1).\nModel 1 is analogous to Equation 1 where Y depended on the main effects of both G and E1 and an interaction effect between G and E1. The unobserved exposure variable E1 was binary with frequency 0.3. The main genetic effect βG took on values of 0.01, 0.05, and 0.1, and the interaction effect βGE1 was varied between −1 and 1 by a grid of 0.1. The main exposure effect βE1 was fixed at 0.3 when βGE1 was positive and −0.3 when βGE1 was negative.\nFor Model 2, Y was a function of main effects due to two unobserved exposures (E1 and E2; both binary with frequency 0.3) and interaction effects between the exposures and G. βGE1 was always positive and less than 1, whereas βGE2 was varied between −1 and 1 by a grid of 0.1. βE1 was fixed at 0.3, whereas βE2 was fixed at 0.3 when βGE2 was positive and −0.3 when βGE2 was negative.\nFor Model 3, Y depended only on the interaction between G and E1. For this model, the interaction effect βGE1 and exposure frequency were chosen such that the observed marginal effect of G was fixed at 10% of the trait standard deviation.\nIn all cases, the working association model corresponded to Equation 2 because information on E1 and E2 was assumed to be unavailable.\nTo assess the type 1 error level of the joint location-scale methods at 0.05, 0.005, and 0.0005 levels, we simulated 100,000 replicate samples of n = 2,000 subjects each from the null model with no genetic association (i.e., βG = 0 and βGE = 0). (Results of n = 1,000 and 4,000 are qualitatively similar.) To examine the behavior of the testing methods under small group sizes, we conducted additional simulations under varied MAF (0.3, 0.2, 0.1, 0.05, and 0.03) as well as under fixed genotype group sizes where the rare homozygote group size was small (2, 5, 7, 10, 15, or 20) with the other genotype group sizes determined with respect to Hardy-Weinberg equilibrium. For comparison, empirical type 1 error rates of the individual location-only and scale-only tests are also studied, in addition to the JLS-Fisher and JLS-minP tests, and the LRT of Cao et al.;17 the distribution test of Aschard et al.16 has the correct type 1 error by design. Type 1 error control at the genome-wide level was assessed by phenotype-permutation analysis of the 866,995 T1D GWAS SNPs and 565,884 CF GWAS SNPs.\nFor the sensitivity analysis of genotype imputation uncertainty, simulated true genotypes were converted to probabilistic genotype data using a Dirichlet distribution with scale parameters a for the correct genotype category and (1 − a)/2 for the other two;39 a was fixed at values of 1, 0.9, 0.8, 0.7, 0.6, and 0.5. Based on the simulated posterior probabilities, the most-likely genotype for each subject was the genotype with the highest posterior probability (i.e., the “hard call”); the incorrect call rate under this Dirichlet model ranges from 0% to 50% on average. The most-likely genotypes were then used to assess type 1 error control at the 0.05, 0.005, and 0.0005 levels, using 100,000 simulated replicate samples of n = 2,000, under the null model of no genetic association (i.e., βG = 0 and βGE = 0), and MAF = 0.3 for each level of genotype imputation uncertainty (a).\nFor power evaluation, as in Aschard et al.,16 the results presented focused on MAF = 0.3 and n = 2,000 for Models 1 and 2 and n = 4,000 for Model 3. Power (at the 5 × 10−8 level) was estimated from 500 replicates, based on asymptotic p values of the tests considered, with the exception of the distribution test. For the distribution test, p values required estimation by permutation, and corresponding power results were from Aschard et al.,16 kindly provided by Drs. Aschard and Kraft.","divisions":[{"label":"title","span":{"begin":0,"end":17}},{"label":"p","span":{"begin":18,"end":214}},{"label":"p","span":{"begin":215,"end":490}},{"label":"p","span":{"begin":491,"end":936}},{"label":"p","span":{"begin":937,"end":1319}},{"label":"p","span":{"begin":1320,"end":1558}},{"label":"p","span":{"begin":1559,"end":1693}},{"label":"p","span":{"begin":1694,"end":2788}},{"label":"p","span":{"begin":2789,"end":3672}}],"tracks":[]}