Average χ² statistics for LT versus other approaches in simulated data.

<p>For each statistic we display average results across 1,000,000 simulations, for various effect sizes <i>γ</i>. All statistics are χ²(1 dof). Logistic regression with an interaction term (G+GxE) values been converted from χ²(2 dof) to the equivalent χ²(1 dof) value. At an effect size of 0 all statistics give the expected value under the null. OR LBMI is the odds ratio computed from cases with BMI = 24. OR HBMI is the odds ratio for cases with BMI = 35.</p

Summary statistics across all datasets.

<p>The sum of each of the test statistics across all of the SNPs in each of the diseases. LTPub vs LogR is the % increase of LTPub compared to LogR. It has a median value of 16%. Type 2 diabetes (T2D), prostate cancer (PC), lung cancer (LC), breast cancer (BC), rheumatoid arthritis (RA), end-stage kidney disease (ESKD), and age-related macular degeneration (AMD).</p

Inferred covariates and effect sizes on the liability scale.

<p>LT model is the liability threshold model for each disease with parameters estimated using the LTPub method. For diseases with multiple covariates, models with all covariates and each covariate separately are given. %Variance Explained is the fraction of variance explained on the liability scale in the study data for each of the covariates in each of the diseases when all covariates are used in the model, and is specific to the distribution of covariates in each particular study. BMI30 is a binary variable, which is 1 if an individual's BMI is greater than 30 and 0 otherwise. Type 2 diabetes (T2D), prostate cancer (PC), lung cancer (LC), breast cancer (BC), rheumatoid arthritis (RA), end-stage kidney disease (ESKD), and age-related macular degeneration (AMD).</p

Power calculations for LogR, G+GxE, and LT approaches in simulated data.

<p>For each statistic we display power to attain P<5<b>×</b>10⁻⁸ based on 1,000,000 simulations of 3000 cases and 3000 controls, for various effect sizes <i>γ</i>. The increase in power (ratio of y-axis values) for LT versus LogR is 22.8% for <i>γ</i> = 0.1, and 23.0% when computing average power across all values of <i>γ</i>. For γ = 0 the power was 5.0% for all statistics when the P-value threshold is 0.05. G+GxE performs worse due to an extra degree of freedom.</p

Illustration of liability threshold model: simulated T2D example.

<p>The posterior mean of <i>ε</i> for low-BMI and high-BMI cases is the expected value of <i>ε</i> given that it exceeds <u>c(t</u>−)+m. High-BMI cases have a lower posterior mean relative to low-BMI cases since they require a smaller contribution from genetics to exceed the threshold in the liability threshold model.</p

Illustration of liability threshold model: simulated T2D example.

<p>Posterior mean value of residual quantitative trait <i>ε</i> (adjusted for BMI) as a function of BMI and case-control status. We also list allele frequencies specified in simulated genotype data.</p