Power heatplots.

Abstract

<p>Power for the combination of screens and gain through a priori filtering for varying configurations of effect sizes across the 4 strata. The figures illustrate (A) the power to detect age-difference, sex-difference or age-sex-difference in at least one of our scans (on <i>P</i>_{<i>agediff</i>}, <i>P</i>_{<i>sexdiff</i>} and <i>P</i>_{<i>agesexdiff</i>}, with and without a priori filtering); and (B) a power comparison, comparing approaches with and without a priori filtering on <i>P</i>_{<i>Overall</i>} < 1x10^-5. We here assume four equally sized strata and a total sample size of N = 300,000 (comparable to the sample size in our BMI analyses). We set b_F≤50y = 0.033 (corresponding to a known and mean BMI effect in <i>MAP2K5</i> region with R² = 0.037%), b_M>50y = 0, and vary b_F>50y and b_M≤50 on the axes. This strategy allows us to cover the most interesting and plausible interaction effects: Two-way interactions, such as (i) pure age-difference (b_≤50y = 0.033, b_>50y = 0) and (ii) pure sex-difference (b_F = 0.033, b_M = 0); and three-way interactions, such as (iii) extreme three-way interaction with opposite direction across AGE and SEX, (iv) 1-strata interaction (b_F≤50y = 0.033, b_F>50y = b_M≤50y = b_M>50y = 0), and (v) 3-strata interaction (b_F≤50y = b_F>50y = b_M≤50y = 0.033, b_M>50y = 0).</p