Fig. 2

Comparison of statistical power across different options for the analytic sample for the effectiveness analysis. The x-axis shows the intervention effect size, parameterized as the percentage decrease in the expected number of days of acute care utilization comparing patients with OUD (recognized or unrecognized) in the intervention versus usual care arm. All options for the analytic sample (described in Table 2) use pre-randomization data. Each panel represents a different true prevalence of OUD (1%, 2%, or 4%). Options 3a, 3b, and 3c correspond to different assumptions of the properties of an algorithm for defining “increased risk” of OUD (see Table 3). Higher sensitivity includes more patients with true OUD whereas higher specificity excludes more patients without true OUD. Power calculations were based on closed form sample size formula based on Poisson regression (details are in the Additional File)