Statistical Analysis
REGRESSION, SECONDARY
A sample of 900 patients provided ≥80% power to detect an 11% improvement in our primary outcome (eg, from 34% referral rate for current estimates to a clinically relevant 45%), using a two-sided type 1 error rate of 5% and an interclass correlation of 0.07, for planned comparisons between usual care and each nudge arm. We analyzed our binary outcome using logistic regression with generalized estimating equations (GEE). The study design is factorial, and models contained binary predictor terms for clinician and/or patient nudges. We included covariates from patients (eg, race) and clinicians (eg, clinician type) and controlled for time between visits in days. We controlled for type 1 error inflation by hierarchical testing, starting with the overall model significance, followed by effects of each nudge. Once we fitted the main effects model, we tested for interaction between nudges and retained the interaction term if significant. We followed the primary modeling with post hoc assessments of predictors, including our a priori interest in race, to assess interactions with study arm. Our primary analysis was intent-to-treat (ITT) so that all patients who completed the subsequent visit were included regardless of whether all interventions were received (N = 2,146). In a secondary analysis, we examined a GEE model that included only encounters wherein all nudges were received as intended (ie, a completer-only analysis; N = 1,795).