Primary outcomes
NDD
We calculated summary statistics (proportions, means, and 95 % confidence intervals [CIs]) at baseline and follow up, overall and by randomization arm. For the primary analyses, we used mixed effects modeling of the follow up time points, using Intention to Treat. The models included random effects for participants, and fixed effects for timepoint (dummy variable for 6 or 9 month), study arm, and the interaction of time and study arm, as well as patient sex and the baseline outcome measurement (i.e. NDD, PEth, or viral suppression). We used the negative binomial distribution for NDD as recommended for alcohol use outcomes (We conducted sensitivity analyses to examine the effect of missing follow-up observations, by setting missing data points to the baseline value. We examined effect modification of the treatment effect for both outcomes by sex, baseline NDD (median split), baseline PEth (median split), self-reported very high-risk alcohol use (baseline AUDIT-C≥8, based on literature showing this cutoff indicated high mean alcohol consumption (