Statistical analyses
Feasibility and acceptability measures were examined descriptively. Unadjusted comparisons of outcomes at 3 and 6 months were performed using t-tests or non-parametric tests (i.e., the Wilcoxon rank-sum tests for independent samples) for outcomes not approximately normally distributed, such as count-like variables (i.e., percent heavy drinking or drug using days, substance use services received per day). Adjusted analyses used longitudinal modeling for repeated measures of the outcomes (3 and 6 months) with study group as the independent variable and baseline value as a covariate. The technique for longitudinal modeling was generalized estimating equations with weighted estimation approach that allowed for data missing at random, so that all participants with at least one non-missing follow-up observation were included. The error distribution was chosen based on each outcome’s distribution: Normal (scale score; readiness and self-efficacy), or Negative Binomial for over-dispersed count outcomes (all other outcomes). In the Negative Binomial models, log link was used, and differences between logarithms of group means were evaluated. To facilitate the interpretation on the original measurement scale, the estimated of logarithms were then back transformed (exponentiated) to the original scale. As a result of exponentiation, the differences between logarithms of two group means corresponded to the ratios of exponentiated estimates of the means. We obtained 95% confidence intervals for the differences of group means or logarithms of the means along with effect sizes (Cohen’s d) for the differences between two groups.