2.4. Data analysis

We anticipated 85% retention for SUT transition and 100% retention for readmission to detoxification, as readmission does not rely on self-report. We assumed 10% of MI participants would transition to SUT and 40% would be readmitted within 12-months. Original calculations for n = 700 estimated 80% power to detect an 8% increase in transition to SUT and an 11% decrease in readmission. Updated calculations (n = 440) estimate 80% power to detect a minimum increase in transition to SUT of 10% and a 13% decrease in readmission.

We will examine descriptive statistics by study arm for all variables. Inferential analysis will follow the intent-to-treat principle. We will employ generalized linear models with canonical links as appropriate for the type of distribution and outcome. Models will be specified to reflect periods when participants were not at risk for the outcomes, due to incarceration or mortality. If study variables are unbalanced by chance at baseline, sensitivity analyses will include those variables in the regression analysis to account for potential confounding. We will use Tobit regression to test whether TTR delays time between discharge and first readmission, or whether readmission was prevented entirely over 12-months.

We will use cost-benefit and cost-effectiveness analyses for the economics evaluation. Successful transition within 30-days after discharge and fewer detoxification readmissions within 12-months will extrapolate to downstream cost-savings resulting in reduced substance use consumption, substance use-related consequences, and healthcare utilization. The primary economic outcome is the incremental cost-effectiveness ratio, measured as improvements demonstrated by the intervention relative to the control, divided by the incremental cost of treatment. Analyses will be conducted from the perspectives of the payer of healthcare services, given their role in sustaining the intervention, and society, given the interest of social efficiency related to resource allocation [44]. We will model the person period by 6-month intervals. Separate multivariable generalized-linear models will be estimated to predict the mean value of each resource category, as well as the number of binge drinking episodes and the HRQL preference weights, at each time point [45]. Recycled predictions will be used to obtain the final predicted mean values for each study group and resource/outcome, which will be summed and tested according to relevant perspectives [45]. To account for sampling uncertainty in point estimates, p-values, standard errors, and confidence intervals for the incremental cost-effective ratio will be estimated using nonparametric bootstrapping techniques within the multivariable framework. Sensitivity analyses will account for uncertain precision in assumptions and parameter estimates applied in the analysis [44].