Power for the primary hypotheses

Power analyses are based on the sub-group contrasts identified for each of the primary hypotheses. The analyses are based on a two sided alpha of .0125 (.05/4 outcome variables–number of treatment sessions attended, urinalysis-confirmed abstinence, days of self-reported drug use, and cost of acute care), an estimated correlation of .5 between the repeated measurements where applicable, and a 20 % attrition rate by month 12. Power calculations were based on Diggle, Heagerty, Liang, and Zeger [58] for the mixed effects models, Hedeker, Gibbons, and Waternaux [59] for the GEE models, and Cohen [60] for the cost-related hypotheses. With a sample size of 100 per condition in the illicit drug sub-group, we will have 80 % power to detect moderate effects of the intervention (d = .5) for the mixed effects models and cost-related analysis and 80 % power to detect a 20 % difference between the two groups for the GEE model. With a sample size of 200 per condition in the alcohol/marijuana sub-group, we will have 80 % power to detect smaller effects of the intervention (d = .25–.30) for the mixed effects models and cost-related analysis and 80 % power to detect smaller differences (13–15 %) between the two groups for the GEE model.