Power based on three-arm design
Key Assumptions	13 clusters per arm (alpha=0.05/2=0.025); m = 79; ICC = 0.012; CV = 0.47
Primary Outcome Comparison	Expected Effect Size	Power
Combined Interventions (PD+CD) vs. Control Arm	30% (PD+CD) – 8% (Control) = 22 percentage points	99.8%
Combined Interventions (PD+CD) vs. Client Directed Intervention (CD)	30% (PD+CD) – 14.6% (CD) = 15.4 percentage points	86.0%

Notes: m, expected median cluster size by the end of the study; ICC, intraclass correlation coefficient; CV, coefficient of variation of cluster size