Power analysis, Aim 2 effectiveness

We performed a power analysis for the stepped wedge effectiveness component to determine sample size. Conventional power calculation programs are not able to consider both the intra-class correlation (ICC) for the intervention clusters, and the ICC for repeated measures of individuals over time. Therefore, we performed 1000 simulations using the stepped wedge design, for both continuous outcomes (analyzed using mixed-effects regression) and binary outcome (analyzed using mixed-effects logistic regression) [31, 32]. We conservatively set cluster-level ICC to be 0.10, based on two previous community or classroom studies that found an ICC of 0.05 [33, 34]. Individual-level ICC was set to range from 0.2 to 0.4, as is typical for correlations between repeated measurements of an individual. We set retention rates at 85, 80, and 75% at waves 2 through 4, a conservative estimate given our prior study with 80% retention at 18 months. Expected effect sizes (0.10 to 0.20 for continuous outcomes; odds ratios ranging from 1.2 to 2.2 for dichotomous outcomes) were based on significant outcomes in our previous efficacy study [10, 11] or, for comprehensive HIV knowledge and sexually transmitted infection (STI) prevalence, a 2010 national survey [35]. With 80% statistical power, the sample of 432 persons (youth or adults) with retention rates of 75% at the last wave, supported a minimum detectable effect size of 0.13 for continuous outcome variables, and a minimum detectable odds ratio of size 1.36. Thus, we have sufficient power to detect all expected intervention effects for outcome variables for adults and youth separately.