Here is the design of a clinical trial:

Official Title: Lay-Delivered Behavioral Activation in Senior Centers

Included conditions:
- Depression

Study Armgroups:
- {'label': 'Volunteer-delivered Behavioral Activation - "Do More, Feel Better"', 'type': 'EXPERIMENTAL', 'description': '"Do More, Feel Better" (DMFB) is a streamlined, simplified version of Behavioral Activation (BA) delivered by lay volunteers to depressed senior center clients.', 'interventionNames': ['Behavioral: Volunteer-delivered Behavioral Activation']}
- {'label': "Master's Level Clinician-delivered Behavioral Activation", 'type': 'ACTIVE_COMPARATOR', 'description': "Traditional Behavioral Activation (BA) delivered by master's level mental health clinicians", 'interventionNames': ["Behavioral: Master's level clinician-delivered Behavioral Activation"]}

Interventions:
- {'type': 'BEHAVIORAL', 'name': 'Volunteer-delivered Behavioral Activation', 'description': 'Behavioral Activation as delivered by trained volunteers', 'armGroupLabels': ['Volunteer-delivered Behavioral Activation - "Do More, Feel Better"']}
- {'type': 'BEHAVIORAL', 'name': "Master's level clinician-delivered Behavioral Activation", 'description': "Behavioral Activation as delivered by trained master's level clinicians", 'armGroupLabels': ["Master's Level Clinician-delivered Behavioral Activation"]}

Primary Outcomes:
- {'measure': 'Hamilton Rating Scale for Depression (HAM-D)', 'description': 'The HAM-D will be used as measure of depressive symptom severity. The HAM-D is a clinically administered measure and has been validated in a variety of psychiatric populations.', 'timeFrame': 'Change from Baseline HAM-D at 3, 6, 9, 24, and 36 weeks after treatment starts'}
- {'measure': 'Behavioral Activation Scale (BADS)', 'description': 'The BADS will be used as the primary target measure, and yields a total score reflecting level of engagement in reinforcing activities. The BADS has shown good psychometric properties; studies have validated the BADS as a mechanism by which behavioral activation interventions reduces depression.', 'timeFrame': 'Change from Baseline BADS at 3, 6, 9, 24, and 36 weeks after treatment starts'}

Please estimate the sample size based on the assumption: 
The assumptions included an ICC of 5%, intercept variance of 0.80, residual variance of 0.2, a 20% attrition rate, a Type 1 one-sided error rate of 0.05, and equal numbers of clients within providers and across conditions.
Power and sample size
          
            H1 and H2
            We used Monte Carlo simulation studies to determine power and sample size.53 Data were simulated from a two-level structural equation model (repeated measures and growth factors at level 1, provider at level 2). The test statistic was the effect of intervention condition on the slopes of activity level and depression. The model was parameterised such that the slope represented the total amount of change from baseline to 9 weeks. We powered the trial to detect a non-inferiority margin for Cohenâs d effect size >0.2. We set the ICC to 5%, consistent with meta-analyses that suggest therapist effects explain 5% of the variability in psychotherapy outcomes.54 55 We set the intercept variance to 0.80 and residual variance of the repeated measures to 0.2, implying a reliability for HAM-D of 0.80, consistent with meta-analysis.56 Growth factor variances were set to levels typically observed, with the within-cluster slope variance set to 10% of the intercept variance.56 We also conservatively assumed a 20% attrition rate over the course of the study. We used a Type 1 one-sided error rate of 0.05, and equal numbers of clients within providers and across conditions. To determine sample size, we simulated 2000 data sets each across a range of possible sample sizes. Results indicated that to achieve 80% power, we would need a total sample size of 288 clients, 144 in each condition.
          
          
            H3
            Data were simulated from a parallel process growth curve model.57 To reduce model complexity (ie, keep the number of model parameters < the number of clusters), we ignored clustering at the provider level, but otherwise kept the sample size fixed at 288 and used the same parameters described for the aim 1 simulations. We varied the size of the effect across simulations to determine the minimum possible effect identifiable with 80% power. We found that we have 81% power to detect effects as small as b=0.4.