Here is the design of a clinical trial:

Official Title: On Track Chile For First Episode Psychosis

Included conditions:
- Psychosis

Study Armgroups:
- {'label': 'OTCH', 'type': 'EXPERIMENTAL', 'description': 'OTCH is based on OTNY, a Coordinated Specialty Care program for people with first-episode psychosis. The program is implemented by a multidisciplinary team, who provide coordinated, evidence-based services based on the interests, needs, and preferences of each participant.', 'interventionNames': ['Behavioral: OTCH']}
- {'label': 'Usual FEP services', 'type': 'PLACEBO_COMPARATOR', 'description': 'This is generally provided in mental health outpatient clinics which serve a population enrolled in the public health care system.', 'interventionNames': ['Behavioral: Usual FEP Services']}

Interventions:
- {'type': 'BEHAVIORAL', 'name': 'OTCH', 'description': 'OTCH is structured in three phrases (i. engagement and initial needs assessment, ii. ongoing intervention and monitoring, and iii. transition to long-term services) and lasts an average of two years. OTCH will maintain the central characteristics of the OnTrack model, as well as its core principles, which include (1) Person-centered care, (2) Shared decision-making, (3) Recovery orientation, and (4) Culturally-competent care.', 'armGroupLabels': ['OTCH']}
- {'type': 'BEHAVIORAL', 'name': 'Usual FEP Services', 'description': 'These include services such as psychiatric medication, psychotherapy, and psychoeducation for people with FEP and are usually provided at outpatient mental health clinics.', 'armGroupLabels': ['Usual FEP services']}

Primary Outcomes:
- {'measure': 'Adapted version of the OTNY Fidelity Scale', 'description': 'This scale will assess the degree to which the participating clinics deliver OTCH. The scale 24 dimensions rated on a 3-score rating where 0=unmet, 1=partially met, and 2=totally met. Higher scores mean better Fidelity.', 'timeFrame': '24 months'}
- {'measure': "Change on Providers' attitudes using the Evidence-Based Practice Attitude Scale", 'description': "Providers' attitudes to evidence-based practices will be measured by the evidence-based attitude scale (EBPAS). The EBPAS consists of 15 items rated on a five-point scale from 0=Not at all to 4=Very great extent. Higher scores mean better attitudes to evidence-based practices.", 'timeFrame': 'baseline, 12 months, 24 months'}
- {'measure': 'Change on Adoption of OTCH among patients using the CollaboRATE', 'description': 'This is a 3-item scale rated on a ten-point scale from 0=No effort was made to 9=Every effort was made. Higher scores mean better Adoption.', 'timeFrame': 'baseline, 12 months, 24 months'}
- {'measure': 'Change on Adoption of OTCH among providers using the Shared Decision Making Questionnaire Physician Version', 'description': 'This questionnaire continues with nine items about the steps in the adoption of the shared-decision making approach, one of the key components of OTCH. Each item is rated on a six-point scale from 0=Completely disagree to 5=Completely agree. Higher scores indicate more shared-decision making.', 'timeFrame': 'baseline, 12 months, 24 months'}
- {'measure': 'Change on Adoption of OTCH among both patients and providers using the Recovery Self-Assessment scale', 'description': 'This is a 32-item, self-administered rating scale that will measure perceptions about recovery principles and overall quality of services. Each item is rated on a five-point scale from 1=Strongly disagree to 5=Strongly agree. Higher scores indicate greater quality care.', 'timeFrame': 'baseline, 12 months, 24 months'}

Please estimate the sample size based on the assumption: 
Alpha of 0.05, 80% power, intra-class correlation of 0.05, 10% dropout rate, and 2-tailed tests. For mediation effects, path a=.26 and b=.26 with over 80% power.
Sample size and power analysis
        The first phase of the study which focused on the qualitative data collection did not include any formal power calculation to determine the sample size. Instead, we took a multistakeholder approach to include participants at different levels involved in the care for people with FEP including users and their family members. To incorporate a variety of stakeholder perspectives, we aimed to conduct 10 focus groups with 6â8 stakeholders.
        For the cluster trial, power was calculated conservatively based on the participation of 270 participants (rather than the full 300 to be enrolled), anticipating a possible participant drop-out of ~10%. We estimated that, with at least 10 clinics in each condition, we will have 80% power to detect a difference in mean outcomes between study conditions with a moderate effect size of Cohenâs d = 0.35 following the standard detectible effect size formula for clustered randomized trials [15, 16]. This power calculation was derived assuming an intra-class correlation of 0.05 for outcomes by clinic (15 participants nested within 21 clinics). We also assume an alpha of 0.05 and that all tests are 2-tailed. Previous research has shown interventions like OTCH to have moderate to large effects on implementation and service outcomes, such as medication adherence, service utilization, and engagement in treatment [5, 17]. We have also shown that FEP providers in Chile rely primarily upon medication and are usually not trained to promote shared decision-making, recovery orientation, or person-centered care [9]. Then it is reasonable to anticipate at least moderate (and probably large) effects of OTCH on these indicators of implementation. Finally, evidence for the expected effect on participant-level symptoms and functioning comes from the RAISE Connection Program study, which indicated improvement over 24 months for participants enrolled (e.g., PANSS improvement effect size 0.91, occupational functioning 1.2, and social functioning 0.72) [17]. Power to detect mediation effects (Aim 2b) depends on the size of the effect of intervention on implementation and service outcomes (path a), and the correlation between implementation and services outcomes and participant level symptoms, functioning, and recovery (path b). Based on tabulated recommendations for sample sizes needed to test mediation effects with a sample of size N=270 with follow-up data, we have over 80% power to detect a significant mediation effect with path a=.26 and b=.26. Path a is expected to be >0.35 (argued for Aim 1 above), and we expect based on our previous work that there will be at least moderate associations between implementation and clinical outcomes (r>0.40), assuming no confounding of mediator-outcome relationship.