Here is the design of a clinical trial:

Official Title: Computerized Detection and Internet-based Treatment of Common Mental Disorders Among College Students in Two Latin American LMICs

Included conditions:
- Major Depressive Disorder
- Generalized Anxiety Disorder

Study Armgroups:
- {'label': 'Clinician-Guided iCBT', 'type': 'EXPERIMENTAL', 'description': 'Both help-seeking students recruited from university clinics and non-help-seeking students recruited from needs assessment survey and outreach will receive internet delivered cognitive behavioral therapy guided by clinicians', 'interventionNames': ['Behavioral: Yo Puedo Sentirme Bien- Clinician-Guided version']}
- {'label': 'Self-guided iCBT', 'type': 'ACTIVE_COMPARATOR', 'description': 'Help-seeking students recruited from university clinics will receive self-guided internet delivered cognitive behavioral therapy while on waitlist. Non-help seeking students recruited from needs assessment survey and outreach will receive the self-guided version of internet delivered cognitive behavioral therapy.', 'interventionNames': ['Behavioral: Yo Puedo Sentirme Bien- Self-Guided version']}

Interventions:
- {'type': 'BEHAVIORAL', 'name': 'Yo Puedo Sentirme Bien- Clinician-Guided version', 'description': 'Internet delivered Cognitive Behavioral Therapy- Guided version', 'armGroupLabels': ['Clinician-Guided iCBT']}
- {'type': 'BEHAVIORAL', 'name': 'Yo Puedo Sentirme Bien- Self-Guided version', 'description': 'Internet delivered Cognitive Behavioral Therapy- Self-Guided version', 'armGroupLabels': ['Self-guided iCBT']}

Primary Outcomes:
- {'measure': 'Patient Health Questionnaire-9 (PHQ-9)', 'description': 'Self-report measure of depressive symptoms in the prior 2 weeks. Scores range from 0 to 27 with higher scores representing greater depressive symptomatology.', 'timeFrame': '90 days'}
- {'measure': 'Generalized Anxiety Disorder-7 (GAD-7)', 'description': 'Self-report measure of anxiety symptoms in the prior 2 weeks. Scores range from 0 to 21 with higher scores representing greater anxiety.', 'timeFrame': '90 days'}
- {'measure': 'Patient Health Questionnaire-9 (PHQ-9)', 'description': 'Self-report measure of depressive symptoms in the prior 2 weeks. Scores range from 0 to 27 with higher scores representing greater depressive symptomatology.', 'timeFrame': '12 months'}
- {'measure': 'Generalized Anxiety Disorder-7 (GAD-7)', 'description': 'Self-report measure of anxiety symptoms in the prior 2 weeks. Scores range from 0 to 21 with higher scores representing greater anxiety.', 'timeFrame': '12 months'}

Please estimate the sample size based on the assumption: 
The study is powered to detect a 5% difference in remission rates with 0.8 power based on 0.05-level two-sided tests. The study also accounts for loss to follow-up and uses simulation to estimate the required sample sizes.
Sample size {14}
        
          Expected number of subjects
          We expect to randomize at least 1500 participants in the first year trial and 1000 in each of the second and third year trials.
        
        
          Expected effect size and power calculations
          We powered the study to estimate heterogeneity of treatment effects as defined by the increase in the proportion of patients we would expect to remit from the primary outcomes based on optimized rather than randomized treatment of 5%. We considered this the minimum difference of interest. Although we will be interested both in continuous (i.e., differences in mean scores on symptom rating scales) and categorical (i.e., probabilities of treatment response and remission) outcomes, we evaluated statistical power for a categorical measure of episode remission because this is of greatest clinical importance and because larger samples are required for powerful detection of effects on categorical than continuous outcomes. Meta-analyses of previous iCBT trials for CMDs show that treatment response is approximately 50% and remission is approximately 30%, with rates roughly half these values for control conditions. Closed-form solutions show that samples with fewer than 150 patients per arm provide adequate statistical power (.8 power based on .05-level two-sided tests) to detect effect sizes this large even after making reasonable adjustments for loss to follow-up. However, estimating power to detect heterogeneity of treatment effects is more complex because closed-form solutions do not exist and simulation is needed to determine required sample sizes.
          We carried out such a simulation by building a series of hypothetical population models that assumed that each patient was randomized either to iCBT or a control condition; that the aggregate remission rates after adjusting for loss to follow-up were 27.5% and 17.5% in the two treatment arms, respectively; and that a series of relatively complex nonlinear-interactive multivariate associations existed between 20 predictors and remission. The assumed distributions of predictors and interaction values among predictors were consistent with those found in previous studies. We varied these coefficient values in different models to maintain the same aggregate remission rates but to have the difference between remission rates based on randomized versus optimized treatment vary between 0 and 15%. In each model, the remission rate if intervention assignment was randomized was set at 10% (i.e., 27.5â17.5%), but the remission rate if intervention assignment was optimized (i.e., if each student who would have a better outcome if assigned to iCBT was, in fact, assigned to iCBT and all other students were assigned to the control condition, which in some cases could involve these students receiving treatment at the student clinic and having better outcomes than if they received iCBT) was varied between 0 and 15%. We used a state-of-the-art ensemble machine learning method detailed in the proposal to estimate heterogeneity of treatment response. We discovered that adequate statistical power (again defined as .8 power based on .05-level two-sided tests) to detect a difference between the two remission rates of 5%, which we considered the minimum difference of interest, would require a sample of at least 500 patients per treatment arm [59]. A difference of 5% would represent a 50% increase on the 10% aggregate base of the difference in the remission rate between intervention and control groups. Based on a review of previous precision treatment analyses of CMDs, a difference of this magnitude is plausible. Based on this result, we designed the study to have a sample size of 500 per treatment arm. As noted above in the discussion of the sample design, we will have 1500 eligible students to randomize across three arms in the first trial, making it possible for us to estimate a precision treatment model based on data obtained in this trial. However, as noted above in the section on study design, the 12-month follow-up data for these students will not be available until YR2 and it will be possible to use the results of the model for the trial 2 randomization for the first time in YR3. We will replicate the model with follow-up data for students randomized in YR2 and use the harmonized precision treatment model results obtained in YR3 for a final Trial in YR4.