Here is the design of a clinical trial:

Official Title: Health Outcomes Via Positive Engagement in Schizophrenia (HOPE-S)

Included conditions:
- Schizophrenia Spectrum Disorders

Study Armgroups:
- {'label': 'Participants with schizophrenia spectrum disorders', 'description': 'Within 8 weeks post discharge from hospitalization at the Institute of Mental Health', 'interventionNames': ['Other: Observational']}

Interventions:
- {'type': 'OTHER', 'name': 'Observational', 'description': "Participants will not receive any study intervention.\n\nDuring the 24-week study period, participants will complete five assessment visits and passive digital data from participant's smartphone and study-provided wrist wearable device will be collected.", 'armGroupLabels': ['Participants with schizophrenia spectrum disorders']}

Primary Outcomes:
- {'measure': 'Clinical Global Impression scale - Severity', 'description': "A single item measuring severity of illness at the point of assessment relative to a clinician's experience with patients of the same diagnosis on a 7-point scale; a higher rating indicates greater severity.", 'timeFrame': 'up to 24 weeks'}

Please estimate the sample size based on the assumption: 
A 10% drop-out rate is assumed, and the study aims for an 80% probability to observe at least 30 participants who relapse within 6 months.
Sample size calculation
        As this is an observational study, sample size was determined based on feasibility. Several studies suggested that a sample size of at least 30 participants generally allow adequate hypothesis testing while providing reasonable effect size.50â52 Assuming a 10% drop-out rate, a sample size of 100 will provide 80% probability to observe at least 30 participants who relapse within 6 months, if true relapse rate is 37%. This relapse rate is an assumption derived based on binomial distribution as information on relapse rates is unavailable. If the true relapse rate is lower than 37%, the probability to observe at least 30 participants who relapse within 6 months will be less than 80%. If the true relapse rate is higher than 37%, then the probability will be more than 80%.