Here is the design of a clinical trial:

Official Title: A Cluster-Randomized Trial of the Northwestern Embedded Emergency Department Physical Therapy (NEED-PT) Protocol for Acute Low Back Pain

Included conditions:
- Low Back Pain

Study Armgroups:
- {'label': 'Embedded ED Physical Therapy (NEED-PT)', 'type': 'EXPERIMENTAL', 'description': "An ED physical therapist will be embedded with the primary treatment team to evaluate patients presenting with low back pain at the beginning of the overall treatment course. The physical therapist will utilize a clinical protocol (NEED-PT) that matches the patient's history and exam findings to an appropriate treatment classification consisting of directional preference exercises, manual traction, stabilization exercises, non-thrust manipulation/mobilization, and/or psychologically informed rehabilitation. The NEED-PT intervention will supplement any usual care performed by the treating physician.", 'interventionNames': ['Other: ED Physical Therapy']}
- {'label': 'Usual Care', 'type': 'OTHER', 'description': "Usual care consists of any ED testing or treatment not involving an ED physical therapist in accordance with the treating physician's usual and customary practice. This could include diagnostic imaging, patient education and reassurance, and administration and/or prescribing of analgesic medications.", 'interventionNames': ['Other: Usual Care']}

Interventions:
- {'type': 'OTHER', 'name': 'ED Physical Therapy', 'description': 'All ED Physical Therapy treatment classifications involve a combination of exercise, range of motion, education, prognostic guidance, and reassurance. Patients are provided with an individualized home exercise plan based on their matched treatment classification and/or active rest.', 'armGroupLabels': ['Embedded ED Physical Therapy (NEED-PT)']}
- {'type': 'OTHER', 'name': 'Usual Care', 'description': "Includes any diagnostic imaging, patient education and reassurance, and administration or prescribing of analgesic medications, as per the treating physician's usual and customary practice.", 'armGroupLabels': ['Usual Care']}

Primary Outcomes:
- {'measure': 'PROMIS Pain Interference (PROMIS-PI)', 'description': 'PROMIS-PI measures the self-reported consequences of pain on relevant aspects of a person\'s life, including social, cognitive, emotional, physical, and recreational activities. We will use the computer-adaptive format to minimize respondent burden. Scores are standardized to the general U.S. population, with a score of 50 representing the population mean. The time frame of interest for the PROMIS-PI is "in the past 7 days," meaning that participants provide responses based on their symptoms over the last week.', 'timeFrame': 'Three months after the index ED visit.'}

Please estimate the sample size based on the assumption: 
Two-sided 5% level of significance, 84% power, 20% dropout rate, correlation of approximately 0.50 between baseline and follow-up.
Power and sample size
        We used âThe Shiny CRT Calculatorâ to explore varying assumptions on cluster size (ie, average number of participants per physician), number of clusters (or physicians) and intracluster correlation (ICC). Under the parallel-arm, âcohortâ design, with baseline measurement of the primary outcome, the calculator also allows for an assumption on correlation between baseline and follow-up. The table in the Statistical Analysis Plan (SAP, online supplemental appendix file 1) illustrates power to detect at least a 3.5 mean difference across study arms if we assume just two time points (baseline and 3âmonths, which we deem conservative as we will have up to seven time points of observation, including baseline) per participant with a correlation of approximately 0.50. We conservatively estimate that we will need to enrol up to 360 total participants to account for worst-case (20%) scenario dropout for both physicians and participants. Thus, after accounting for physician and participant dropout, a final sample size of 16 physicians per arm and 7 participants per physician (n=224 total or 112 per arm) achieves 84% power to detect a mean between-arm difference of 3.5 PROMIS-PI points assuming SD of 10 points, ICC coefficient of 0.10, and a two-sided 5% level of significance.
        
          10.1136/bmjopen-2022-061283.supp1
          Supplementary data
          


        
        In our pilot work, we found a small ICC (0.01â0.04),13 indicating minimal within-physician effects that were not significant; however, we use a more conservative estimate of the ICC at 0.10 in the event that greater than anticipated within-physician effects are encountered. In the event that ICC is lower than expected or dropout rate is lower than 20%, we anticipate often over 90% power to detect a meaningful difference across arms. Since our target final analytic sample size is 224 total participants, if we can reach our target with fewer participants enrolled than 360, we will consider stopping enrolment under the guidance of the Data Safety and Monitoring Board (DSMB). We will plan to monitor dropout rates, ICC, SD, and within-participant correlation throughout the course of the trial and will formally present these data to the DSMB at regular intervals.