Here is the design of a clinical trial:

Official Title: Vitamin D Supplementation in Individuals With a Chronic Spinal Cord Injury - a Placebo-controlled Randomized Double-blinded Study

Included conditions:
- Spinal Cord Injuries
- Vitamin D Deficiency

Study Armgroups:
- {'label': '"Low" dose', 'type': 'EXPERIMENTAL', 'description': "One vial with 600 µg cholecalciferol (corresponding to a total of 24'000 IU vitamin D) and one vial with placebo every month.", 'interventionNames': ['Drug: Cholecalciferol (Vitamin D3)', 'Other: Placebo']}
- {'label': '"High" dose', 'type': 'EXPERIMENTAL', 'description': "Two vials with 600 µg cholecalciferol each (corresponding to a total of 48'000 IU vitamin D) every month.", 'interventionNames': ['Drug: Cholecalciferol (Vitamin D3)']}
- {'label': 'Placebo', 'type': 'PLACEBO_COMPARATOR', 'description': 'Two vials with a placebo every month.', 'interventionNames': ['Other: Placebo']}

Interventions:
- {'type': 'DRUG', 'name': 'Cholecalciferol (Vitamin D3)', 'description': 'Vi-De 3® Monthly Dose from Dr. Wild \\& Co. AG (Muttenz, Switzerland) is a commercially available vitamin D3 supplement.', 'armGroupLabels': ['"High" dose', '"Low" dose'], 'otherNames': ['Vi-De 3® Monthly Dose']}
- {'type': 'OTHER', 'name': 'Placebo', 'description': 'A placebo will be produced, consisting of the same ethanol solution as Vi-De 3® Monthly Dose, but without cholecalciferol.', 'armGroupLabels': ['"Low" dose', 'Placebo']}

Primary Outcomes:
- {'measure': 'Vitamin D status', 'description': 'Serum levels of 25(OH)D in nmol/L', 'timeFrame': '0 to 12 months'}

Please estimate the sample size based on the assumption: 
Assuming a significance level of 5% and a power of 0.80, with between-group variances ranging from 1000 to 3500 and correlations between repeated measures ranging from 0.1 to 0.9.
Sample size
        We defined the minimal sample size as the sample size needed to detect a statistically meaningful difference in the time course of the primary outcome vitamin D status across the three intervention groups. For this, we estimated the sample size needed to detect an interaction between treatment and time across the three intervention groups using the power analysis package for repeated measures in Stata software, V.16.0 (StataCorp, 2019). The expected mean vitamin D status at each time point was calculated for each intervention group using the generalised pharmacokinetic curve equation of Heaney, et al35 which we parametrised for the purpose of this study using the available data for vitamin D supplementation in chronic SCI.23 36
        Assuming a significance level of 5% and a power of 0.80, minimal sample sizes were calculated for a range of between-group variances (ie, 1000â3500, with 500 incremental steps) and correlations between repeated measures (ie, 0.1â0.9, with 0.1 incremental steps; online supplemental file 3). Based on this power analysis for sample size, we conservatively plan for 45 participants with a full data set, implying 15 participants in each of the three intervention groups. In the case of dropouts or a large amount of missing data for a given participant, recruitment will be continued until the minimal sample size of 15 participants per intervention groups is effectively achieved. Sample size calculation did not take secondary outcome parameters into account. Since long-term studies among the chronic SCI population are rare, this study may inform the minimal sample size needed for future studies targeting the dynamics of secondary outcome parameters in response to vitamin D supplementation.
        
          10.1136/bmjopen-2021-053951.supp3
          Supplementary data