Here is the design of a clinical trial:

Official Title: The Effects of Additional Home-based Strengthening Exercises in Shoulder Impingement Rehabilitation (The SEXSI-Trial): A Pragmatic Randomized Controlled Trial.

Included conditions:
- Subacromial Impingement Syndrome

Study Armgroups:
- {'label': 'Strengthen your Shoulder & Usual Care', 'type': 'EXPERIMENTAL', 'description': 'Instructions in a home-based intervention consisting of progressive high volume resistance training with an elastic band. Instructions provided 0, 2, 5, and 10 weeks after baseline. Usual care includes all treatment received by a patient during the time between baseline and follow-up, except that included in "Strengthen your Shoulder".', 'interventionNames': ['Other: Strengthen your Shoulder', 'Other: Usual Care']}
- {'label': 'Usual Care', 'type': 'ACTIVE_COMPARATOR', 'description': 'Includes all treatment received by a patient during the time between baseline and follow-up, except that included in "Strengthen your Shoulder".', 'interventionNames': ['Other: Usual Care']}

Interventions:
- {'type': 'OTHER', 'name': 'Strengthen your Shoulder', 'description': 'A simple home-based elastic band strengthening exercise intervention. This program consists of progressive high volume resistance training exercises with an elastic band.', 'armGroupLabels': ['Strengthen your Shoulder & Usual Care']}
- {'type': 'OTHER', 'name': 'Usual Care', 'description': 'Usual care, consisting of a referral to general rehabilitation in the municipal under the Danish Health Act § 140, most often with the alternative option to choose a private physiotherapeutic clinic, partly at their own expense. Also includes any additional treatment the patient receives between baseline and follow-up, except that included in "Strengthen your Shoulder".', 'armGroupLabels': ['Strengthen your Shoulder & Usual Care', 'Usual Care']}

Primary Outcomes:
- {'measure': 'SPADI', 'description': 'Shoulder Pain And Disability Index score (continuous)\n\nFor all continuous outcomes with Time Frame 16 weeks, a constrained Linear Mixed Model (cLMM) is applied to compare the change from baseline to 16 weeks in the intervention group (IG) to that in the control group (CG), with the outcome at 16 weeks as dependent variable, treatment group (IG or CG) as main effect and both baseline score and any additional follow up measurements as repeated measurements. The covariance structures will be selected based on the MAICE procedure. These analyses will be conducted as intention to treat (ITT) analyses, including all randomized participants, regardless of protocol adherence. Participants will be analysed as randomized.', 'timeFrame': '16 weeks'}

Please estimate the sample size based on the assumption: 
A significance level of 5% and a power of 95% are assumed. The impact of dropouts is considered, with a power of 89.7% for a 20% dropout rate and 85.4% for a 40% dropout rate.
Sample size
        The sample size estimation is based on the primary outcome SPADI. Studies on patients with SIS have shown standard deviations (SD) for SPADI change score after 11â12 weeks of between 17 [12] and 18.5 [56], while longer durations seem to entail larger SDs, with a SD of 22 reported for SPADI change from 0 to 22 weeks [12]. The latter is similar to our own unpublished data from SIS patients, showing a SD of 22.5 for SPADI change from 0 to 6 months. Based on this previous data, we expect a common SD of 19.5 for SPADI change values from week 0 to 16, the primary outcome. For the purpose of this study, the MCID for SPADI will be considered to be 10 points, based on previous studies [45, 48]. The negative effect that any dropouts will have on the statistical power will, to some degree, be reduced by the use of multiple imputation. However, the imputation of data will not fully redeem this, as multiple imputation can cause an underestimation of the effect and a larger variation in outcomes. Therefore, we aim at having a high power of 95% to verify an effect equal to or higher than the MCID of 10 points on SPADI, at a 5% significance level. To obtain this, a total of 200 patients will be required (100 in each group). This corresponds to a power of 89.7% in case of a 20% dropout and a power of 85.4% in case of a 40% dropout.