Here is the design of a clinical trial:

Official Title: Protein Supplementation Versus Standard Feeds in Underweight Critically Ill Children: A Dual-Centre Randomized Controlled Pilot Trial

Included conditions:
- Critically Ill

Study Armgroups:
- {'label': 'Standard care group', 'type': 'NO_INTERVENTION', 'description': 'The participants will receive feeding as per standard of care (without protein or any other supplementations).'}
- {'label': 'Study interventional group', 'type': 'EXPERIMENTAL', 'description': 'The participants will receive protein supplementation to reach a final goal of 1.5 g/kg/day of protein on full feeds.', 'interventionNames': ['Dietary Supplement: Enteral protein supplementation']}

Interventions:
- {'type': 'DIETARY_SUPPLEMENT', 'name': 'Enteral protein supplementation', 'description': "The participants in the study interventional group will receive protein supplementation to reach a final goal of 1.5 g/kg/day of protein on full feeds. This will be via 100% whey protein isolate (Nestle Beneprotein). Doses will be calculated on the patient's admission weight and rounded up to the nearest 1g. Doses will not be adjusted to account for weight changes in the PICU.\n\nProtein supplementation will continue for a total of 7 days from the start of enrolment into the study or until PICU discharge, whichever is earlier. If the patient is able to take solid feeds during the study intervention period, the intervention will be stopped. However, if the device required for feeding is removed but the patient takes milk/liquid feeds fully, protein supplementation will continue.", 'armGroupLabels': ['Study interventional group'], 'otherNames': ['Protein isolate (Nestle Beneprotein)']}

Primary Outcomes:
- {'measure': 'Proportion of eligible patients approached for consent', 'description': 'Number of eligible patients who are approached for consent', 'timeFrame': 'Throughout study period, over 36 months'}
- {'measure': 'Proportion of participants receiving their first protein supplementation within 72 hours of enrolment', 'description': 'Number of patients who received protein supplementation within 72 hours of enrolment', 'timeFrame': 'Throughout the study, over 24 months'}
- {'measure': 'Participant accrual rate', 'description': 'Average monthly enrolment at each centre', 'timeFrame': 'Throughout the study, over 24 months'}
- {'measure': 'Protocol adherence', 'description': '\\>80% of protein target administered according to the protocol in the intervention arm', 'timeFrame': 'Throughout study period, over 24 months'}

Please estimate the sample size based on the assumption: 
The study aims for a power ≥90% to detect the effect size, with a one-sided significance level (α) set at 50%. The dropout rate is assumed to be 10%-12%.
Sample size and interim analysis
        The purpose of this pilot study is to investigate whether protein supplementation has promising efficacy and is worth further investigation. A large randomised study with usual care as the active control would be inappropriate as insufficient evidence of benefit of protein supplementation exists to justify such a study. In circumstances involving uncertainty of benefit and need for parsimony in resource expenditures, a small randomised study invoking the âselection theoryâ approach proposed by Simon et al22 23 can provide an initial assessment of benefit. In the selection theory approach, the objective is to rank multiple potential treatments and then select those with the best responses for further study. However, our study involves only two treatmentsâprotein supplementation versus standard feedsâwhich simplifies the approach in a determination of whether protein supplementation is better than standard feeds.
        In the absence of any prior rates of clinical outcomes or effect size, our study will allow a response assessment and the potential for demonstrating greater efficacy of protein supplementation versus standard feeds in underweight critically ill children, with high statistical power, using a procedure that circumvents a formal hypothesis test.
        Effect size is defined as Î´=(Î¼1âÎ¼2)/Ï, where Î¼1 and Î¼2 represent clinical endpoint population means for the protein supplementation and standard feeds arms, respectively. In calculating sample size in the context of selection theory, we postulate the conventional underlying null and alternative hypotheses of H0: Î´â¤0 versus H1: Î´>0, respectively. In our pilot study, we will target an effect size of Î´=0.33, which is considered a small-to-moderate effect size and often viewed as representing a clinically important difference.24 If protein supplementation is superior to standard feeds by Î´â¥0.33, we desire to detect this difference with power â¥90%. However, under a true null hypothesis, we will choose to ignore the type I error rate, and so set Î±=50%âequivalent to random chance. Performing the sample size calculation based on a one-sided hypothesis test of two independent means using a two-sample t-test with one-sided Î±=0.50, a sample size of n=35 per group achieves power=0.92 to detect an effect size of Î´=0.33. (PASS commercial software was used to perform the sample size calculation.)
        From our preliminary data, we expect to have approximately 48 patients per year meet eligibility criteria for our pilot study. Our projection is that we will see 144 eligible patients over the 3-year recruitment period (3Ã48). Assuming a conservative consent rate of 55%, we anticipate at least 80 patients with BMI z-score â¤â2 which will provide 40 patients in each study arm. Accounting for a dropout rate of 10%â12% due to mortality and other causes, we would anticipate n=35 patients per arm completing the study (total N=70), which for Î´â¥0.33 achieves >90% probability for demonstrating superiority of protein supplementation to standard feeds. To ensure we are able to assess feasibility and test study procedures and infrastructure at each site, we aim to enrol 26 or 27 patients per centre per year (13 or 14 per arm).
        It is emphasised that under the selection theory paradigm, the best treatment for further consideration in a subsequent larger trial is selected on the basis of descriptive statisticsâin this case, higher mean value. Hence, given an effect size of Î´â¥0.33, the proposed procedure and sample size will ensure a >90% probability of protein supplementation as the better treatment, demonstrated by a higher mean value, without a formal hypothesis test. A 95% CI will be calculated on the protein supplementation versus standard feeds mean difference for the clinical efficacy variables.
        Should recruitment be slow and challenging, the study team will meet and decide on the best method in increasing enrolment. Some a priori strategies that we will consider include (but not limited to) changing the criteria to include:
        
          
            Children on non-invasive ventilation or respiratory distress, and requiring any form of tube feeding
          
          
            Children with BMI â¤â1 on PICU admission