Here is the design of a clinical trial:

Official Title: Biomarker Research in ADHD: the Impact of Nutrition (BRAIN). An Open-label Trial to Investigate the Mechanisms Underlying the Effects of a Few-foods Diet on ADHD Symptoms in Children

Included conditions:
- Attention Deficit-Hyperactivity Disorder

Study Armgroups:
- {'label': 'Few-foods diet intervention', 'type': 'EXPERIMENTAL', 'interventionNames': ['Other: Few-foods diet']}

Interventions:
- {'type': 'OTHER', 'name': 'Few-foods diet', 'description': "The few-foods diet (FFD) is followed for 5-weeks preceded by a 1-week transition period during which the child's eating pattern will be gradually adjusted. The diet consists of rice, meat (turkey and lamb), a range of vegetables, pear, rice milk with added calcium and water, and is complemented with foods such as potatoes, fruits, corn, some sweets and wheat, which are allowed in small quantities only. Normal quantities of vegetables, rice and meat are allowed every day. If necessary the diet will be adjusted to avoid foods that the child dislikes or has cravings for. If the child does not respond to the initial FFD, i.e. no change in behaviour after the first two weeks, interim adjustments to the FFD will be made in consultation with the parents.", 'armGroupLabels': ['Few-foods diet intervention'], 'otherNames': ['Restricted Elimination Diet']}

Primary Outcomes:
- {'measure': 'Change in neural activation patterns during execution of tasks', 'description': 'Using fMRI, blood oxygen-level-dependent (BOLD) signal changes will be measured whilst performing cognitive tasks that assess inhibitory control and selective attention, i.e. a stop-signal task (response inhibition) and a Flanker task (response conflict and associated error monitoring). fMRI BOLD responses will be assessed between variable task-elements and performance. Region of interest (ROI; anatomically defined regions in the brain) analyses of the BOLD responses will be performed.', 'timeFrame': 'Before and at the end of the FFD intervention (i.e. at the end of week 2 and at the end of week 8)'}
- {'measure': 'Change in peripheral blood metabolite concentrations', 'description': 'Global metabolite profiles will be examined in plasma (or alternatively serum) obtained from whole blood using mass-spectrometry profiling. Phenylalanine and tyrosine plasma levels represent primary outcomes.', 'timeFrame': 'Before and at the end of the FFD intervention (i.e. at the end of week 2 and at the end of week 8)'}
- {'measure': 'Change in functional composition of the gut microbiota', 'description': 'Metagenome profiling will be performed on stool samples, leveraging Illumina next-generation sequencing technology. Sequence read data will be used for abundance profiling of microbiota genes that encode enzymes directly involved in the production or degradation of the dopamine and noradrenaline precursors phenylalanine and tyrosine.', 'timeFrame': 'Before and at the end of the FFD intervention (i.e. at the end of week 2 and at the end of week 8)'}
- {'measure': 'Change in ADHD symptom scores', 'description': 'ADHD symptoms will be scored using the 18-item ADHD rating scale, which is based on the Diagnostic and Statistical Manual of Mental Disorders (DSM)-IV and consists of 9 items that assess inattention and 9 items that focus on hyperactivity and impulsivity.', 'timeFrame': 'Before and at the end of the FFD intervention (i.e. at the end of week 2 and at the end of week 8)'}

Please estimate the sample size based on the assumption: 
The study aims to achieve at least 80% power with a Bonferroni-adjusted error probability of 0.002 (0.05/25) and an outcome allocation ratio of 2.2. Sample size calculations were conducted using t statistics and comparing two-sample independent means (two-tailed).
Sample size calculation
        This study aims to assess the effects of an FFD on brain and MGB axis parameters in relation to ADHD symptoms. FFD responders are defined as children showing at least 40% reduction on the ARS at T2, compared with T1.26 It is assumed that 55% of the children will respond to the FFD, 25% will not respond to the FFD (nresponder/nnon-responder=2.2), and 20% will drop out.26

        To our best knowledge, no studies have been published that were conducted on a cohort of ADHD patients and that investigated the effect of an FFD on the brain and MGB axis parameters in relation to ADHD symptoms. Consequently, due to the lack of data on the amplitude and variability in MGB axis parameters induced by an FFD, it is not straightforward to estimate the required sample size to obtain adequate levels of statistical power. Therefore, we based our sample size estimates for primary study outcome parameters on publicly available datasets serving as a proxy for the expected differences and variation.
        Sample size calculations were conducted in G*Power87 (V.3.1.9.2), using t statistics and comparing two-sample independent means (two tailed). To have a sufficient likelihood of detecting a difference between FFD responders and non-responders for the primary study outcomes, we aim to achieve at least 80% power with a Bonferroni-adjusted error probability of 0.002 (0.05/25) and an outcome allocation ratio (nresponder/nnon-responder) of 2.2. Based on the sample size estimates per outcome variable, as specified below, we will include 100 participants. Of note, this sample size calculation is conservative, since it is based on a simple Studentâs t-test comparing the primary measurements between responders and non-responders. The actual analysis (eg, multiple linear regression analysis) will most likely provide additional power.
        
          
            Neural activation: In a study on striatal activation during task performance in boys with ADHD (n=10; 8â13âyears) and healthy controls (n=6; 8â12âyears), activation was higher in controls than in boys with ADHD (Cohenâs d: 1.33Â±0.13).88 The required sample size to detect this difference in striatal activation is 46 (nresponder=32; nnon-responder=14). We expect a comparable difference between FFD responders and non-responders, as the response to the FFD can be to such extent, that responders no longer meet the criteria for ADHD.26

          
          
            Phenylalanine and tyrosine plasma levels: In a study on the effect of a diet intervention trial in 66 healthy adults (31 male and 35 female; 18â70âyears), baseline plasma metabolites were used to predict outcome (liver dysfunction or no dysfunction; Cohenâs d: 1.03Â±0.24).89 The required sample size to detect these differences in metabolites is 74 (nresponder=51âand nnon-responder=23).
          
          
            Gene abundance in stool microbiota related to phenylalanine and tyrosine metabolism: As no suitable, publicly available dataset was present at the time of writing this protocol, it was anticipated that gene abundance differences between FFD responders and non-responders will be 25%, with a variance of 25% (Cohenâs d: 1.00Â±0.25). To detect this difference, a sample size of 70 is required (nresponder=48âand nnon-responder=22).