Here is the design of a clinical trial:

Official Title: Role of Gut Microbe Composition in Psychosocial Symptom Response to Exercise Training in Breast Cancer Survivors (ROME Study)

Included conditions:
- Breast Cancer
- Gut Microbiome
- Exercise
- Fatigue

Study Armgroups:
- {'label': 'Aerobic Exercise Training', 'type': 'EXPERIMENTAL', 'description': 'Progressive aerobic exercise training sessions supervised by exercise specialists who have experience training cancer survivors.', 'interventionNames': ['Other: Aerobic Exercise Training']}
- {'label': 'Attention Control', 'type': 'ACTIVE_COMPARATOR', 'description': 'The non-aerobic exercise attention control condition will control for the effects of attention with flexibility/toning activities.', 'interventionNames': ['Other: Attention Control']}

Interventions:
- {'type': 'OTHER', 'name': 'Aerobic Exercise Training', 'description': 'Each session will last 20 to 60 minutes depending on the stage of progression (shorter duration in the first few weeks). Sessions will occur on nonconsecutive days of the week. Moderate-intensity, continuous aerobic exercise will be used to target large muscle groups (e.g., legs) with the principal goal of increasing cardiorespiratory fitness. Exercise intensity will be gradually increased. To mitigate stagnation and support continued improvement of cardiorespiratory fitness, high-intensity interval exercise will be added in later weeks of the intervention.', 'armGroupLabels': ['Aerobic Exercise Training']}
- {'type': 'OTHER', 'name': 'Attention Control', 'description': 'The flexibility/toning control condition will be delivered using the same frequency as the aerobic condition (i.e., 3 times per week) and use light resistance bands of least difficulty. The flexibility/toning sessions will last about 40 minutes, be led by trained exercise specialists. Flexibility/toning activities will target the head/neck, shoulder, elbow/forearm, hand/wrist, trunk/hip, and ankle/foot. The progression of activities over the 10-week period will involve performing additional exercises and sets along with using progressively thicker elastic resistance bands (i.e., Thera-bands) that provide minimal resistance.', 'armGroupLabels': ['Attention Control']}

Primary Outcomes:
- {'measure': 'Composition of gut microbiota as measured by fecal samples', 'description': 'Using standard diversity and taxa comparison metrics', 'timeFrame': 'Baseline'}
- {'measure': 'Composition of gut microbiota as measured by fecal samples', 'description': 'Using standard diversity and taxa comparison metrics', 'timeFrame': '5 weeks after baseline'}
- {'measure': 'Composition of gut microbiota as measured by fecal samples', 'description': 'Using standard diversity and taxa comparison metrics', 'timeFrame': '10 weeks after baseline'}
- {'measure': 'Composition of gut microbiota as measured by fecal samples', 'description': 'Using standard diversity and taxa comparison metrics', 'timeFrame': '15 weeks after baseline'}

Please estimate the sample size based on the assumption: 
Two-tailed test, power of 0.8, significance level (alpha) of 0.05, and consideration of dropout rates.
Sample size and power considerations
          Sample size is based on detecting alpha diversity and beta diversity taxa comparisons. The power calculation is based on two-tailed test at power of 0.8 using software G*Power V.3.1.9.2.109 110 Our pre-COVID-19 pandemic sample size was estimated at 126 (63 in each group) with 100 (50 per study group) remaining after dropouts. This sample size would have allowed us to detect a medium effect size (d=0.57; power of 0.8, p<0.05) in alpha diversity which is sufficient for detecting effects related to associations with fatigue and intervention effects falling midway between that found in our two pilot studies. Relevant to taxa comparisons, we have >0.8 power to detect the effect of any of the taxa after multiple testing correction (q value <0.05).111â113 Due to the detrimental impact of the COVID-19 pandemic on recruitment into on-site, supervised exercise trials, we provide revised contingency power calculations in figure 4, where we can see that with sample size decreasing, the effect size we can detect changes from moderate to large. For example, for enrolling at 100%, 75% (74 samples with 37 per group) and 50%, the effect size that can be detected changes from 0.57, to 0.67, and to 0.81 (with power of 0.8 and alpha of 0.05). Of note, larger effect sizes are possible in this study (compared with our pilot studies) because the study will provide controlled feeding (reducing variability), select low fit individuals (greater chance of improvement) and manipulate the exercise exposure (standardise the exercise exposure). Also relevant, the sample sizes in our pilot studies (N=12âand 37) were smaller than our proposed study even with dropped enrolment yet yielded statistically significant results (eg, a significant association between alpha diversity and cardiorespiratory fitness in 37 breast cancer survivors).7 13

          
            Figure 4
            
              Revised contingency power curve.