Here is the design of a clinical trial:

Official Title: Short and Medium-term Effects of a Multicomponent Physical Exercise Program With a Mediterranean Diet on Bone Mineral Density, Gait, Balance, and Fall Risk for Patients With Alzheimer's Disease: Randomized Controlled Clinical Trial Study Protocol

Included conditions:
- Alzheimer Disease
- Physical Exercise
- Bone Density
- Fall

Study Armgroups:
- {'label': 'Experimental Group', 'type': 'EXPERIMENTAL', 'description': 'Patients allocated to the intervention group will perform a MPEP during 6 months, with a frequency of 3 sessions per week, and approximately 45-50 minutes of duration each session. In addition, they will have a Mediterranean Diet.\n\nThe patients in the MPEP will be carried out in small groups of 5-8 people. Structure of sessions: 3 different parts: an initial warm-up, a main part and a final cool-down and relaxation.', 'interventionNames': ['Other: Multicomponent physical exercise program associated with a Mediterranean diet']}
- {'label': 'Control Group', 'type': 'ACTIVE_COMPARATOR', 'description': 'Participants allocated to the control group will receive usual care and continue with their life normally, without participating in a standardized exercise program. They will be instructed to maintain their current physical activity level.', 'interventionNames': ['Other: Usual care']}

Interventions:
- {'type': 'OTHER', 'name': 'Multicomponent physical exercise program associated with a Mediterranean diet', 'description': 'In this basic structure of each sessions, traditional exercises of mobility, strength, balance and coordination are included with the main objective of improving functional capacities. But, besides, games and some activities are also included with the aim, not only of improving the functional capacity, but also working the cognitive functions to reinforce the global effects.\n\nThe Mediterranean diet will based in these main foods: 1) vegetables; 2) fruits; 3) fish or seafood; 4) legumes; 5) nuts; 6) bread or cereals; 7) white meat; 8) eggs; and 9)olive oil.', 'armGroupLabels': ['Experimental Group']}
- {'type': 'OTHER', 'name': 'Usual care', 'description': 'Usual care and participants continue with their life normally, without participating in a standardized exercise program, and they will be instructed to maintain their current physical activity level.', 'armGroupLabels': ['Control Group']}

Primary Outcomes:
- {'measure': 'Change in gait and balance 1', 'description': "Tinetti's Performance Oriented Mobility Assessment (POMA-T) will be used (points). the original POMA-T 28-point version. It consists of a balance scale (Balance performance oriented mobility assessment (POMA-B) can score 16 points) and a gait scale (Gait performance oriented mobility assessment (POMA-G) can score 12 points )", 'timeFrame': '6 months. 4 time points: 1) Baseline (pre-intervention); 2) 1st post-intervention (1 month); 3) 2nd post-intervention (3 months); 4) Final, 3rd post-intervention (6 months)]'}
- {'measure': 'Change in gait and balance 2', 'description': 'Timed up and go test (TUG) will be used (s). IT measures the time in seconds for the subjects to get up from a standard armchair, walk 3 metres, turn, walk back to the chair and sit down. The cut-off point for normal mobility is 12 seconds and values \\> 30 s indicate a high level of dependence. (a time \\<10s it is considered normal; \\<20s mobility difficulties and low or moderate risk of falls; \\> 20 mobility problems with need of help and high risk of falls)', 'timeFrame': '6 months. 4 time points: 1) Baseline (pre-intervention); 2) 1st post-intervention (1 month); 3) 2nd post-intervention (3 months); 4) Final, 3rd post-intervention (6 months)]'}
- {'measure': 'Change in Bone Mineral Density (BMD)', 'description': 'Bone health status will be assessed by ultrasound calcaneus densitometry/sonometry. As primary outcome we will assess the estimated BMD (g/cm2).', 'timeFrame': '6 months. 4 time points: 1) Baseline (pre-intervention); 2) 1st post-intervention (1 month); 3) 2nd post-intervention (3 months); 4) Final, 3rd post-intervention (6 months)]'}
- {'measure': 'Change in T-Score as primary parameter of bone health', 'description': 'Bone health status will be assessed by ultrasound calcaneus densitometry/sonometry. As primary outcome we will assess the T-Score. A T-score shows how much the BMD is higher or lower than the BMD of a healthy 30-year old adult. (-1.0 or above normal BMD; From -1.0 to -2.5 low BMD or osteopenia; -2.5 or below very low BMD and diagnosis of osteoporosis.', 'timeFrame': '6 months. 4 time points: 1) Baseline (pre-intervention); 2) 1st post-intervention (1 month); 3) 2nd post-intervention (3 months); 4) Final, 3rd post-intervention (6 months)]'}

Please estimate the sample size based on the assumption: 
Alpha risk of 0.05, beta risk of 0.2 (power of 80%), and a dropout rate of 33%.
2.8
        Sample size calculation
        The sample size calculation has been made based on the potential modification of the score of the POMA-T. For this, we have considered the results obtained in the previous pilot study with 9 patients in a 1-month follow-up, and the preliminary trial with 72 participants with a ratio of 3:1 to the intervention group and the control one during 6 months. In the pilot study, the POMA-T was modified by 1.7 points. Then, in the preliminary trial, we accepted to calculate the sample size, as statistically significant, with a difference greater than or equal to 1.7 points with a dropTout rate of 15%.
        In our current study, the sample size has been estimated to conduct a randomized controlled clinical trial with a 1:1 ratio between the 2 groups. In this new calculation, considering the data from the pilot study and some of the available data from the preliminary trial, we have reduced the minimal detectable change in the POMA-T to 1.5 points, with a standard deviation of 2 points and we have increased the drop-out estimated rate during the study to 33% by the difficulty to avoid intervention biases in the control group fundamentally. Therefore, with this, and accepting an alpha risk of 0.05 and a beta risk of 0.2 in a 2-sided test, 84 subjects are necessary, 42 in each group. The sample size calculation was made with the software âGRANMO sample size and power calculatorâ (7.12 version).