Here is the design of a clinical trial:

Official Title: Adjuvant Effects of Vitamin A and Vitamin D Supplementation on Treatment of Children With ADHD:A Randomized, Double Blind, Placebo-controlled, Multicentric Trial.

Included conditions:
- ADHD

Study Armgroups:
- {'label': 'vitamin AD group', 'type': 'ACTIVE_COMPARATOR', 'description': 'The patients aged 6-12 with a diagnose of ADHD of this group is deficient or insufficient in vitamin A and vitamin D. They will receive vitamin A 6000 IU/day and vitamin D 2100 IU/day supplementation in addition to methylphenidate for 8 weeks.', 'interventionNames': ['Dietary Supplement: vitamin AD']}
- {'label': 'vitamin D group', 'type': 'EXPERIMENTAL', 'description': 'The patients aged 6-12 with a diagnose of ADHD of this group is deficient or insufficient in vitamin A and vitamin D. They will receive vitamin D 2100 IU/day supplementation in addition to methylphenidate for 8 weeks. After the study, vitamin D group will be administrated with vitamin A on the basis of serum retinol concentration after the study.', 'interventionNames': ['Dietary Supplement: vitamin D']}
- {'label': 'placebo group', 'type': 'PLACEBO_COMPARATOR', 'description': 'The patients aged 6-12 with a diagnose of ADHD of this group is deficient or insufficient in vitamin A and vitamin D. They will receive placebo once a day in addition to methylphenidate for 8 weeks. After the study, the placebo group will be prescribed with vitamin A and vitamin D supplementation on the grounds of retinol and 25 (OH)D concentration.', 'interventionNames': ['Drug: Placebos']}

Interventions:
- {'type': 'DRUG', 'name': 'Placebos', 'description': 'Placebo, vitamin AD and vitamin D are identical in the appearance to guarantee blind. The patients need to administrate 3 capsules once a day for 8 weeks.', 'armGroupLabels': ['placebo group']}
- {'type': 'DIETARY_SUPPLEMENT', 'name': 'vitamin AD', 'description': 'A vitamin AD capsule contains vitamin A 2000 IU and vitamin D 700 IU. The patients need to administrate 3 capsules once a day for 8 weeks.', 'armGroupLabels': ['vitamin AD group']}
- {'type': 'DIETARY_SUPPLEMENT', 'name': 'vitamin D', 'description': 'A vitamin D capsule contains vitamin D 400 IU. The patients need to asministrate 6 capsules/time, once a day for 2 weeks, then change to 5 capsules/time, once a day for 6 weeks.', 'armGroupLabels': ['vitamin D group']}

Primary Outcomes:
- {'measure': 'The changes in ADHD clinical symptoms-Predominantly Inattentive subtype estimated by Chinese version of Vanderbilt parent assessment scale', 'description': 'The Vanderbilt parent assessment scale is designed to measure the severity of ADHD symptoms for children aged 6 to 12. It has 2 components: symptom assessment and impairment in performance. The symptom assessment screens for symptoms relevant to inattentive (items 1-9) and hyperactive (items 10-18) ADHD. The items 49-56 are performance measures. The symptom measures in the scale, scored 0 to 3. A positive response in symptom assessment part is a 2 or 3 (often, very often). The performance measures in the scale, scored 1 to 5, with 4 and 5 being somewhat of a problem/problematic.\n\nThe scoring standard for Predominantly Inattentive subtype: Must score a 2 or 3 on 6 out of 9 items on questions 1-9 AND Score a 4 or 5 on any of the Performance questions 49-56. The higher scores mean a worse outcome.', 'timeFrame': 'at baseline'}
- {'measure': 'The changes in ADHD clinical symptoms-Predominantly Inattentive subtype estimated by Chinese version of Vanderbilt teacher assessment scale', 'description': 'The Vanderbilt teacher assessment scale is designed to measure the severity of ADHD symptoms for children aged 6 to 12. It has 2 components: symptom assessment and impairment in performance. The symptom assessment screens for symptoms relevant to inattentive (items 1-9) and hyperactive (items 10-18) ADHD. The items 36-43 are performance measures. The symptom measures in the scale, scored 0 to 3. A positive response in symptom assessment part is a 2 or 3 (often, very often). The performance measures in the scale, scored 1 to 5, with 4 and 5 being somewhat of a problem/problematic.\n\nThe scoring standard for Predominantly Inattentive subtype: Must score a 2 or 3 on 6 out of 9 items on questions 1-9 AND Score a 4 or 5 on any of the Performance questions 36-43. The higher scores mean a worse outcome.', 'timeFrame': 'at baseline'}
- {'measure': 'The changes in ADHD clinical symptoms-Predominantly Hyperactive/Impulsive subtype estimated by Chinese version of Vanderbilt parent assessment scale', 'description': 'The Vanderbilt parent assessment scale is designed to measure the severity of ADHD symptoms for children aged 6 to 12. It has 2 components: symptom assessment and impairment in performance. The symptom assessment screens for symptoms relevant to inattentive (items 1-9) and hyperactive (items 10-18) ADHD. The items 49-56 are performance measures. The symptom measures in the scale, scored 0 to 3. A positive response in symptom assessment part is a 2 or 3 (often, very often). The performance measures in the scale, scored 1 to 5, with 4 and 5 being somewhat of a problem/problematic.\n\nThe scoring standard for Predominantly Hyperactive/Impulsive subtype: Must score a 2 or 3 on 6 out of 9 items on questions 10-18 AND Score a 4 or 5 on any of the Performance questions 49-56. The higher scores mean a worse outcome.', 'timeFrame': 'at baseline'}
- {'measure': 'The changes in ADHD clinical symptoms-Predominantly Hyperactive/Impulsive subtype estimated by Chinese version of Vanderbilt teacher assessment scale', 'description': 'The Vanderbilt teacher assessment scale is designed to measure the severity of ADHD symptoms for children aged 6 to 12. It has 2 components: symptom assessment and impairment in performance. The symptom assessment screens for symptoms relevant to inattentive (items 1-9) and hyperactive (items 10-18) ADHD. The items 36-43 are performance measures. The symptom measures in the scale, scored 0 to 3. A positive response in symptom assessment part is a 2 or 3 (often, very often). The performance measures in the scale, scored 1 to 5, with 4 and 5 being somewhat of a problem/problematic.\n\nThe scoring standard for Predominantly Hyperactive/Impulsive subtype: Must score a 2 or 3 on 6 out of 9 items on questions 10-18 AND Score a 4 or 5 on any of the Performance questions 36-43. The higher scores mean a worse outcome.', 'timeFrame': 'at baseline'}
- {'measure': 'The changes in ADHD clinical symptoms-ADHD Combined Inattention/Hyperactivity estimated by Chinese version of Vanderbilt parent assessment scale', 'description': 'The Vanderbilt parent assessment scale is designed to measure the severity of ADHD symptoms for children aged 6 to 12. It has 2 components: symptom assessment and impairment in performance. The symptom assessment screens for symptoms relevant to inattentive (items 1-9) and hyperactive (items 10-18) ADHD. The items 49-56 are performance measures. The symptom measures in the scale, scored 0 to 3. A positive response in symptom assessment part is a 2 or 3 (often, very often). The performance measures in the scale, scored 1 to 5, with 4 and 5 being somewhat of a problem/problematic.\n\nThe scoring standard for ADHD Combined Inattention/Hyperactivity: Must score a 2 or 3 on 6 out of 9 items not only on questions 1-9 but also on questions 10-18. AND Score a 4 or 5 on any of the Performance questions 49-56. The higher scores mean a worse outcome.', 'timeFrame': 'at baseline'}
- {'measure': 'The changes in ADHD clinical symptoms-ADHD Combined Inattention/Hyperactivity estimated by Chinese version of Vanderbilt teacher assessment scale', 'description': 'The Vanderbilt teacher assessment scale is designed to measure the severity of ADHD symptoms for children aged 6 to 12. It has 2 components: symptom assessment and impairment in performance. The symptom assessment screens for symptoms relevant to inattentive (items 1-9) and hyperactive (items 10-18) ADHD. The items 36-43 are performance measures. The symptom measures in the scale, scored 0 to 3. A positive response in symptom assessment part is a 2 or 3 (often, very often). The performance measures in the scale, scored 1 to 5, with 4 and 5 being somewhat of a problem/problematic.\n\nThe scoring standard for ADHD Combined Inattention/Hyperactivity: Must score a 2 or 3 on 6 out of 9 items not only on questions 1-9 but also on questions 10-18. AND Score a 4 or 5 on any of the Performance questions 36-43. The higher scores mean a worse outcome.', 'timeFrame': 'at baseline'}
- {'measure': 'The changes in ADHD clinical symptoms-Predominantly Inattentive subtype estimated by Chinese version of Vanderbilt parent follow-up assessment', 'description': 'The Vanderbilt parent follow-up assessment is designed to track treatment effect over time for ADHD children aged 6 to 12. It has 2 components: symptom assessment and impairment in performance. The symptom assessment screens for symptoms relevant to inattentive (items 1-9) and hyperactive (items 10-18) ADHD. The items 19-26 are performance measures. The symptom measures in the scale, scored 0 to 3 (Never, Occasionally, Often, Very Often). The performance measures in the scale, scored 1 to 5 (Excellent, Above Average, Average, Somewhat of a Problem, Performance Problematic).\n\nThe scoring standard for Predominantly Inattentive subtype: 1) Calculate Total Symptom Score for questions 1-18. 2) Calculate Average Performance Score for questions 19-26. The higher scores mean a worse outcome.', 'timeFrame': 'at weeks 4 and 8'}
- {'measure': 'The changes in ADHD clinical symptoms-Predominantly Inattentive subtype estimated by Chinese version of Vanderbilt teacher follow-up assessment', 'description': 'The Vanderbilt teacher follow-up assessment is designed to track treatment effect over time for ADHD children aged 6 to 12. It has 2 components: symptom assessment and impairment in performance. The symptom assessment screens for symptoms relevant to inattentive (items 1-9) and hyperactive (items 10-18) ADHD. The items 19-26 are performance measures. The symptom measures in the scale, scored 0 to 3 (Never, Occasionally, Often, Very Often). The performance measures in the scale, scored 1 to 5 (Excellent, Above Average, Average, Somewhat of a Problem, Performance Problematic).\n\nThe scoring standard for Predominantly Inattentive subtype: 1) Calculate Total Symptom Score for questions 1-18. 2) Calculate Average Performance Score for questions 19-26. The higher scores mean a worse outcome.', 'timeFrame': 'at weeks 4 and 8'}
- {'measure': 'The changes in ADHD clinical symptoms-Predominantly Hyperactive/Impulsive subtype estimated by Chinese version of Vanderbilt parent follow-up assessment', 'description': 'The Vanderbilt parent follow-up assessment is designed to track treatment effect over time for ADHD children aged 6 to 12. It has 2 components: symptom assessment and impairment in performance. The symptom assessment screens for symptoms relevant to inattentive (items 1-9) and hyperactive (items 10-18) ADHD. The items 19-26 are performance measures. The symptom measures in the scale, scored 0 to 3 (Never, Occasionally, Often, Very Often). The performance measures in the scale, scored 1 to 5 (Excellent, Above Average, Average, Somewhat of a Problem, Performance Problematic).\n\nThe scoring standard for Predominantly Hyperactive/Impulsive subtype: 1) Calculate Total Symptom Score for questions 1-18. 2) Calculate Average Performance Score for questions 19-26. The higher scores mean a worse outcome.', 'timeFrame': 'at weeks 4 and 8'}
- {'measure': 'The changes in ADHD clinical symptoms-Predominantly Hyperactive/Impulsive subtype estimated by Chinese version of Vanderbilt teacher follow-up assessment', 'description': 'The Vanderbilt teacher follow-up assessment is designed to track treatment effect over time for ADHD children aged 6 to 12. It has 2 components: symptom assessment and impairment in performance. The symptom assessment screens for symptoms relevant to inattentive (items 1-9) and hyperactive (items 10-18) ADHD. The items 19-26 are performance measures. The symptom measures in the scale, scored 0 to 3 (Never, Occasionally, Often, Very Often). The performance measures in the scale, scored 1 to 5 (Excellent, Above Average, Average, Somewhat of a Problem, Performance Problematic).\n\nThe scoring standard for Predominantly Hyperactive/Impulsive subtype: 1) Calculate Total Symptom Score for questions 1-18. 2) Calculate Average Performance Score for questions 19-26. The higher scores mean a worse outcome.', 'timeFrame': 'at weeks 4 and 8'}
- {'measure': 'The changes in ADHD clinical symptoms-ADHD Combined Inattention/Hyperactivity estimated by Chinese version of Vanderbilt parent follow-up assessment', 'description': 'The Vanderbilt parent follow-up assessment is designed to track treatment effect over time for ADHD children aged 6 to 12. It has 2 components: symptom assessment and impairment in performance. The symptom assessment screens for symptoms relevant to inattentive (items 1-9) and hyperactive (items 10-18) ADHD. The items 19-26 are performance measures. The symptom measures in the scale, scored 0 to 3 (Never, Occasionally, Often, Very Often). The performance measures in the scale, scored 1 to 5 (Excellent, Above Average, Average, Somewhat of a Problem, Performance Problematic).\n\nThe scoring standard for ADHD Combined Inattention/Hyperactivity: 1) Calculate Total Symptom Score for questions 1-18. 2) Calculate Average Performance Score for questions 19-26. The higher scores mean a worse outcome.', 'timeFrame': 'at weeks 4 and 8'}
- {'measure': 'The changes in ADHD clinical symptoms-ADHD Combined Inattention/Hyperactivity estimated by Chinese version of Vanderbilt teacher follow-up assessment', 'description': 'The Vanderbilt teacher follow-up assessment is designed to track treatment effect over time for ADHD children aged 6 to 12. It has 2 components: symptom assessment and impairment in performance. The symptom assessment screens for symptoms relevant to inattentive (items 1-9) and hyperactive (items 10-18) ADHD. The items 19-26 are performance measures. The symptom measures in the scale, scored 0 to 3 (Never, Occasionally, Often, Very Often). The performance measures in the scale, scored 1 to 5 (Excellent, Above Average, Average, Somewhat of a Problem, Performance Problematic).\n\nThe scoring standard for ADHD Combined Inattention/Hyperactivity: 1) Calculate Total Symptom Score for questions 1-18. 2) Calculate Average Performance Score for questions 19-26. The higher scores mean a worse outcome.', 'timeFrame': 'at weeks 4 and 8'}
- {'measure': 'The changes in ADHD clinical symptoms', 'description': "The Questionnaire - Children with Difficulties (QCD) measures the daily-life problems in children aged 6-18 years during the special time of the day, including in the morning, during school, after school, in the evening, and overall difficulties over the entire day and night. It has been proved the Chinese version of QCD has good validity and reliability. Filled in by the parents, the scale consists of 20 questions with regard to ADHD-related difficulties. Each question is scored on a four-point scale: 0 = completely disagree, 1 = somewhat (partially) agree, 2 = mostly agree, and 3 = completely agree. Score of 30 - 35 is considered as cut-off value for functional impairment and score of less than 30 is considered as functional impairment (Full marks: 57). The lower scores indicate lower life functioning and more difficulty in children's daily activities.", 'timeFrame': 'at baseline, weeks 4 and 8'}

Please estimate the sample size based on the assumption: 
An alpha of 0.05, power of 80%, and a dropout rate of 10% were assumed.
Sample size
        Based on an alpha of 0.05, power of 80% and a dropout rate of 10%, we adopted an analysis of variance F-test by using the PASS software 2020 to evaluate the sample size. This study is a randomised double-blind controlled trial. Intervention groups are vitamin AD group and vitamin D group, while the control is the placebo group. The primary outcome index is changes in ADHD symptoms as evaluated by Vanderbilt assessment scales at weeks 4 and 8 compared with that at baseline. In the study conducted by Mohammadpour et al,25 where the score generated using Connerâs Parent Rating Scale (CPRS) was considered the main outcome, the meanÂ±SD of ADHD index in CPRS was 55.84Â±10.20 for the vitamin D+methylphenidate group (n=25) and 56.79Â±9.60 for the placebo +methylphenidate group (n=29). The Vanderbilt assessment scale is considered as effective as the CPRS in assessing the changes of ADHD symptoms.31 Based on the hypothesis described above, vitamin A, along with vitamin D, promotes the improvement of ADHD symptoms. We cautiously presume that the mean scoreÂ±SD for vitamin AD+methylphenidate group is lower than that of vitamin D+methylphenidate group, while the control group scores the highest using the Vanderbilt assessment scales, with a score of 54.00Â±9.88 for the vitamin AD+methylphenidate group, 55.84Â±10.20 for the vitamin D+methylphenidate group and 56.79Â±9.60 for the control group. The number of subjects to be enrolled in the study is 504.