Here is the design of a clinical trial:

Official Title: Multicenter, Randomized, Open-Label Trial in Children and Adolescents to Establish Optimal Number of Doses for HPV Vaccination in Children and Adolescents Living With HIV

Included conditions:
- HIV Infection

Study Armgroups:
- {'label': 'Arm 1 (3 doses of 9vHPV vaccine)', 'type': 'EXPERIMENTAL', 'description': 'Participants living with HIV receive recombinant human papillomavirus nonavalent vaccine IM at enrollment, and at 2 and 6 months. Participants also receive recombinant human papillomavirus nonavalent vaccine booster dose IM at 30 months.', 'interventionNames': ['Biological: Recombinant Human Papillomavirus Nonavalent Vaccine']}
- {'label': 'Arm 2 (2 doses of 9vHPV vaccine)', 'type': 'EXPERIMENTAL', 'description': 'Participants living with HIV receive recombinant human papillomavirus nonavalent vaccine IM at enrollment and at 6 months. Participants also receive recombinant human papillomavirus nonavalent vaccine booster dose IM at 30 months.', 'interventionNames': ['Biological: Recombinant Human Papillomavirus Nonavalent Vaccine']}
- {'label': 'Arm 3 (1 dose of 9vHPV vaccine)', 'type': 'EXPERIMENTAL', 'description': 'Participants living with HIV receive recombinant human papillomavirus nonavalent vaccine IM at enrollment. Participants also receive recombinant human papillomavirus nonavalent vaccine booster dose IM at 24 months and recombinant human papillomavirus nonavalent vaccine completion dose IM at 30 months.', 'interventionNames': ['Biological: Recombinant Human Papillomavirus Nonavalent Vaccine']}
- {'label': 'Arm 4 (1 dose of 9vHPV vaccine)', 'type': 'ACTIVE_COMPARATOR', 'description': 'Participants without HIV receive recombinant human papillomavirus nonavalent vaccine IM at enrollment . Participants also receive recombinant human papillomavirus nonavalent vaccine booster dose IM at 24 months and recombinant human papillomavirus nonavalent vaccine completion dose IM at 30 months.', 'interventionNames': ['Biological: Recombinant Human Papillomavirus Nonavalent Vaccine']}

Interventions:
- {'type': 'BIOLOGICAL', 'name': 'Recombinant Human Papillomavirus Nonavalent Vaccine', 'description': 'Given IM', 'armGroupLabels': ['Arm 1 (3 doses of 9vHPV vaccine)', 'Arm 2 (2 doses of 9vHPV vaccine)', 'Arm 3 (1 dose of 9vHPV vaccine)', 'Arm 4 (1 dose of 9vHPV vaccine)'], 'otherNames': ['Gardasil 9', 'Nonavalent HPV VLP Vaccine', 'Recombinant HPV Nonavalent Vaccine', 'Recombinant Human Papillomavirus 9-valent Vaccine']}

Primary Outcomes:
- {'measure': 'Human papillomavirus type 16 (HPV16) neutralizing antibody geometric mean titers (GMTs) (Arm 1 versus [vs.] Arm 2)', 'description': 'Pseudovirion (PsV)-based neutralization assays will be used to establish HPV 16 neutralizing antibody GMT.', 'timeFrame': 'At 24 months after the last dose of each vaccine regimen'}

Please estimate the sample size based on the assumption: 
74-97% power for the primary comparison using a non-inferiority margin of 0.35 for the ratio of GMT between the 2- and 3-dose arms.
Sample size and power
        In absence of any previously collected data on HPV16 GMT 24 months after 2 vs. 3 doses in CLWH, assumptions were made on the distribution of the primary endpoint based on data accrued in previous trials [6, 10]. We used estimates for HPV16 neutralizing antibody GMT 12 months after 2 or 3 doses for HIV-negative children [6] and data for HPV16 neutralizing antibody GMT values after 3 doses in CLWH and HIV-negative children [10]. These data were used to bridge estimates for the mean GMT level for CLWH for both of those dose groups. Under reasonable assumptions for the pooled standard deviation, we anticipate having 74â97% power for the primary comparison using a non-inferiority margin of 0.35 for the ratio of GMT between the 2- and 3-dose arms, i.e. 74â97% power to show that the response in Arm 2 is at least 35% of the response in Arm 1.