Here is the design of a clinical trial:

Official Title: Vaginal Progesterone as Luteal Support for Improvement of Live Birth in Frozen/Thawed In-vitro Fertilization Natural Cycles; a Multicenter, Open, Randomized Trial

Included conditions:
- Infertility
- Embryo Transfer

Study Armgroups:
- {'label': 'No progesterone', 'type': 'NO_INTERVENTION', 'description': 'Patients will have FET in natural cycles with no extra intervention.'}
- {'label': 'Progesterone for 3 weeks', 'type': 'EXPERIMENTAL', 'description': 'At day LH+3 patients will start treatment with vaginal progesterone tablet at 100mg three times daily for three weeks.', 'interventionNames': ['Drug: Progesterone vaginal tablet']}
- {'label': 'Progesterone for 7 weeks', 'type': 'EXPERIMENTAL', 'description': 'At day LH+3 patients will start treatment with vaginal progesterone tablet at 100mg three times daily for seven weeks.', 'interventionNames': ['Drug: Progesterone vaginal tablet']}

Interventions:
- {'type': 'DRUG', 'name': 'Progesterone vaginal tablet', 'description': 'The study drug is progesterone 100 mg administrated as a vaginal tablet three times daily.', 'armGroupLabels': ['Progesterone for 3 weeks', 'Progesterone for 7 weeks'], 'otherNames': ['Lutinus, manufactured by Ferring GmbH. ATC code G03DA04']}

Primary Outcomes:
- {'measure': 'Number of participants with live birth', 'description': 'A child born alive. Also, the outcome will be reported according to Core Outcome Measure for Infertility Trials (Duffy et al., 2020) in a separate appendix.', 'timeFrame': 'Up to 41 weeks after embryo transfer.'}

Please estimate the sample size based on the assumption: 
Power of 0.80, significance level of 0.05, and a two-sided Fisher’s exact test.
Sample size calculation
        In order to find an effect size of a 7% increase in LBR per randomised patient, measured as a difference in proportions between no progesterone (0.33) and any progesterone group (0.40), 1800 subjects are needed if allocated 1:2. In order to find a difference between no progesterone (0.33) and progesterone for 3 weeks (0.41) and 7 weeks (0.41), respectively, 1200 subjects are needed if allocated 1:1. Also, for the comparison between the progesterone groups, 1200 subjects are needed if allocated 1:1, to detect a difference of 8%, (0.38 for 3 weeks of progesterone vs 0.46 for 7 weeks). For all comparisons above, except for the primary analysis, a difference between groups of 8% is used. If 1800 women are allocated 1:1:1, 600 to no progesterone, 600 to progesterone 3 weeks and 600 to progesterone 7âweeks, all four sample size calculations are fulfilled under the condition of a power of 0.80, a significance level 0.05 and a two-sided Fisherâs exact test.
        We thus have two primary superiority analyses in this study. The first is the comparison of LBR between no progesterone and the combined group of any progesterone with Fisherâs exact test on significance level 0.05. If this test is significant the probability mass of 5% will be transferred to the second comparison of live birth between progesterone for 3 weeks compared with progesterone for 7 weeks. If the first test is significant, we have been able to show that any progesterone gives significantly higher LBR than in women without progesterone. If in the second comparison 7 weeks shows significantly higher LBR than 3 weeks, we have also confirmed superiority regarding 7 weeks over 3 weeks. If the first analysis is non-significant, we have not been able to show any confirmative results in this study. The comparisons between no progesterone and 3 weeks progesterone and between no progesterone and 7 weeks progesterone is performed to calculate mean difference with 95%âCI between these groups.