Here is the design of a clinical trial:

Official Title: ANTIcoagulation in Severe COVID-19 Patients: a Multicenter, Parallel-group, Open-label, Randomized Controlled Trial

Included conditions:
- Severe COVID-19 Pneumonia

Study Armgroups:
- {'label': 'Low dose prophylactic anticoagulation', 'type': 'EXPERIMENTAL', 'description': 'LD-PA', 'interventionNames': ['Drug: Tinzaparin, Low dose prophylactic anticoagulation']}
- {'label': 'High dose prophylactic anticoagulation', 'type': 'EXPERIMENTAL', 'description': 'HD-PA', 'interventionNames': ['Drug: Tinzaparin, High dose prophylactic anticoagulation']}
- {'label': 'Therapeutic anticoagulation', 'type': 'EXPERIMENTAL', 'description': 'TA', 'interventionNames': ['Drug: Tinzaparin,Therapeutic anticoagulation']}

Interventions:
- {'type': 'DRUG', 'name': 'Tinzaparin, Low dose prophylactic anticoagulation', 'description': 'Participants randomized to the LD-PA strategie will receive the low weight molecular heparin (LMWH) tinzaparin, considering its contraindications, recommended dose ranges and monitoring if applicable, as follows: LD-PA : 3500 IU/24h. Depending on the type of tinzaparin pre-filled syringe available in the participating center, the dose of 4000 IU/24h will be allowed in place of 3500 IU/24h.\n\nIf tinzaparin is not punctually available, the use of enoxaparin will be allowed as follows: LD-PA: 4000 IU/24h.\n\nAfter day-14, or hospital discharge, or in case of an indication for TA, or of serious adverse event related to anticoagulation, the investigational anticoagulation strategy will be discontinued and anticoagulation treatment will be left at the discretion of attending physicians.\n\nRecommendations for the management of COVID-19 pneumonia will be followed, including the use of dexamethasone. These recommendations will be subject to modifications based on the new literature data.', 'armGroupLabels': ['Low dose prophylactic anticoagulation'], 'otherNames': ['LD-PA']}
- {'type': 'DRUG', 'name': 'Tinzaparin, High dose prophylactic anticoagulation', 'description': 'Participants randomized to the HD-PA strategie will receive the low weight molecular heparin (LMWH) tinzaparin, considering its contraindications, recommended dose ranges and monitoring if applicable, as follows: HD-PA : 7000 IU/24h.\n\nIf tinzaparin is not punctually available, the use of enoxaparin will be allowed as follows: HD-PA: 4000 IU/12h.\n\nAfter day-14, or hospital discharge, or in case of an indication for TA, or of serious adverse event related to anticoagulation, the investigational anticoagulation strategy will be discontinued and anticoagulation treatment will be left at the discretion of attending physicians.\n\nRecommendations for the management of COVID-19 pneumonia will be followed, including the use of dexamethasone. These recommendations will be subject to modifications based on the new literature data.', 'armGroupLabels': ['High dose prophylactic anticoagulation'], 'otherNames': ['HD-PA']}
- {'type': 'DRUG', 'name': 'Tinzaparin,Therapeutic anticoagulation', 'description': 'Participants randomized to the TA strategie will receive the low weight molecular heparin (LMWH) tinzaparin, considering its contraindications, recommended dose ranges and monitoring if applicable, as follows: TA : 175 IU/kg/24h.\n\nIf tinzaparin is not punctually available, the use of enoxaparin will be allowed as follows: TA: 100 IU/kg/12h.\n\nAfter day-14, or hospital discharge, or in case of an indication for TA, or of serious adverse event related to anticoagulation, the investigational anticoagulation strategy will be discontinued and anticoagulation treatment will be left at the discretion of attending physicians.\n\nRecommendations for the management of COVID-19 pneumonia will be followed, including the use of dexamethasone. These recommendations will be subject to modifications based on the new literature data.', 'armGroupLabels': ['Therapeutic anticoagulation'], 'otherNames': ['TA']}

Primary Outcomes:
- {'measure': 'All-cause mortality', 'timeFrame': 'Day-28'}
- {'measure': 'Number of days to clinical improvement', 'description': 'Clinical improvement will be assessed through a seven-category ordinal scale derived from the WHO scale, using the following categories: 1. not hospitalized with resumption of normal activities; 2. not hospitalized, but unable to resume normal activities; 3. hospitalized, not requiring supplemental oxygen; 4. hospitalized, requiring supplemental oxygen; 5. hospitalized, requiring nasal high-flow oxygen therapy, noninvasive mechanical ventilation, or both; 6. hospitalized, requiring ECMO, invasive mechanical ventilation, or both; and 7. death. As all included patients will at least require oxygen supplementation, live discharge from hospital will represent a minimal 2-points decrease in the 7-points scale, thus a clinical improvement.', 'timeFrame': 'Day-28'}

Please estimate the sample size based on the assumption: 
Two-sided alpha of 0.017 using Bonferroni correction for multiple testing, 80% power, 5% of patients alive at day 28 without clinical improvement, Weibull distribution for survival curves, normal distribution for time to clinical improvement.
Sample size and its statistical justification
        The required number of participants to be randomised is 300 patients (from 353 included). Estimates, derived from prior studies led in similar populations,16 showed that a sample of at least 300 patients (100 per group) suffices to achieve â¥80% power that is required to detect a statistically significant difference in the ranked composite primary endpoint. The analyses rely on two-sided alpha of 0.017 using Bonferroni correction for multiple testing considering three pairwise comparisons between the randomised arms. Sample size calculation assumed having day 28 mortality of 24%, 21% and 18%, and time to clinical improvement of 16Â±3 days (SD), 14Â±3 days and 12Â±3 days, with LD-PA, HD-PA and TA, respectively. We hypothesise that the rate of positive CTPA would be 15%.18 19 For such, we aim to include 353 patients in order to randomise 300.
        Sample size calculation also considered the pairwise comparisons between the groups. For each performed comparison, 5000 samples were simulated using R software. For the first component of the hierarchical primary endpoint (mortality), survival curves were simulated based on a Weibull distribution using the R package simsurv. For the second component of the hierarchical primary endpoint (time to clinical improvement) assessed in alive patients, two different approaches, taking into account the distribution of this parameter, were used to test the robustness of results in relation with the retained hypotheses. First, a normal distribution was hypothesised with meansÂ±SD of 16Â±3, 14Â±3 and 12Â±3 days in LD-PA, HD-PA and TA, respectively. Second, incidence curves of clinical improvement were simulated based on Weibull distribution using the R package simsurv, with survival medians of 16, 14 and 12 days in LD-PA, HD-PA and TA groups, respectively. With both approaches, 5% of patients were systematically identified through simulation as alive patients at day 28 but without achieving clinical improvement, which is consistent with Cao et al.16 SD and mean number of days to clinical improvement, as well as shape and scale parameters of Weibull survival curves simulations were determined from the study of Cao et al.16 considering median (IQR) survival time and Kaplan-Meier curves. Within each sample/pairwise comparison, an individual score is calculated by comparing each patient in one group with all patients in the second group (23). These scores are then compared between groups using Mann-Whitney/Wilcoxon test in each of the 5000 samples, and the p value of each test is recorded. For each pairwise comparison, the percentage of tests with a p<0.017 is calculated, which gives an estimate of the achieved statistical power.