Here is the design of a clinical trial:

Official Title: Vestibular Schwannoma - Radiosurgery or Expectation

Included conditions:
- Vestibular Schwannoma

Study Armgroups:
- {'label': 'gamma knife radiosurgery', 'type': 'EXPERIMENTAL', 'description': 'Single fraction gamma knife radiosurgery given at 12 Gy to tumor periphery for vestibular schwannoma', 'interventionNames': ['Radiation: gamma knife radiosurgery']}
- {'label': 'Expectation', 'type': 'NO_INTERVENTION', 'description': 'No active treatment given for vestibular schwannoma'}

Interventions:
- {'type': 'RADIATION', 'name': 'gamma knife radiosurgery', 'description': 'Leksell Perfection model gamma knife.', 'armGroupLabels': ['gamma knife radiosurgery']}

Primary Outcomes:
- {'measure': 'Relative Tumor volume', 'description': 'Growth measured as volume ratio V4years/Vbaseline and 1/volume doubling time', 'timeFrame': '4 years'}

Please estimate the sample size based on the assumption: 
Scenario 1: Significance level 0.05, power 90%; Scenario 2: Significance level 0.05, power 90%, SD 35; Scenario 3: Significance level 0.10, power 95%, SD 35; Tumor growth endpoint: Power 80%
Sample size
        We performed two power analyses based on data from our own VS database.
        
          Based on hearing outcomes
          In the first power analysis, we examined the number of patients needed to demonstrate if the two groups would be similar or different in hearing outcome (figures 1â3).
          
            Figure 1
            
              Hearing acuity as suggested endpoint.
            
            
          
          
            Figure 2
            
              Hearing acuity as suggested endpoint.
            
            
          
          
            Figure 3
            
              Hearing acuity as suggested endpoint.
            
            
          
          Test for difference:
          
            
              
                
                  Power(1âtype 2 error):
                  0.8 or 0.9
                  The probability of reject H0 when H0 is false
                
              
              
                
                  Type 1 error:
                  0.05
                  The probability of reject H0 when H0 is true
                
              
            
          
          One usually wants a power of 80% or more and a low type 1 error.
        
        
          Scenario 1âdifference in proportions (Gardner-Robertson)
          We want to determine the sample size for a 5-year VS trial with Gamma Knife therapy and a control group with no treatment. The primary outcome is hearing loss, defined as useful to no useful hearing (binary outcome). We desire a 0.05-significance level test with 90% statistical power. The proportion of no useful hearing at a 5-year follow-up in a similar population is 54%. We plan to have an equal allocation to the two treatment groups.
        
        
          Scenario 2âdifference in means (% of perfect hearing)
          We want to determine the sample size for a 5-year VS trial with Gamma Knife therapy and a control group with no treatment. The primary outcome is hearing loss, defined as the percentage of perfect hearing (100% excellent hearing and 0% deaf). We desire a 0.05 significance level test with 90% statistical power. The SD observed from a similar population is 35. We plan to have an equal allocation to the two treatment groups.
          Test for equivalence:
          
            
              
                
                  Power(1âtype 2 error):
                  0.90 or 0.95
                  The probability of reject H0 when H0 is false
                
              
              
                
                  Type 1 error:
                  0.10
                  The probability of reject H0 when H0 is true
                
              
            
          
          One usually wants a higher power (90% or more) and a higher type 1 error.
        
        
          Scenario 3âequivalence in means (% of perfect hearing)
          We want to determine the sample size for a 5-year VS equivalence trial with Gamma Knife therapy and a control group with no treatment. The primary outcome is hearing loss, defined as the percentage of perfect hearing (100% excellent hearing and 0% deaf). We desire a 0.10-significance level test with 95% statistical power and decide that the zone of equivalence is (â15%, 15%) and that the true difference in means does not exceed 0%. The SD observed from a similar population is 35. We plan to have an equal allocation to the two treatment groups (figures 1â3).
        
        
          Tumour growth as the endpoint
          The second endpoint concerning changes in tumour size (figure 4). The analysis indicates that a sample of about 100 patients divided into two groups would be sufficient to demonstrate a difference in tumour size within 2âyears at a power of 80.
          
            Figure 4
            
              Tumour size as the suggested endpoint.
            
            
          
          Based on the power analysis, the study seemed to be feasible only to demonstrate the effect of GKRS on tumour volume, as the number of patients needed to demonstrate difference or similarity in hearing outcomes was unrealistically high.