Sample Size
Sample Size
Running CompARE
For each composite component, the user is prompted for the anticipation of:
 The probability of having the event in the reference group
 The relevant effect (HR) to detect
 The correlation between endpoints
CompARE computes the Sample Size^{1} for each of the components as well as for the composite endpoint (CE) consiting of the union of both endpoints.
Input Items
 P_{01}: Probability of event for the relevant endpoint in control group
 P_{02}: Probability of successes for the additional endpoint in control group
 HR_{1}: Hazard Ratio on the Endpoint 1
 HR_{2}: Hazard Ratio on the Endpoint 2
 ρ: Correlation between endpoints (assumed equal in both groups)
 α: Significance level. Probability of detecting some treatment effect when it does not exist.
 1  β: Power. Probability of detecting some treatment effect when it exists.
Output Items
 Total sample size depending on correlation. Different SS according to the correlation. Point is drawn in the selected correlation.
 Total sample size for endpoints and CE according to different methods:

 Endpoint 1. Sample size (SS) needed in a study using only the Endpoint 1
 Endpoint 2. Sample size (SS) needed in a study using only the Endpoint 2
 Composite (Naive). Sample size (SS) for the CE obtained from aplying the classical formulas (Freedman or Schoendfeld) to the average HR of the 2 components (not recommended method)
 Composite (ARE). Sample size (SS) for the CE using the ARE to approximate the total sample size (recommended method)
 Max. HR*(t). Sample size (SS) considering the worst scenario for the HR*(t), that is, the minimum effect along time. Choose this SS to be sure that the target power is achieved
 Average HR*(t). Sample size (SS) considering the averaged HR*(t), that is, the minimum effect along time. This SS should be close to the Composite (ARE) for scenarios with HR*(t) reasonably constant over time
 Min HR*(t). Sample size (SS) considering the better scenario for the HR*(t), that is, the maximum effect along time. This is a lower bound for the SS
References
 Gomez, G., GomezMateu, M. The asymptotic relative efficiency and the ratio of sample sizes when testing two different null hypotheses.. 2014. SORT 38:73–88.