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 Size1 for each of the components as well as for the composite endpoint (CE) consiting of the union of both endpoints.

### Input Items

• P01: Probability of event for the relevant endpoint in control group
• P02: Probability of successes for the additional endpoint in control group
• HR1: Hazard Ratio on the Endpoint 1
• HR2: 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

1. Gomez, G., Gomez-Mateu, M. The asymptotic relative efficiency and the ratio of sample sizes when testing two different null hypotheses.. 2014. SORT 38:73–88.