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 Assympotic Relative Efficiency1 (ARE), so that if the ARE is higher than 1, the use of the composite endpoint (CE) consiting of the union of both endpoints is recommended as the primary endpoint of the trial. If the ARE is lower than 1, the use of the Relevant endpoint is preferred over the CE as the primary endpoint of the trial.
- P01: Probability of event for the Endpoint 1 in control group
- P02: Probability of event for the Endpoint 2 in control group
- HR1: Hazard Ratio on the Endpoint 1
- HR2: Hazard Ratio on the Endpoint 2
- ρ: Spearman correlation between endpoints (assumed equal in both groups)
- Plot: Graphical representation of the ARE value according to different values of the Spearman correlation (X-axis) and different values of HR2 (lines). A point representing the selected ρ in the left panel is drawn over each line. If the whole line is above the value 1, then the use of the Composite endpoint is recommended regardless of the correlation value. On the other hand, if the whole line is below the value 1, then the use of the Composite endpoint is not recommended in any case.
- Table: ARE value according to different correlations (ρ) and different values of HR2. The other parameters are fixed:
- β1 and β2 are the selected shape parameters from the weibull distribution for the 2 endpoints: 0.5, 1 or 2 depending if the hazards are decreasing, constant or increasing over time, respectively
- P01 and P02 are the selected probabilities of having the event in the control group
- HR1 is the selected Hazard Ratio for the Endpoint 1
Zodiac Trial compared the efficacy of the Vandetanib plus docetaxel versus docetaxel as second-line treatment in patients with advanced non-small-cell lung cancer. The main endpoint is the Progression Free Survival (PFS) composed by Overall Survival (OS, Endpoint 1) and the Objective Tumor Progression (OTP, Endpoint 2). The probabilities of observing each component in the control group were P01=0.59 and P02=0.74, respectively. The reported cause-specific HRs for each component were HR1=0.91 for the OS and HR2=0.77 for the OTP. The correlation between endpoints is not reported, but it is known than the HR for the Composite endpoint (PFS) is 0.79. Under this situation, if we assume constant hazards (Risk over time) for both endpoints, the use of PFS as composite endpoint is preferred. In fact, in any combination of hazards (increasing, decreasing or constant), the design with the PFS as the primary endpoint is mors efficient than the use of the Endpoint 1.
- Gomez G, Lagakos SW. Statistical considerations when using a composite endpoint for comparing treatment. 2013. Statistics in Medicine. 32(5):719-38. doi: 10.1002/sim.5547.