Help Document: The Input Panel

CompARE Team

Running CompARE

The Input Panel provides the user with a number of input parameters to chose from. The input panel of CompARE-Time to Event is composed of three different tabs:


This is the main part of the input parameters.


Let \(T_1\) and \(T_2\) be a random variable for time to event with Weibull distribution and let \(\tau\) be the time of follow-up, then the probabilities of observing the event are:

  • \(p_1^{(0)}=P(T_1<\tau)\) in case that Endpoint 2 was not death.
  • \(p_1^{(0)}=P(T_1<\tau | T_1<T_2)\) in case that Endpoint 2 was death.
  • \(p_1^{(0)}=P(T_2<\tau)\) in case that Endpoint 1 was not death.
  • \(p_1^{(0)}=P(T_2<\tau | T_2<T_1)\) in case that Endpoint 1 was death.

Hazard Ratios for the components are assumed constant over time:

  • \(HR_1=\frac{\lambda_1^{(1)}}{\lambda_1^{(0)}}\)
  • \(HR_2=\frac{\lambda_2^{(1)}}{\lambda_2^{(0)}}\)


Set the strength of correlation between endpoints by means of Spearman’s \(\rho\) or Kendall’s \(\tau\) correlation coefficients:


  • It is assumed that the correlation between endpoints is the same in both arms.
  • It is assumed that the correlation between endpoints should be positive since it is the usual situation.
  • When there is no correlation (or weak correlation) then \(\rho = 0\) (or close to \(0\)).
  • Since most of the times, information regarding to correlation is unavailable, CompARE produces plots to visualize how much the correlation impacts on the results.
  • When some copula does not allow some ccorrelation value, the program replaces too small (large) values by lower (upper) bound. For instance, for FGM Spearman’s \(\rho\) must be in [-1/3,1/3]; a value of 0.5 will be considered as 1/3.

Alpha and Power

Set the type I and type II errors as well as the formula to perform sample size calculations:


The number of events are estimated as follows:

  • Schoendfeld \(\rightarrow\) \(E=\frac{4\cdot(Z_{1-\alpha} + Z_{\beta})^2}{\big(ln(HR)\big)^2}\)
  • Freedman \(\rightarrow\) \(E=\frac{(Z_{1-\alpha} + Z_{\beta})^2\cdot(1+HR)^2}{(1-HR)^2}\)


Define the study times:


  1. Plana O. Using Gumbel copula to assess the efficiency of the main endpoint in a randomized clinical trial and comparison with Frank copula. Master thesis, 2012. Available here:
  2. Schoenfeld D. Sample-size formula for the proportional-hazards regression model. Biometrics 1983;39:499-503
  3. Freedman LS. Tables of the number of patients required in clinical trials using the logrank test. Statistics in Medicine 1982, 1, 121-129
  4. Hsieh FY. Comparing sample size formulae for trials with unbalanced allocation using the logrank test. Stat Med 1992;11:1091-8.