Running CompARE
The Input Panel provides the user with a number of input parameters to chose from. The input panel of CompARE-Binary is composed of three different tabs:
- Endpoints
- Association
- Alpha and beta
Endpoints
This is the main part of the input parameters.
- \(p_1^{(0)}\): Probability of observing the event for the endpoint 1 in control group
- \(p_2^{(0)}\): Probability of observing the event for the endpoint 2 in control group
- Measure for quantifying the effect for Endpoint 1 and/or Endpoint 2. The user can choose between:
- Odds Ratio
- Risk Ratio (or relative risk)
- Risk Difference (or difference in proportions)
- Effect\(_1\): Expected effect size (Odds Ratio / Risk Ratio / Risk Difference ) on the Endpoint 1
- Effect\(_2\): Expected effect size (Odds Ratio / Risk Ratio / Risk Difference ) on the Endpoint 2
The following table summarizes the statistical problem in each case:
| Risk difference |
\(\delta_* = p_*^{(1)} - p_*^{(0)}\) |
\(\delta_* = 0\) |
\(\delta_* < 0\) |
| Relative risk |
\(\textrm{R}_* = p_*^{(1)}/p_*^{(0)}\) |
\(\log( \textrm{R}_* ) = 0\) |
\(\log( \textrm{R}_* ) < 0\) |
| Odds ratio |
\(\textrm{OR}_* = \frac{p_*^{(1)}/q_*^{(1)}}{p_*^{(0)}/q_*^{(0)}}\) |
\(\log( \textrm{OR}_* ) = 0\) |
\(\log( \textrm{OR}_* ) < 0\) |
Correlation
Set the strength of correlation between endpoints by means of Pearson’s correlation coefficient (\(\rho\)).
Remarks:
- The correlation is bounded and its bounds depend on the marginal parameters. See Association Tab for more information.
- When there is not correlation (or weak correlation) then \(\rho = 0\) (or close to \(0\)).
Since most of the times this information is unavailable, CompARE will produce plots to visualize how much the correlation impacts on the calculations.
Alpha and Power
- \(\alpha\): Significance level. Probability of detecting some treatment effect when it does not exist.
- \(\beta\): Power. Probability of detecting some treatment effect when it exists.
- Formula: Unpooled or pooled variance estimator.