# 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:

Parameter Effect Parameter Effect Null hypothesis Alternative hypothesis
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.