## 3-Step Tool for composite binary endpoints

Set the input parameters in the left panel according to the available information:
1. Endpoints. Essential information relative to the outcomes.
2. Correlation. Relationship between endpoints.
3. Power. Define the error probabilities to perform sample size calculations.
Select the output using the menu bar on the top of the page:
1. Summary. A brief report of general results.
2. Sample size. Total sample size needed for different scenarios.
3. Effect size. Effect size according to the correlation.
4. Endpoint selection. Choose between using a composite endpoint or one of its components as the primary endpoint of the study.
Use the explanation boxes in each tab to fully understand the results. Extra information can be find in the help menu.

#### Key questions and Summary

Correlation bounds

#### Correlation bounds

Lower Bound:

Upper Bound:

#### Control Group

Lower Bound:

Upper Bound:

#### Treatment Group

Lower Bound:

Upper Bound:

Relative Overlap

#### Control group

Probability of the composite endpoint:

Probability of the overlap:

Relative overlap:

#### Treatment group

Probability of the composite endpoint:

Probability of the overlap:

Relative overlap:

Effect Size

Risk Difference using Endpoint 1:

Risk Difference using Endpoint 2:

Risk Difference for Composite Endpoint:

#### Effect size bounds

Lower Bound:

Upper Bound:

#### Risk Difference depending on the correlation

Risk Ratio using Endpoint 1:

Risk Ratio using Endpoint 2:

Risk Ratio for Composite Endpoint:

#### Effect size bounds

Lower Bound:

Upper Bound:

#### Risk Ratio depending on the correlation

Odds Ratio using Endpoint 1:

Odds Ratio using Endpoint 2:

Odds Ratio for Composite Endpoint:

#### Effect size bounds

Lower Bound:

Upper Bound:

Sample Size

#### Please insert an interval of plausible values for the event rates

Using Endpoint 1 as the Primary Endpoint:

Using Endpoint 2 as the Primary Endpoint:

Using Composite Endpoint as the Primary Endpoint:

#### Sample size bounds

Lower Bound:

Upper Bound:

#### Sample size according to different correlation categories

(Under construction)
Using Endpoint 1 as the Primary Endpoint:

Using Endpoint 2 as the Primary Endpoint:

Using Composite Endpoint as the Primary Endpoint:

#### Sample size bounds

Lower Bound:

Upper Bound:

#### Sample size according to different correlation categories

(Under construction)
Using Endpoint 1 as the Primary Endpoint:

Using Endpoint 2 as the Primary Endpoint:

Using Composite Endpoint as the Primary Endpoint:

#### Sample size bounds

Lower Bound:

Upper Bound:

### Power calculation varying the correlation between the components

##### Suppose that we carry out a trial with a total sample size calculated using the correlation categories Weak, Moderate, Strong. The following plot illustrates the achieved power in each case.
Sample size assuming strong correlation:

Sample size assuming moderate correlation:

Sample size assuming weak correlation:

Examine how the power behaves with respect to the correlation:

Help Document

#### Sample Size accounting for departures of the anticipated values

(Under construction)

Endpoint Selection

The Asymptotic Relative Efficiency (ARE) is:

##### ARE in terms of the correlation and varying the effect on the Endpoint 2

(Under construction)