This function calculates the probability of the composite binary endpoint formed by a combination of two events (E1 and E2).
This probability is calculated by means of the probabilities of the composite components (E1 and E2) and the correlation between them in terms of Pearson's correlation coefficient.

prob_cbe(p_e1, p_e2, rho)

## Arguments

p_e1 |
numeric parameter, probability of the event E1 |

p_e2 |
numeric parameter, probability of the event E2 |

rho |
numeric parameter, Pearson's correlation between E1 and E2 |

## Value

Returns the probability of the composite endpoint (E1 or E2).

## Details

The input parameters stand for the probability of the composite components and Pearson's correlation between the two components.
Note that Pearson's correlation takes values between two bounds that depend on the probabilities p0_e1 and p0_e2.
To calculate the correlation bounds you can use the R functions lower_corr and upper_corr, available in this package.

## References

Bofill Roig, M., & Gomez Melis, G. (2019). A new approach for sizing trials with composite binary endpoints using anticipated marginal values and accounting for the correlation between components. Statistics in Medicine, 38(11), 1935-1956. https://doi.org/10.1002/sim.8092

## Examples

CompAREdesign::prob_cbe(p_e1=0.1, p_e2=0.2, rho=0)

#> [1] 0.28