# Draws a causal diagram depicting the median informational coefficients of correlation (or odds ratios) between the counterfactuals for a specified range of values of the ICA in the binary-binary setting.

### Description

This function provides a diagram that depicts the medians of the informational coefficients of correlation (or odds ratios) between the counterfactuals for a specified range of values of the individual causal association in the binary-binary setting (*R_{H}^{2}*).

### Usage

1 2 3 | ```
CausalDiagramBinBin(x, Values="Corrs", Theta_T0S0, Theta_T1S1,
Min=0, Max=1, Cex.Letters=3, Cex.Corrs=2, Lines.Rel.Width=TRUE,
Col.Pos.Neg=TRUE, Monotonicity, Histograms.Correlations=FALSE)
``` |

### Arguments

`x` |
An object of class |

`Values` |
Specifies whether the median informational coefficients of correlation or median odds ratios between the counterfactuals should be depicted, i.e., |

`Theta_T0S0` |
The odds ratio between |

`Theta_T1S1` |
The odds ratio between |

`Min` |
The minimum value of |

`Max` |
The maximum value of |

`Cex.Letters` |
The size of the symbols for the counterfactuals ( |

`Cex.Corrs` |
The size of the text depicting the median odds ratios between the counterfactuals. Default= |

`Lines.Rel.Width` |
Logical. When |

`Col.Pos.Neg` |
Logical. When |

`Monotonicity` |
Specifies the monotonicity scenario that should be considered (i.e., |

`Histograms.Correlations` |
Should histograms of the informational coefficients of association |

### Value

The following components are stored in the fitted object if histograms of the informational correlations are requested in the function call (i.e., if `Histograms.Correlations=TRUE`

and `Values="Corrs"`

in the function call):

`R2_H_T0T1` |
The informational coefficients of association |

`R2_H_S1T0` |
The informational coefficients of association |

`R2_H_S0T1` |
The informational coefficients of association |

`R2_H_S0S1` |
The informational coefficients of association |

`R2_H_S0T0` |
The informational coefficients of association |

`R2_H_S1T1` |
The informational coefficients of association |

### Author(s)

Wim Van der Elst, Ariel Alonso, & Geert Molenberghs

### References

Alonso, A., Van der Elst, W., Molenberghs, G., Buyse, M., & Burzykowski, T. (submitted). On the relationship between the causal inference and meta-analytic paradigms for the validation of surrogate markers.

Van der Elst, W., Alonso, A., & Molenberghs, G. (submitted). An exploration of the relationship between causal inference and meta-analytic measures of surrogacy.

### See Also

ICA.BinBin

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
# Compute R2_H given the marginals specified as the pi's
ICA <- ICA.BinBin.Grid.Sample(pi1_1_=0.2619048, pi1_0_=0.2857143,
pi_1_1=0.6372549, pi_1_0=0.07843137, pi0_1_=0.1349206, pi_0_1=0.127451,
Seed=1, Monotonicity=c("General"), M=1000)
# Obtain a causal diagram that provides the medians of the
# correlations between the counterfactuals for the range
# of R2_H values between 0.1 and 1
# Assume no monotonicty
CausalDiagramBinBin(x=ICA, Min=0.1, Max=1, Monotonicity="No")
# Assume monotonicty for S
CausalDiagramBinBin(x=ICA, Min=0.1, Max=1, Monotonicity="Surr.Endp")
# Now only consider the results that were obtained when
# monotonicity was assumed for the true endpoint
CausalDiagramBinBin(x=ICA, Values="ORs", Theta_T0S0=2.156, Theta_T1S1=10,
Min=0, Max=1, Monotonicity="True.Endp")
``` |