CausalDiagramBinBin {Surrogate}

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

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, 
Densities.Correlations=FALSE)

Arguments

x

An object of class ICA.BinBin. See ICA.BinBin.

Values

Specifies whether the median informational coefficients of correlation or median odds ratios between the counterfactuals should be depicted, i.e., Values="Corrs" or Values="ORs".

Theta_T0S0

The odds ratio between T and S in the control group. This quantity is estimable based on the observed data. Only has to be provided when Values="ORs".

Theta_T1S1

The odds ratio between T and S in the experimental treatment group. This quantity is estimable based on the observed data. Only has to be provided when Values="ORs".

Min

The minimum value of R_{H}^{2} that should be considered. Default=-1.

Max

The maximum value of R_{H}^{2} that should be considered. Default=1.

Cex.Letters

The size of the symbols for the counterfactuals (S_0, S_1), T_0, T_1). Default=3.

Cex.Corrs

The size of the text depicting the median odds ratios between the counterfactuals. Default=2.

Lines.Rel.Width

Logical. When Lines.Rel.Width=TRUE, the widths of the lines that represent the odds ratios between the counterfactuals are relative to the size of the odds ratios (i.e., a smaller/thicker line is used for smaller/higher odds ratios. When Lines.Rel.Width=FALSE, the width of all lines representing the odds ratios between the counterfactuals is identical. Default=TRUE. Only considered when Values="ORs".

Col.Pos.Neg

Logical. When Col.Pos.Neg=TRUE, the color of the lines that represent the odds ratios between the counterfactuals is red for odds ratios below 1 and black for the ones above 1. When Col.Pos.Neg=FALSE, all lines are in black. Default=TRUE. Only considered when Values="ORs".

Monotonicity

Specifies the monotonicity scenario that should be considered (i.e., Monotonicity=c("No"), Monotonicity=c("True.Endp"), Monotonicity=c("Surr.Endp"), or Monotonicity=c("Surr.True.Endp")).

Histograms.Correlations

Should histograms of the informational coefficients of association R_{H}^{2} be provided? Default Histograms.Correlations=FALSE.

Densities.Correlations

Should densities of the informational coefficients of association R_{H}^{2} be provided? Default Densities.Correlations=FALSE.

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 R_{H}^{2} between T_0 and T_1.

R2_H_S1T0

The informational coefficients of association R_{H}^{2} between S_1 and T_0.

R2_H_S0T1

The informational coefficients of association R_{H}^{2} between S_0 and T_1.

R2_H_S0S1

The informational coefficients of association R_{H}^{2} between S_0 and S_1.

R2_H_S0T0

The informational coefficients of association R_{H}^{2} between S_0 and T_0.

R2_H_S1T1

The informational coefficients of association R_{H}^{2} between S_1 and T_1.

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

# 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")