ICA.BinBin.CounterAssum: ICA (binary-binary setting) that is obtaied when the counterfactual correlations are assumed to fall within some prespecified ranges.

Description

Shows the results of ICA (binary-binary setting) in the subgroup of results where the counterfactual correlations are assumed to fall within some prespecified ranges.

Usage

ICA.BinBin.CounterAssum(x, r2_h_S0S1_min, r2_h_S0S1_max, r2_h_S0T1_min, 
r2_h_S0T1_max, r2_h_T0T1_min, r2_h_T0T1_max, r2_h_T0S1_min, r2_h_T0S1_max, 
Monotonicity="General", Type="Freq", MainPlot=" ", Cex.Legend=1, 
Cex.Position="topright", ...)

Arguments

x: An object of class ICA.BinBin. See ICA.BinBin.
r2_h_S0S1_min: The minimum value to be considered for the counterfactual correlation \(r^2_h(S_0,S_1)\).
r2_h_S0S1_max: The maximum value to be considered for the counterfactual correlation \(r^2_h(S_0,S_1)\).
r2_h_S0T1_min: The minimum value to be considered for the counterfactual correlation \(r^2_h(S_0,T_1)\).
r2_h_S0T1_max: The maximum value to be considered for the counterfactual correlation \(r^2_h(S_0,T_1)\).
r2_h_T0T1_min: The minimum value to be considered for the counterfactual correlation \(r^2_h(T_0,T_1)\).
r2_h_T0T1_max: The maximum value to be considered for the counterfactual correlation \(r^2_h(T_0,T_1)\).
r2_h_T0S1_min: The minimum value to be considered for the counterfactual correlation \(r^2_h(T_0,S_1)\).
r2_h_T0S1_max: The maximum value to be considered for the counterfactual correlation \(r^2_h(T_0,S_1)\).
Monotonicity: Specifies whether the all results in the fitted object ICA.BinBin should be shown (i.e., Monotonicity=c("General")), or a subset of the results arising under specific assumptions (i.e., Monotonicity=c("No"), Monotonicity=c("True.Endp"), Monotonicity=c("Surr.Endp"), or Monotonicity=c("Surr.True.Endp")). Default Monotonicity=c("General").
Type: The type of plot that is produced. When Type="Freq" or Type="Density", the Y-axis shows frequencies or densities of \(R^2_{H}\). When Type="All.Densities" and the fitted object of class ICA.BinBin was obtained using a general analysis (i.e., conducting the analyses assuming no monotonicity, monotonicity for \(S\) alone, monotonicity for \(T\) alone, and for both \(S\) and \(T\), so using Monotonicity=c("General") in the function call of ICA.BinBin), the density plots are shown for the four scenarios where different assumptions regarding monotonicity are made. Default "Freq".
MainPlot: The title of the plot. Default " ".
Cex.Legend: The size of the legend when Type="All.Densities" is used. Default Cex.Legend=1.
Cex.Position: The position of the legend, Cex.Position="topright" or Cex.Position="topleft". Default Cex.Position="topright".
...: Other arguments to be passed to the plot() function.

Author

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.

Examples

Run this code

if (FALSE)  #Time consuming (>5 sec) code part
# Compute R2_H given the marginals specified as the pi's, making no 
# assumptions regarding monotonicity (general case)
ICA <- ICA.BinBin.Grid.Sample(pi1_1_=0.261, pi1_0_=0.285, 
pi_1_1=0.637, pi_1_0=0.078, pi0_1_=0.134, pi_0_1=0.127,  
Monotonicity=c("General"), M=5000, Seed=1)

# Obtain a density plot of R2_H, assuming that 
# r2_h_S0S1>=.2, r2_h_S0T1>=0, r2_h_T0T1>=.2, and r2_h_T0S1>=0
ICA.BinBin.CounterAssum(ICA, r2_h_S0S1_min=.2, r2_h_S0S1_max=1, 
r2_h_S0T1_min=0, r2_h_S0T1_max=1, r2_h_T0T1_min=0.2, r2_h_T0T1_max=1, 
r2_h_T0S1_min=0, r2_h_T0S1_max=1, Monotonicity="General",
Type="Density") 

# Now show the densities of R2_H under the different 
# monotonicity assumptions 
ICA.BinBin.CounterAssum(ICA, r2_h_S0S1_min=.2, r2_h_S0S1_max=1, 
r2_h_S0T1_min=0, r2_h_S0T1_max=1, r2_h_T0T1_min=0.2, r2_h_T0T1_max=1, 
r2_h_T0S1_min=0, r2_h_T0S1_max=1, Monotonicity="General",
Type="All.Densities", MainPlot=" ", Cex.Legend=1, 
Cex.Position="topright", ylim=c(0, 20))