The function plot.PPE.BinBin plots the distribution of \(PPE\), \(RPE\) or \(R^2_{H}\) in the setting where both surrogate and true endpoints are binary in the single-trial causal-inference framework. See Details below.
# S3 method for PPE.BinBin
plot(x,Type="Density",Param="PPE",
Xlab.PE,main.PE,ylab="density",
Par=par(mfrow=c(1,1),oma=c(0,0,0,0),mar=c(5.1,4.1,4.1,2.1)),
Cex.Legend=1,Cex.Position="bottomright", lwd=3,linety=1,color=1,
Breaks=0.05,xlimits=c(0,1), ...)An object of class PPE.BinBin. See PPE.BinBin.
The type of plot that is produced. When Type="Freq", a histogram is produced. When Type="Density", a density is produced. Default Type="Density".
The parameter that is to be plotted: Param="PPE", Param="RPE" or Param="ICA". Default Param="PPE".
The label of the X-axis when density plots or histograms are produced.
Title of the density plot or histogram.
The label of the Y-axis for the density plots. Default ylab="density".
Graphical parameters for the plot. Default par(mfrow=c(1,1),oma=c(0,0,0,0),mar=c(5.1,4.1,4.1,2.1)).
The size of the legend. Default Cex.Legend=1.
The position of the legend. Default Cex.Position="bottomright".
The line width for the density plot. Default lwd=3.
The line types for the density. Default linety=1.
The color of the density or histogram. Default color=1.
The breaks for the histogram. Default Breaks=0.05.
The limits for the X-axis. Default xlimits=c(0,1).
Other arguments to be passed.
An object of class PPE.BinBin with components,
count variable
The vector of Monotonicity assumptions
The vector of the PPE values.
The vector of the RPE values.
The vector of the \(PPE_T\) values indicating the probability on a prediction error without using information on \(S\).
The vector of the \(R_H^2\) values.
The vector of the entropies of \(\Delta_T\).
The vector of the entropies of \(\Delta_S\).
The vector of the mutual information of \(\Delta_S\) and \(\Delta_T\).
An object of class data.frame that contains the valid \(\pi\) vectors.
In the continuous normal setting, surroagacy can be assessed by studying the association between the individual causal effects on \(S\) and \(T\) (see ICA.ContCont). In that setting, the Pearson correlation is the obvious measure of association.
When \(S\) and \(T\) are binary endpoints, multiple alternatives exist. Alonso et al. (2016) proposed the individual causal association (ICA; \(R_{H}^{2}\)), which captures the association between the individual causal effects of the treatment on \(S\) (\(\Delta_S\)) and \(T\) (\(\Delta_T\)) using information-theoretic principles.
The function PPE.BinBin computes \(R_{H}^{2}\) using a grid-based approach where all possible combinations of the specified grids for the parameters that are allowed that are allowed to vary freely are considered. It additionally computes the minimal probability of a prediction error (PPE) and the reduction on the PPE using information that \(S\) conveys on \(T\). Both measures provide complementary information over the \(R_{H}^{2}\) and facilitate more straightforward clinical interpretation.
Alonso A, Van der Elst W, Molenberghs G, Buyse M and Burzykowski T. (2016). An information-theoretic approach for the evaluation of surrogate endpoints based on causal inference.
Alonso A, Van der Elst W and Meyvisch P (2016). Assessing a surrogate predictive value: A causal inference approach.
# NOT RUN {
# }
# NOT RUN {
# time consuming code part
PANSS <- PPE.BinBin(pi1_1_=0.4215, pi0_1_=0.0538, pi1_0_=0.0538,
pi_1_1=0.5088, pi_1_0=0.0307,pi_0_1=0.0482,
Seed=1,Monotonicity=c( "No"), M=1000000)
plot(PANSS,Type="Freq",Param="ICA",color="grey",Breaks=0.02,xlimits=c(0,0.8),main="PANSS")
# }
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