Surrogate (version 2.0)

plot.PPE.BinBin: Plots the distribution of either $PPE$, $RPE$ or $R_H^2$ either as a density or as a histogram in the setting where both $S$ and $T$ are binary endpoints

Description

The function plot.PPE.BinBin plots the distribution of $PPE$, $RPE$ or $R_H^2$ in the setting where both surrogate and true endpoints are binary in the single-trial causal-inference framework. See Details below.

Usage

# S3 method for PPE.BinBin
plot(x,Type="Density",Param="PPE",Xlab.PE,main.PE,
ylab="density",Cex.Legend=1,Cex.Position="bottomright", lwd=3,linety=1,color=1,
Breaks=0.05, xlimits=c(0,1), …)

Arguments

x

An object of class PPE.BinBin. See PPE.BinBin.

Type

The type of plot that is produced. When Type="Freq", a histogram is produced. When Type="Density", a density is produced. Default Type="Density".

Param

Parameter to be plotted: is either "PPE", "RPE" or "ICA"

Xlab.PE

The label of the X-axis when density plots or histograms are produced.

main.PE

Title of the density plot or histogram.

ylab

The label of the Y-axis for the density plots. Default ylab="density".

Cex.Legend

The size of the legend. Default Cex.Legend=1.

Cex.Position

The position of the legend. Default Cex.Position="bottomright".

lwd

The line width for the density plot. Default lwd=3.

linety

The line types for the density. Default linety=1.

color

The color of the density or histogram. Default color=1.

Breaks

The breaks for the histogram. Default Breaks=0.05.

xlimits

The limits for the X-axis. Default xlimits=c(0,1).

...

Other arguments to be passed.

Value

An object of class PPE.BinBin with components,

index

count variable

PPE

The vector of the PPE values.

RPE

The vector of the RPE values.

PPE_T

The vector of the $PP{E}_T$ values indicating the probability on a prediction error without using information on $S$.

R2_H

The vector of the $R_H^2$ values.

H_Delta_T

The vector of the entropies of ${\mathrm{\Delta }}_T$.

H_Delta_S

The vector of the entropies of ${\mathrm{\Delta }}_S$.

I_Delta_T_Delta_S

The vector of the mutual information of ${\mathrm{\Delta }}_S$ and ${\mathrm{\Delta }}_T$.

Pi.Vectors

An object of class data.frame that contains the valid $\pi$ vectors.

Details

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 $S$ (${\mathrm{\Delta }}_S$) and $T$ (${\mathrm{\Delta }}_T$) 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.

References

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.

Meyvisch P., Alonso A.,Van der Elst W, Molenberghs G. (2018). Assessing the predictive value of a binary surrogate for a binary true endpoint, based on the minimum probability of a prediction error.

See Also

PPE.BinBin

Examples

# NOT RUN {
# Time consuming 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, M=2500) 
                   
plot(PANSS,Type="Freq",Param="RPE",color="grey",Breaks=0.05,xlimits=c(0,1),main="PANSS")
# }