The function PROC.BinBin assesses the ICA and RPE in the single-trial causal-inference framework when both the surrogate and the true endpoints are binary outcomes. It additionally allows to account for sampling variability by means of bootstrap. See Details below.
PROC.BinBin(Dataset=Dataset, Surr=Surr, True=True, Treat=Treat,
BS=FALSE, seqs=250, MC_samples=1000, Seed=1)A data.frame that should consist of one line per patient. Each line contains (at least) a binary surrogate value, a binary true endpoint value, and a treatment indicator.
The name of the variable in Dataset that contains the binary surrogate endpoint values. Should be coded as \(0\) and \(1\).
The name of the variable in Dataset that contains the binary true endpoint values. Should be coded as \(0\) and \(1\).
The name of the variable in Dataset that contains the treatment indicators. The treatment indicator should be coded as \(1\) for the experimental group and \(-1\) for the control group.
Logical. If TRUE, then Dataset will be bootstrapped to account for sampling variability. If FALSE, then no bootstrap is performed. See the Details section below. Default FALSE.
The number of copies of the dataset that are produced or alternatively the number of bootstrap datasets that are produced. Default seqs=250.
The number of Monte Carlo samples that need to be obtained per copy of the data set. Default MC_samples=1000.
The seed to be used. Default Seed=1.
An object of class PPE.BinBin with components,
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.
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 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 \(T\) (RPE). Both measures provide complementary information over the \(R_{H}^{2}\) and facilitate more straightforward clinical interpretation. No assumption about monotonicity can be made. The function PROC.BinBin makes direct use of the function PPE.BinBin. However, it is computationally much faster thanks to equally dividing the number of Monte Carlo samples over copies of the input data. In addition, it allows to account for sampling variability using a bootstrap procedure. Finally, the function PROC.BinBin computes the marginal probabilities directly from the input data set.
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.. Assessing the predictive value of a binary surrogate for a binary true endpoint, based on the minimum probability of a prediction error.
# NOT RUN {
# Conduct the analysis
# }
# NOT RUN {
# time consuming code part
library(Surrogate)
# load the CIGTS data
data(CIGTS)
CIGTS_25000<-PROC.BinBin(Dataset=CIGTS, Surr=IOP_12, True=IOP_96,
Treat=Treat, BS=FALSE,seqs=250, MC_samples=100, Seed=1)
# }
# NOT RUN {
# }
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