PROC.BinBin {Surrogate}

Evaluate the individual causal association (ICA) and reduction in probability of a prediction error (RPE) in the setting where both S and T are binary endpoints

Description

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.

Usage

PROC.BinBin(Dataset=Dataset, Surr=Surr, True=True, Treat=Treat, 
BS=FALSE, seqs=250, MC_samples=1000, Seed=1)

Arguments

Dataset

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.

Surr

The name of the variable in Dataset that contains the binary surrogate endpoint values. Should be coded as 0 and 1.

True

The name of the variable in Dataset that contains the binary true endpoint values. Should be coded as 0 and 1.

Treat

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.

BS

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.

seqs

The number of copies of the dataset that are produced or alternatively the number of bootstrap datasets that are produced. Default seqs=250.

MC_samples

The number of Monte Carlo samples that need to be obtained per copy of the data set. Default MC_samples=1000.

Seed

The seed to be used. Default Seed=1.

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 (\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.

Value

An object of class PPE.BinBin with components,

PPE

The vector of the PPE values.

RPE

The vector of the RPE values.

PPE_T

The vector of the PPE_T values indicating the probability on a prediction error without using information on S.

R2_H

The vector of the R_H^2 values.

Author(s)

Paul Meyvisch, Wim Van der Elst, Ariel Alonso, Geert Molenberghs

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.. 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

# 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)

## End(Not run)