comb27.BinBin: Assesses the surrogate predictive value of each of the 27...

In Surrogate: Evaluation of Surrogate Endpoints in Clinical Trials

Assesses the surrogate predictive value of each of the 27 prediction functions in the setting where both S and T are binary endpoints

Description

The function comb27.BinBin assesses a surrogate predictive value of each of the 27 possible prediction functions in the single-trial causal-inference framework when both the surrogate and the true endpoints are binary outcomes. The distribution of frequencies at which each of the 27 possible predicton functions are selected provides additional insights regarding the association between S (\Delta_S) and T (\Delta_T). See Details below.

Usage

comb27.BinBin(pi1_1_, pi1_0_, pi_1_1, pi_1_0, 
pi0_1_, pi_0_1, Monotonicity=c("No"),M=1000, Seed=1)

Arguments

pi1_1_	A scalar that contains values for P(T=1,S=1|Z=0), i.e., the probability that S=T=1 when under treatment Z=0.
pi1_0_	A scalar that contains values for P(T=1,S=0|Z=0).
pi_1_1	A scalar that contains values for P(T=1,S=1|Z=1).
pi_1_0	A scalar that contains values for P(T=1,S=0|Z=1).
pi0_1_	A scalar that contains values for P(T=0,S=1|Z=0).
pi_0_1	A scalar that contains values for P(T=0,S=1|Z=1).
Monotonicity	Specifies which assumptions regarding monotonicity should be made, only one assumption can be made at the time: Monotonicity=c("No"), Monotonicity=c("True.Endp"), Monotonicity=c("Surr.Endp"), or Monotonicity=c("Surr.True.Endp"). Default Monotonicity=c("No").
M	The number of random samples that have to be drawn for the freely varying parameters. Default M=100000.
Seed	The seed to be used to generate \pi_r. 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 comb27.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 computes the probability of a prediction error for each of the 27 possible prediction functions.The frequency at which each prediction function is selected provides additional insight about the minimal probability of a prediction error PPE which can be obtained with PPE.BinBin.

Value

An object of class comb27.BinBin with components,

index	count variable
Monotonicity	The vector of Monotonicity assumptions
Pe	The vector of the prediction error values.
combo	The vector containing the codes for the each of the 27 prediction functions.
R2_H	The vector of the R_H^2 values.
H_Delta_T	The vector of the entropies of \Delta_T.
H_Delta_S	The vector of the entropies of \Delta_S.
I_Delta_T_Delta_S	The vector of the mutual information of \Delta_S and \Delta_T.

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.

Alonso A, Van der Elst W and Meyvisch P (2016). Assessing a surrogate predictive value: A causal inference approach.

See Also

PPE.BinBin

Examples

# Conduct the analysis assuming no montonicity
 
## Not run:  # time consuming code part
comb27.BinBin(pi1_1_ = 0.3412, pi1_0_ = 0.2539, pi0_1_ = 0.119, 
              pi_1_1 = 0.6863, pi_1_0 = 0.0882, pi_0_1 = 0.0784,  
              Seed=1,Monotonicity=c("No"), M=500000) 

## End(Not run)

Surrogate documentation built on Sept. 25, 2023, 5:07 p.m.