ECT {Surrogate}

Apply the Entropy Concentration Theorem

Description

The Entropy Concentration Theorem (ECT; Edwin, 1982) states that if N is large enough, then 100(1-F)% of all \bold{p*} and \Delta H is determined by the upper tail are 1-F of a \chi^2 distribution, with DF = q - m - 1 (which equals 8 in a surrogate evaluation context).

Usage

ECT(Perc=.95, H_Max, N)

Arguments

Perc

The desired interval. E.g., Perc=.05 will generate the lower and upper bounds for H(\bold{p}) that contain 95\% of the cases (as determined by the ECT).

H_Max

The maximum entropy value. In the binary-binary setting, this can be computed using the function MaxEntICABinBin.

N

The sample size.

Value

An object of class ECT with components,

Lower_H

The lower bound of the requested interval.

Upper_H

The upper bound of the requested interval, which equals H_Max.

Author(s)

Wim Van der Elst, Paul Meyvisch, & Ariel Alonso

References

Alonso, A., Van der Elst, W., & Molenberghs, G. (2016). Surrogate markers validation: the continuous-binary setting from a causal inference perspective.

See Also

MaxEntICABinBin, ICA.BinBin

Examples

ECT_fit <- ECT(Perc = .05, H_Max = 1.981811, N=454)
summary(ECT_fit)