Surrogate (version 1.7)

ECT: 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 \(H_Max\).

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

Run this code
# NOT RUN {
ECT_fit <- ECT(Perc = .05, H_Max = 1.981811, N=454)
summary(ECT_fit)
# }

Run the code above in your browser using DataCamp Workspace