Hwang-Shih-DeCani Spending Function

The function sfHSD implements a Hwang-Shih-DeCani spending function.

A Hwang-Shih-DeCani spending function takes the form $$f(t;\alpha, \gamma)=\alpha(1-e^{-\gamma t})/(1-e^{-\gamma})$$ where $\gamma$ is the value passed in param. A value of $\gamma=-4$ is used to approximate an O'Brien-Fleming design (see sfExponential for a better fit), while a value of $\gamma=1$ approximates a Pocock design well.

Usage

sfHSD(alpha, t, param)

Arguments

alpha: Real value $> 0$ and no more than 1. Normally, alpha=0.025 for one-sided Type I error specification or alpha=0.1 for Type II error specification. However, this could be set to 1 if for descriptive purposes you wish to see the proportion of spending as a function of the proportion of sample size/information.
t: A vector of points with increasing values from 0 to 1, inclusive. Values of the proportion of sample size/information for which the spending function will be computed.
param: A single real value specifying the gamma parameter for which Hwang-Shih-DeCani spending is to be computed; allowable range is [-40, 40]

Value

An object of type spendfn. See vignette("SpendingFunctionOverview") for further details.

Note

The gsDesign technical manual is available at https://keaven.github.io/gsd-tech-manual/.

References

Jennison C and Turnbull BW (2000), Group Sequential Methods with Applications to Clinical Trials. Boca Raton: Chapman and Hall.

Author

Keaven Anderson keaven_anderson@merck.com