getc: Basic functions

In lilywang1988/GSMC: Group Sequential Design for Maxcombo tests

Description

Some basic functions for information prediction.

Usage

getc(theta, lambda, eps)

uv(e, k, lambda, R, t.star)

v(e, k, lambda)

u(e, k, lambda, R, t.star)

h1(k1, k2, lambda, theta, eps, R, t.star)

h0(k1, k2, lambda, theta, eps, R, t.star)

h.tilde(m, lambda, theta, eps, R, p, t.star)

Arguments

theta	Hazard ratio after the change point (before the change point HR should be 1).
lambda	Event hazard for the control arm.
eps	Change point.
e	Some convenience parameter to control the change point, which is usually set to be eps or tau
k, k1, k2, m	Parameters to control the exponential power of the survival functions (the control arm for the null hypothesis or the weighted sum of two arms for the alternative hypothesis).
R	End of the accrual period.
t.star	Time point we pause the study to check the cumulative results.
p	Treatment assignment probability.

Details

To prepare the values for the prediction of information values. The control arm is following an exponential with rate lambda, the treatment arm is piece-wise exponential with hazard ratio with respect to the control arm to be 1 before the changing point eps, and theta after the change point. Details can be found in the appendix of the reference paper.

Value

getc returns the \exp(-λ*ε*(1-θ)) which is a multiplier for the survival and hazard of the treatment arm after the change point eps.

Author(s)

Lili Wang

References

Wang, L., Luo, X., & Zheng, C. (2021). A Simulation-free Group Sequential Design with Max-combo Tests in the Presence of Non-proportional Hazards. Journal of Pharmaceutical Statistics.

lilywang1988/GSMC documentation built on March 9, 2021, 5:25 p.m.