Compute grid points for first interim analysis in a group sequential design
Usage
h1(r = 18, theta = 0, I = 1, a = -Inf, b = Inf)
Arguments
- r
Integer, at least 2; default of 18 recommended by Jennison and Turnbull
- theta
Drift parameter for first analysis
- I
Information at first analysis
- a
lower limit of integration (scalar)
- b
upper limit of integration (scalar > a)
Value
A list with grid points in z, numerical integration weights in w,
and a normal density with mean mu = theta * sqrt{I} and variance 1 times the weight in w.
Details
Mean for standard normal distribution under consideration is mu = theta * sqrt(I)
Specification
The contents of this section are shown in PDF user manual only.
Examples
# Replicate variance of 1, mean of 35
g <- h1(theta = 5, I = 49)
mu <- sum(g$z * g$h)
var <- sum((g$z - mu)^2 * g$h)
# Replicate p-value of .0001 by numerical integration of tail
g <- h1(a = qnorm(.9999))
sum(g$h)
#> [1] 0.0001000391