Initialize numerical integration for group sequential design

Compute grid points for first interim analysis in a group sequential design

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 tibble 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)

Examples

# Replicate variance of 1, mean of 35
h1(theta = 5, I = 49) %>% summarise(mu = sum(z * h), var = sum((z - mu)^2 * h))
#> # A tibble: 1 x 2
#>      mu   var
#>   <dbl> <dbl>
#> 1  35.0  1.00

# Replicate p-value of .0001 by numerical integration of tail
h1(a = qnorm(.9999)) %>% summarise(p = sum(h))
#> # A tibble: 1 x 1
#>          p
#>      <dbl>
#> 1 0.000100