Group sequential design bounds.
import Pkg; Pkg.add("SeqBounds")
using SeqBounds
bounds([0.25, 0.5, 0.75, 1.0], 0.05; h = 0.05)
Result:
julia> bounds([0.25, 0.5, 0.75, 1.0], 0.05; h = 0.05)
One-sided group sequential design
Alpha spending function: O'Brien-Fleming, Alpha = 0.05
┌─────────┬────────────────┬────────────┬─────────┬────────────┐
│ Portion │ Function value │ Spend │ Z │ Nominal p │
├─────────┼────────────────┼────────────┼─────────┼────────────┤
│ 0.25 │ 8.85754e-5 │ 8.85754e-5 │ 3.74955 │ 8.85754e-5 │
│ 0.5 │ 0.0055746 │ 0.00548602 │ 2.53993 │ 0.00554366 │
│ 0.75 │ 0.0236251 │ 0.0180505 │ 2.01604 │ 0.0218979 │
│ 1.0 │ 0.05 │ 0.0263749 │ 1.72014 │ 0.0427037 │
└─────────┴────────────────┴────────────┴─────────┴────────────┘
bounds(v::Vector, alpha::Float64; side = :one, asf = :obf, h::Float64 = 0.05)
Where:
-
v- vector of information portion for each interim analysis; -
alpha- total alpha level; -
h- grid step multiplier, default 0.05, use 0.025 for better precision. -
v- vector of information portion for each interim analysis; -
alpha- total alpha level; -
side- one- or two- sided test (:one or :two); -
asf- alpha spending function (:obf, :pocock, :power, :ep); -
h- grid step multiplier, default 0.05, use 0.025 for better precision.
asf:
:obf - O'Brien-Fleming function
2(1 - cdf(Normal(), quantile(Normal(), 1 - α / side / 2)/sqrt(t)))
:pocock - Pocock function.
α / side * log(1 + (exp(1) - 1) * t)
:power - power function.
α / side * t^γ
:ep - equal parts.
- Reboussin, D. M., DeMets, D. L., Kim, K., & Lan, K. K. G. (2000). Computations for Group Sequential Boundaries Using the Lan-DeMets Spending Function Method. Controlled Clinical Trials, 21(3), 190–207. doi:10.1016/s0197-2456(00)00057-x
- O’Brien, P. C., & Fleming, T. R. (1979). A Multiple Testing Procedure for Clinical Trials. Biometrics, 35(3), 549. doi:10.2307/2530245
- Lan KKG, DeMets DL. Discrete sequential boundaries for clinical trials. Biometrika. 1983; 70:659-63.
- DeMets DL, Lan G. “The alpha spending function approach to interim data analyses” in Recent Advances in Clinical Trial Design and Analysis, ed. PF Thall. Kluwer Academic Publishers, Boston; 1995.
- Armitage P, McPherson CK, Rowe BC. Repeated significance tests on accumulating data. Journal of the Royal Statistical Society. 1969; 132:235-44
- ldbounds: Lan-DeMets Method for Group Sequential Boundaries - https://CRAN.R-project.org/package=ldbounds (comparation)