CumAlpha: Cumulative Alpha with various z's and ti

In sasLM: 'SAS' Linear Model

Cumulative Alpha with various z's and ti

Description

Cumulative alpha values with repeated hypothesis with changing bound z-value and time of test (ti).

Usage

  CumAlpha(z, side=2, ti=NULL, c0=NULL, Seed=5)

Arguments

z	vector of upper z-value bounds for the repeated hypothesis test
side	1=one-side test, 2=two-side test
ti	vector of times (or information amount) of test. All values should be [0, 1] and sorted. If not specified, equal interval is assumed.
c0	correlation matrix. if not specified, Brownian motion assummed.
Seed	seed value for mtvtnorm::pmvnorm function

Details

It calculates cumulative alpha-values for the repeated hypothesis test with a vector of upper bound z-value. If the times of test is not specified, linear (proportional) increase of information amount and Brownian motion of z-value, i.e. the correlation is sqrt(t_i/t_j).

Value

The result is a matrix.

ti	time of test
cum.alpha	cumulative alpha valued

Author(s)

Kyun-Seop Bae [e-mail]

References

Reboussin DM, DeMets DL, Kim K, Lan KKG. Computations for group sequential boundaries using the Lan-DeMets function method. Controlled Clinical Trials. 2000;21:190-207.

Examples

  CumAlpha(z=rep(qnorm(1 - 0.05/2), 10)) # two-side Z-test with alpha=0.05 for ten times

sasLM documentation built on Nov. 5, 2025, 7:17 p.m.