Method2: Calculate boundaries for a group sequential design using...

In paulowhite/DelayedGSD: Planning and analysis of group sequential trial with pipeline data

Calculate boundaries for a group sequential design using Method 2

Description

Calculate boundaries for a group sequential design with delayed endpoints based planned information using an error spending approach.

Usage

Method2(
  rho_alpha = 2,
  rho_beta = 2,
  alpha = 0.025,
  beta = 0.2,
  Kmax,
  Info.max = NULL,
  InfoR.i = NULL,
  InfoR.d = NULL,
  delta = 0,
  abseps = 1e-06,
  alternative = "greater",
  binding = TRUE,
  Trace = FALSE,
  nWhileMax = 30,
  toldiff = 1e-05,
  tolcoef = 1e-04,
  mycoefMax = 1.2,
  mycoefL = 1,
  myseed = 2902,
  cMin = -Inf
)

Arguments

rho_alpha	rho parameter of the rho-family spending functions (Kim-DeMets) for alpha
rho_beta	rho parameter of the rho-family spending functions (Kim-DeMets) for beta
alpha	type I error
beta	type II error
Info.max	maximum information needed for given beta (type II-error), delta (expected difference), alpha (type I-error) and Kmax. It can be given if it is known. Otherwise it is computed from the values given for alpha, beta, delta and Kmax.
InfoR.i	Expected or observed (wherever possible) information rates at the interim analyses 1:(Kmax-1)
InfoR.d	Expected or observed information rates at all potential decision analyses and final analyses 1:Kmax
delta	expected effect under the alternative (should be on the scale of the test statistc for which If and Info.max relate to one over the variance, e.g. delta=expected log(Hazard ratio))
abseps	tolerance for precision when finding roots or computing integrals
alternative	a character string specifying the alternative hypothesis, "greater" or "less". H0 \theta=0 vs H1 theta<0 ("less") or theta > 0 ("greater"). Note that in Jennison and Turnbull's book chapter (2013) they consider "greater".
binding	whether we assume binding futility boundaries
Trace	Used only if Info.max=NULL. Whether to print informations to follow the progression of the (root finding) algorithm to compute Info.max (from alpha, beta, delta and Kmax).
nWhileMax	Used only if Info.max=NULL. Maximum number of steps in the (root finding) algorithm to compute Info.max (from alpha, beta, delta and Kmax)
toldiff	Used only if Info.max=NULL. Maximum tolerated difference between lower and upper bounds at anaylis Kmax (which souhld be zero), in the root finding algorithm, to find the value of Info.max
tolcoef	Used only if Info.max=NULL. Maximum tolerated difference before stopping the search (in the root finding algorithm), between two successive values for the multiplier coeficient 'coef' such that Info.max=coef*If (some values for coef are given in Table 7.6 page 164 Jennison's book. The value of "If" (which stands for Information for Fixed design) corresponds to the information we need if Kmax=1)
mycoefMax	Used only if Info.max=NULL. Upper limit of the interval of values in which we search for the multiplier coeficient 'coef' such that Info.max=coef*If (in the root finding algorithm).
mycoefL	Used only if Info.max=NULL. Lower limit of the interval (see mycoefMax)
myseed	seed for producing reproducible results. Because we call functions which are based on Monte-Carlo compuation (pmvnorm)
cMin	minimun possible value c for the decision analysis, typically that for a fixed sample test (H & J page 10)
kMax	max number of analyses (including final)

Examples

Example to check that code matches
b1 <- CalcBoundaries(kMax=2,  #max number of analyses (including final)
                    alpha=0.025,  #type I error
                    beta=0.2,  #type II error
                    InfoR.i=c(0.6,1),  #planned information rates
                    rho_alpha=2,  #rho parameter for alpha error spending function
                    rho_beta=2,  #rho parameter for beta error spending function
                    method=1,  #use method 1 or 2 from paper H&J
                    delta=1.5,  #effect that the study is powered for
                    InfoR.d=0.65,
                    bindingFutility=TRUE)

b12 <- Method2(Kmax=2,Info.max=b1$Info.max,delta=1.5,alpha=0.025,InfoR.i=c(0.6,1),InfoR.d=0.65)


b1FT <- CalcBoundaries(kMax=2,  #max number of analyses (including final)
                    alpha=0.025,  #type I error
                    beta=0.2,  #type II error
                    InfoR.i=c(0.6,1),  #planned information rates
                    rho_alpha=2,  #rho parameter for alpha error spending function
                    rho_beta=2,  #rho parameter for beta error spending function
                    method=1,  #use method 1 or 2 from paper H&J
                    delta=1.5,  #effect that the study is powered for
                    InfoR.d=0.65,
                    bindingFutility=TRUE)

b12FT <- Method2(Kmax=2,Info.max=b1FT$Info.max,delta=1.5,binding=TRUE,alpha=0.025,InfoR.i=c(0.6,1),InfoR.d=0.65)

b12FTNoImax <- Method2(Kmax=2,Info.max=NULL,delta=1.5,binding=TRUE,alpha=0.025,InfoR.i=c(0.6,1),InfoR.d=0.65)



all.equal(b1$uk, b12$boundaries[,"b.k"])
all.equal(b1$lk, b12$boundaries[,"a.k"])

b13 <- Method2(Kmax=2,delta=1.5,alpha=0.025,Trace=T,InfoR.i=c(0.6,1))

b14nb <- Method2(Kmax=2,delta=1.5,alpha=0.025,Trace=T,InfoR.i=c(0.6,1),InfoR.d=0.65,binding=F)

b14b <- Method2(Kmax=2,delta=1.5,alpha=0.025,Trace=T,InfoR.i=c(0.6,1),InfoR.d=0.65,binding=T)

paulowhite/DelayedGSD documentation built on Nov. 1, 2023, 5:36 p.m.