In keaven/gsdmvn: Group sequential design with non-constant effect

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
library(gsdmvn)

Overview

This vignette covers how to implement designs for trials with spending assuming non-proportional hazards. We are primarily concerned with practical issues of implementation rather than design strategies, but we will not ignore design strategy.

Scenario for consideration

Here we set up enrollment, failure and dropout rates along with assumptions for enrollment duration and times of analyses.

analysisTimes <- c(18, 24, 30, 36)
enrollRates <- tibble::tibble(Stratum = "All",
                              duration = c(2, 2, 2, 6),
                              rate = c(8, 12, 16, 24))
failRates <- tibble::tibble(Stratum = "All",
                            duration=c(3,100),
                            failRate=log(2)/c(8,14),
                            hr=c(.9,.6),
                            dropoutRate=.001
                           )

Deriving power for a given sample size

We derive statistical information at targeted analysis times.

library(gsDesign2)
xx <- gsDesign2::AHR(enrollRates = enrollRates, failRates = failRates, totalDuration = analysisTimes)
Events <- ceiling(xx$Events)
yy <- gs_info_ahr(enrollRates = enrollRates, failRates = failRates, events = Events)

Now we can examine power using gs_power_npe():

zz <- gs_power_npe(theta = yy$theta, info = yy$info, info0 = yy$info0, 
             upper = gs_spending_bound, lower = gs_spending_bound,
             upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
             lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL)
)
zz

Deriving sample size to power a trial

If we were using a fixed design, we would approximate the sample size as follows:

K <- 4
minx <- ((qnorm(.025) / sqrt(zz$info0[K]) + qnorm(.1) / sqrt(zz$info[K])) / zz$theta[K])^2
minx

If we inflate the enrollment rates by minx and use a fixed design, we will see this achieves the targeted power.

gs_power_npe(theta = yy$theta[K], info = yy$info[K] * minx, info0 = yy$info0[K] * minx, upar = qnorm(.975), lpar = -Inf) %>% 
  filter(Bound == "Upper")

The power for a group sequential design with the same final sample size is a bit lower:

zz <- gs_power_npe(theta = yy$theta, info = yy$info * minx, info0 = yy$info0 * minx, 
             upper = gs_spending_bound, lower = gs_spending_bound,
             upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
             lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL)
)
zz

If we inflate this a bit we will be overpowered.

zz <- gs_power_npe(theta = yy$theta, info = yy$info * minx * 1.2, info0 = yy$info0 * minx * 1.2, 
             upper = gs_spending_bound, lower = gs_spending_bound,
             upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
             lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL)
)
zz

Now we use gs_design_npe() to inflate the information proportionately to power the trial.

theta <- yy$theta
info <- yy$info
info0 <- yy$info0
upper = gs_spending_bound
lower = gs_spending_bound
upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL)
lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL)
alpha = .025
beta = .1
binding = FALSE
test_upper = TRUE
test_lower = TRUE
r = 18
tol = 1e-06

zz <- gs_design_npe(theta = yy$theta, info = yy$info, info0 = yy$info0, 
             upper = gs_spending_bound, lower = gs_spending_bound,
             upar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL),
             lpar = list(sf = gsDesign::sfLDOF, total_spend = 0.025, param = NULL, timing = NULL)
)
zz