Group sequential design with non-constant effect • gsdmvn

The goal of gsdmvn is to enable fixed or group sequential design under non-proportional hazards. Piecewise constant enrollment, failure rates and dropout rates for a stratified population are available to enable highly flexible enrollment, time-to-event and time-to-dropout assumptions. Substantial flexibility on top of what is in the gsDesign package is intended for selecting boundaries. While this work is in progress, substantial capabilities have been enabled. Comments on usability and features are encouraged as this is a development version of the package.

The goal of gsdmvn is to enable group sequential trial design for time-to-event endpoints under non-proportional hazards assumptions. The package is still maturing; as the package functions become more stable, they will likely be included in the gsDesign2 package.

Branch specification

The development branch includes all work under development.
The table_bound branch is branched from the development branch, and it targets to get the outputs of gd_design_ahr(), gs_power_ahr(),gs_desgin_wlr(), etc., into a well-organized form.
The update_futility_bound branch is branched from the development branch, and it targets to develop code so one can update the futility bound.

Installation

You can install gsdmvn with:

remotes::install_github("Merck/gsdmvn")

Specifying enrollment and failure rates

This is a basic example which shows you how to solve a common problem. We assume there is a 4 month delay in treatment effect. Specifically, we assume a hazard ratio of 1 for 4 months and 0.6 thereafter. For this example we assume an exponential failure rate and low exponential dropout rate. The enrollRates specification indicates an expected enrollment duration of 12 months with exponential inter-arrival times.

library(gsdmvn)
library(gsDesign)
library(gsDesign2)
library(dplyr)
library(knitr)

## basic example code

## Constant enrollment over 12 months
## rate will be adjusted later by gsDesignNPH to get sample size
enrollRates <- tibble::tibble(Stratum = "All", duration = 12, rate = 1)

## 12 month median exponential failure rate in control
## 4 month delay in effect with HR=0.6 after
## Low exponential dropout rate
medianSurv <- 12
failRates <- tibble::tibble(
  Stratum = "All",
  duration = c(4, Inf),
  failRate = log(2) / medianSurv,
  hr = c(1, .6),
  dropoutRate = .001
)

The resulting failure rate specification is the following table. As many rows and strata as needed can be specified to approximate whatever patterns you wish.

failRates %>% kable()

Stratum	duration	failRate	hr	dropoutRate
All	4	0.0577623	1.0	0.001
All	Inf	0.0577623	0.6	0.001

Computing a fixed sample size design with 2.5% one-sided Type I error and 90% power. We specify a trial duration of 36 months with analysisTimes. Since there is a single analysis, we specify an upper p-value bound of 0.025 with upar = qnorm(0.975). There is no lower bound which is specified with lpar = -Inf.

design <-
  gs_design_ahr(enrollRates, failRates, upar = qnorm(.975), lpar = -Inf, IF = 1, analysisTimes = 36)

The input enrollment rates are scaled to achieve power:

design$enrollRates %>% kable()

Stratum	duration	rate
All	12	35.05288

The failure and dropout rates remain unchanged from what was input:

design$failRates %>% kable()

Stratum	duration	failRate	hr	dropoutRate
All	4	0.0577623	1.0	0.001
All	Inf	0.0577623	0.6	0.001

Finally, the expected analysis time is in Time, sample size N, events required Events and bound Z are in design$bounds. Note that AHR is the average hazard ratio used to calculate the targeted event counts. The natural parameter (log(AHR)) is in theta and corresponding statistical information under the alternate hypothesis are in info and under the null hypothesis in info0.

design$bounds %>% kable()

Analysis	Bound	Time	N	Events	Z	Probability	AHR	theta	info	info0
1	Upper	36	420.6346	311.0028	1.959964	0.9	0.6917244	0.3685676	76.74383	77.75069