In keaven/gsDesign2: Group Sequential Design with Non-Constant Effect

knitr::opts_chunk$set(fig.width = 5, fig.height = 4, fig.align = 'center') 

library(gt)
library(tibble)
library(dplyr)
library(testthat)
devtools::load_all()
#library(gsDesign2)

Introduction of gs_info_ahr()

tEvents() calculate the analysis time (Time in its output), number of events (Events in its output), average hazard ratio (AHR in its outputs), effect size (theta in its output), statistical information (info and info0 in its output) using an average hazard ratio model.

The aforementioned calculation is based on piecewise model: + piecewise constant enrollment rates + piecewise exponential failure rates + piecewise censoring rates.

Use Cases

Example 1

In this example, we only input the target number of events by events = ..., and derive the time when these events will be arrived.

enrollRates <- tibble(Stratum = "All", duration = c(2, 2, 10), rate = c(3, 6, 9) * 5)
failRates <- tibble(Stratum = "All", duration = c(3, 100), failRate = log(2) / c(9, 18), hr = c(.9, .6), dropoutRate = rep(.001, 2))
ratio <- 1

gs_info_ahr(enrollRates = enrollRates, failRates = failRates,
            ratio = ratio, events = c(50, 80, 100))

Example 2

In this example, we only input the analysis time by analysisTimes = ..., and derive the number of events at these analysis time.

enrollRates <- tibble(Stratum = "All", duration = c(2, 2, 10), rate = c(3, 6, 9) * 5)
failRates <- tibble(Stratum = "All", duration = c(3, 100), failRate = log(2) / c(9, 18), hr = c(.9, .6), dropoutRate = rep(.001, 2))
ratio <- 1

gs_info_ahr(enrollRates = enrollRates, failRates = failRates,
            ratio = ratio, analysisTimes = c(10, 15, 20))

Example 3

In this example, we both input analysisTimes = ... and events = .... In this case, one will see + the derived analysis time (Time column) $\geq$ input analysisTimes + the derived number of event (Events column) $\geq$ input events

enrollRates <- tibble(Stratum = "All", duration = c(2, 2, 10), rate = c(3, 6, 9) * 5)
failRates <- tibble(Stratum = "All", duration = c(3, 100), failRate = log(2) / c(9, 18), hr = c(.9, .6), dropoutRate = rep(.001, 2))
ratio <- 1

gs_info_ahr(enrollRates = enrollRates, failRates = failRates,
            ratio = ratio, analysisTimes = c(10, 15, 20), events = c(80,  # > events in example 2 
                                                                     140, # < > events in example 2 
                                                                     220  # > events in example 2 
                                                                     ))

Inner Logic of gs_info_ahr()

To explain the inner logic of gs_info_ahr(), we discuss 3 scenario.

1. only input analysisTimes
2. only input events
3. both input analysisTimes and events

Scenario 1: only input analysisTimes

If only analysisTimes = ... is input, essentially, gs_info_ahr() uses AHR() to calculate the number of events at these analysisTimes.

enrollRates <- tibble(Stratum = "All", duration = c(2, 2, 10), rate = c(3, 6, 9) * 5)
failRates <- tibble(Stratum = "All", duration = c(3, 100), failRate = log(2) / c(9, 18), hr = c(.9, .6), dropoutRate = rep(.001, 2))
ratio <- 1
analysisTimes <- c(10, 15, 20)

AHR(enrollRates = enrollRates, failRates = failRates, 
    ratio = ratio, totalDuration = analysisTimes) %>% 
  mutate(theta = -log(AHR), Analysis = 1 : length(analysisTimes)) %>% 
  select(Analysis, Time, Events, AHR, theta, info, info0) %>% 
  gt()

This is exactly the output from gs_info_ahr():

gs_info_ahr(enrollRates = enrollRates, failRates = failRates, 
            ratio = ratio, analysisTimes = analysisTimes) %>% gt()

Scenario 2: only input events

If only events = ... is input, essentially, gs_info_ahr() uses tEvents() to calculate the time when these events will be arrived.

enrollRates <- tibble(Stratum = "All", duration = c(2, 2, 10), rate = c(3, 6, 9) * 5)
failRates <- tibble(Stratum = "All", duration = c(3, 100), failRate = log(2) / c(9, 18), hr = c(.9, .6), dropoutRate = rep(.001, 2))
ratio <- 1
events <- c(70, 150, 200)

ans <- NULL
for(i in seq_along(events)){
  ans_new <- gsDesign2::tEvents(enrollRates = enrollRates, failRates = failRates, 
                                ratio = ratio, targetEvents = events[i])
  ans <- rbind(ans, ans_new)
}

ans %>% 
  mutate(theta = -log(AHR), Analysis = 1 : length(analysisTimes)) %>% 
  select(Analysis, Time, Events, AHR, theta, info, info0) %>% 
  gt()

This is exactly the output from gs_info_ahr():

gs_info_ahr(enrollRates = enrollRates, failRates = failRates, 
            ratio = ratio, events = events) %>% gt()

Scenario 3: both input analysisTimes and events

If both analysisTimes = ... and events = ... are input, gs_info_ahr() uses both AHR() and tEvents(). In this way, it is guaranteed that + the derived number of event (Events column) $\geq$ input events + the derived analysis time (Time column) $\geq$ input analysisTimes

enrollRates <- tibble(Stratum = "All", duration = c(2, 2, 10), rate = c(3, 6, 9) * 5)
failRates <- tibble(Stratum = "All", duration = c(3, 100), failRate = log(2) / c(9, 18), hr = c(.9, .6), dropoutRate = rep(.001, 2))
ratio <- 1
analysisTimes <- c(10, 15, 20)
events <- c(70, 150, 200)

ans <- NULL

# first, use `AHR()` to calculate the number of events at the input `analysisTimes`
ans <- AHR(enrollRates = enrollRates, failRates = failRates, 
           ratio = ratio, totalDuration = analysisTimes)

# second, compare if the events derived above meet the targeted number of events input in `events`
for(i in seq_along(events)){
  if (ans$Events[i] < events[i]){
    ans[i,] <- tEvents(enrollRates = enrollRates, failRates = failRates, 
                       ratio = ratio, targetEvents = events[i])
  }
}

ans %>% 
  mutate(theta = -log(AHR), Analysis = 1 : length(analysisTimes)) %>% 
  select(Analysis, Time, Events, AHR, theta, info, info0) %>% 
  gt()

This is exactly the output from gs_info_ahr():

gs_info_ahr(enrollRates = enrollRates, failRates = failRates, 
            ratio = ratio, events = events, analysisTimes = analysisTimes) %>% gt()

keaven/gsDesign2 documentation built on Oct. 13, 2022, 8:42 p.m.