nNormal.R
In gsDesign: Group Sequential Design

## ----include=FALSE--------------------------------------
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  dev = "ragg_png",
  dpi = 96,
  fig.retina = 1,
  fig.width = 7.2916667,
  fig.asp = 0.618,
  fig.align = "center",
  out.width = "80%"
)

## ----echo=FALSE, message=FALSE, warning=FALSE-----------
library(gsDesign)
library(tidyr)
library(knitr)

## -------------------------------------------------------
r <- 2
sigma <- sqrt((1 + r) * (1.6^2 + 1.25^2 / r))
theta <- 0.8 / sigma
((qnorm(.9) + qnorm(.975)) / theta)^2

## -------------------------------------------------------
nNormal(delta1 = 0.8, sd = 1.6, sd2 = 1.25, alpha = 0.025, n = 200, ratio = 2)

## -------------------------------------------------------
pwr <- pnorm(qnorm(.975) - sqrt(200) * theta, lower.tail = FALSE)
pwr

## -------------------------------------------------------
n <- 100:200
pwrn <- nNormal(delta1 = 0.8, sd = 1.6, sd2 = 1.25, alpha = 0.025, n = n, ratio = 2)
plot(n, pwrn, type = "l")

## -------------------------------------------------------
delta1 <- seq(.5, 1, .025)
pwrdelta1 <- nNormal(delta1 = delta1, sd = 1.6, sd2 = 1.25, alpha = 0.025, n = 200, ratio = 2)
plot(delta1, pwrdelta1, type = "l")

## -------------------------------------------------------
nsim <- 1000000
delta <- 0.8
sd1 <- 1.6
sd2 <- 1.25
n1 <- 67
n2 <- 133
deltahat <- rnorm(n = nsim, mean = delta, sd = sd1 / sqrt(n1)) -
  rnorm(n = nsim, mean = 0, sd = sd2 / sqrt(n2))
s <- sqrt(
  sd1^2 * rchisq(n = nsim, df = n1 - 1) / (n1 - 1) / n1 +
    sd2^2 * rchisq(n = nsim, df = n2 - 1) / (n2 - 1) / n2
)
z <- deltahat / s
mean(z >= qnorm(.975))

## -------------------------------------------------------
sqrt(pwr * (1 - pwr) / nsim)

## -------------------------------------------------------
d <- gsDesign(
  k = 2,
  n.fix = nNormal(delta1 = 0.8, sd = 1.6, sd2 = 1.25, alpha = 0.025, beta = .1, ratio = 2),
  delta1 = 0.8
)
d %>%
  gsBoundSummary(deltaname = "Mean difference") %>%
  kable(row.names = FALSE)

## ----results='asis'-------------------------------------
cat(summary(d))

## -------------------------------------------------------
gsDesign(
  k = 2,
  delta = theta,
  delta1 = 0.8
) %>%
  gsBoundSummary(deltaname = "Mean difference") %>%
  kable(row.names = FALSE)