Reproduce Figure 2 of Pocock, et al (2002)

pocock_fig_2.R

# replicate Fig 2 of 
# Pocock, S.J., Assmann, S.E., Enos, L.E. and Kasten, L.E. (2002), 
# Subgroup analysis, covariate adjustment and baseline comparisons in clinical trial reporting: current practiceand problems. 
# Statist. Med., 21: 2917-2930. https://doi.org/10.1002/sim.1296

Z_x <- seq(-2, 2, 0.1)
rho <- c(0, 0.1, 0.3, 0.5, 0.7, 0.9)
d <- expand.grid(Z_x = Z_x, rho = rho)
Z_a <- qnorm(0.025, lower.tail = F)
d$size <- pnorm((Z_a - d$Z_x*d$rho)/sqrt(1 - d$rho^2), 
                lower.tail = F)
d$size2 <- qnorm(d$size)


library(ggplot2)
ggplot(d) +
  aes(x = Z_x, y = size2, color = factor(rho)) +
  geom_line() +
  scale_y_reverse(limits = c(-0.5, -3.1), 
                  breaks = qnorm(c(0.3, 0.2, 0.1, 0.05, 0.025, 
                                   0.01, 0.005, 0.002, 0.001)), 
                  labels = c(0.3, 0.2, 0.1, 0.05, 0.025, 
                             0.01, 0.005, 0.002, 0.001),
                  minor_breaks = NULL) +
  labs(color = "rho", x = "standardized imbalance",
       y = "size of unadjusted test given imblance and correlation")