10  Data generation

This page shows examples of data generation for Emax model with and without covariates.

10.1 Setup and load

library(tidyverse)
library(here)

theme_set(theme_bw(base_size = 12))

set.seed(1234)

10.2 Data generation - No covariate

n <- 20 # number of subjects
E0 <- 5 # effect at 0 concentration
Emax <- 10 # maximal effect
EC50 <- 20 # concentration at half maximal effect
h <- 2 # Hill coefficient

set.seed(130)
c.is <- 50 * runif(n) # exposure

set.seed(130)
eps <- rnorm(n) # residual error

y.is <- E0 + ((Emax * c.is^h) / (c.is^h + EC50^h)) + eps

d_example_emax_nocov <- tibble(Conc = c.is, Y = y.is)

10.2.1 Check data

ggplot(d_example_emax_nocov, aes(Conc, Y)) +
  geom_point() +
  geom_smooth(formula = y ~ x, method = "loess", se = F, col = "darkgrey") +
  scale_x_continuous("Exposure", breaks = c(3, 10, 30, 100))

ggplot(d_example_emax_nocov, aes(Conc, Y)) +
  geom_point() +
  geom_smooth(formula = y ~ x, method = "loess", se = F, col = "darkgrey") +
  scale_x_log10("Exposure", breaks = c(3, 10, 30, 100))

Figure 10.1

Figure 10.2

10.3 Data generation - with covariate

Only one covariate (Prognostic factor positive/negative)

1. Prognostic factor = positive (GpA) is more sensitive to the drug
   • lower Emax in GpA; Emax.GpA = 10; Emax.GpB = 15

Ngp <- 2
N <- 20 * Ngp
GPid <- as.factor(rep(c("A", "B"), each = 20))

# Set parameters
E0 <- 5
EC50 <- 15
h <- 2
beta1 <- .7

# Calc response
set.seed(12345)

d_example_emax_cov <-
  tibble(GP = GPid) |>
  mutate(
    c.is = 50 * runif(N), eps = rnorm(N)
  ) |>
  mutate(
    Emax.i = ifelse(GP == "A", 10, 15)
  ) |>
  mutate(y.is = E0 + ((Emax.i * c.is^h) / (c.is^h + EC50^h)) + eps) |>
  mutate(Conc = c.is, Y = y.is)

10.3.1 Check data

ggplot(d_example_emax_cov, aes(Conc, Y)) +
  geom_point(aes(colour = GP)) +
  geom_smooth(aes(group = GP, colour = GP), se = F) +
  scale_x_continuous("Exposure") +
  theme(legend.position = "top")

`geom_smooth()` using method = 'loess' and formula = 'y ~ x'

Figure 10.3

10.4 Save data

Only run in an interactive session so that the data is not saved every time the document is rendered (by setting eval: FALSE).

write_csv(d_example_emax_nocov, here("data", "d_example_emax_nocov.csv"))
write_csv(d_example_emax_cov, here("data", "d_example_emax_cov.csv"))