Plotting a graph with sample sizes and power estimates - r

Question

I have simulated a linear model 1000 times using a randomly generated height and weight values, and randomly assigned each participant to a treatment or non-treatment (factor of 1 and 0). Let's say the model was:
lm(bmi~height + weight + treatment, data = df)
I am now struggling for the following:
The model now needs to cycle through the sample sizes between 300 and 500 in steps of 10 for each of the 1000 replications and store the proportion of simulated experiments with p values less than 0.05 for the purpose of estimating the power that can detect a change of 0.5 in bmi between two treatment groups at 5% significance level.
After doing the above, I then need to create a figure that best depicts the sample sizes on x-axis, and the estimated power on the y-axis, and also reflect the smallest sample size to achieve a 80% power estimate by a distinct color.
Any ideas how and where to go from here?
Thanks,
Chris

Answer 1

I would do it something like this:
library(dplyr)
library(ggplot2)
# first, encapsulate the steps required to generate one sample of data
# at a given sample size, run the model, and extract the treatment p-value
do_simulate <- function(n) {
# use assumed data generating process to simulate data and add error
data <- tibble(height = rnorm(n, 69, 0.1),
weight = rnorm(n, 197.8, 1.9),
treatment = sample(c(0, 1), n, replace = TRUE),
error = rnorm(n, sd = 1.75),
bmi = 703 * weight / height^2 + 0.5 * treatment + error)
# model the data
mdl <- lm(bmi ~ height + weight + treatment, data = data)
# extract p-value for treatment effect
summary(mdl)[["coefficients"]]["treatment", "Pr(>|t|)"]
}
# second, wrap that single simulation in a replicate so that you can perform
# many simulations at a given sample size and estimate power as the proportion
# of simulations that achieve a significant p-value
simulate_power <- function(n, alpha = 0.05, r = 1000) {
p_values <- replicate(r, do_simulate(n))
power <- mean(p_values < alpha)
return(c(n, power))
}
# third, estimate power at each of your desired
# sample sizes and restructure that data for ggplot
mx <- vapply(seq(300, 500, 10), simulate_power, numeric(2))
plot_data <- tibble(n = mx[1, ],
power = mx[2, ])
# fourth, make a note of the minimum sample size to achieve your desired power
plot_data %>%
filter(power > 0.80) %>%
top_n(-1, n) %>%
pull(n) -> min_n
# finally, construct the plot
ggplot(plot_data, aes(x = n, y = power)) +
geom_smooth(method = "loess", se = FALSE) +
geom_vline(xintercept = min_n)