simulation lol

library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.3.3

library(dplyr)

## Warning: package 'dplyr' was built under R version 4.3.3

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

set.seed(123)

N <- 10000
mean_g0 <- 99
mean_g1 <- 87

group <- rbinom(N, 1, 0.25)
trait <- ifelse(group == 0,
                rnorm(N, mean_g0, 15),
                rnorm(N, mean_g1, 20))

df <- data.frame(group = group, trait = trait)

reg_full <- lm(trait ~ group, data = df)
beta_full <- coef(reg_full)["group"]

subgroup filtered by trait

df_selected <- df %>% filter(trait > 110)
reg_selected <- lm(trait ~ group, data = df_selected)
beta_selected <- coef(reg_selected)["group"]

bootstrap

boot_betas <- replicate(1000, {
    sample_df <- df_selected %>% slice_sample(n = nrow(df_selected), replace = TRUE)
    coef(lm(trait ~ group, data = sample_df))["group"]
})

boot_df <- data.frame(beta = boot_betas)

ggplot(boot_df, aes(x = beta)) +
    geom_histogram(bins = 50, fill = "salmon", color = "black", alpha = 0.8) +
    geom_vline(xintercept = mean(boot_betas), color = "red", linetype = "dashed",
               size = 1.1) +
    geom_vline(xintercept = 0, color = "black", linetype = "dotted") +
    labs(
        title = "Bootstrap Distribution of Beta (Trait ~ Group)\nSubsample: Trait > 110",
        x = "Beta Coefficient",
        y = "Frequency"
    ) +
    theme_minimal()

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

list(
    beta_full = beta_full,
    beta_selected = beta_selected,
    CI_95 = quantile(boot_betas, probs = c(0.025, 0.975))
)

## $beta_full
##     group 
## -12.19174 
## 
## $beta_selected
##    group 
## 1.470894 
## 
## $CI_95
##      2.5%     97.5% 
## 0.4637232 2.4700854