A simulated dataset representing a two-arm clinical trial with 300
subjects nested within 20 clusters (e.g., hospitals), one continuous
covariate, and two binary outcomes. It serves as the underlying data
for bglmm_fit and can be used to illustrate
bglmm.
Format
A data frame with 300 rows and 5 columns:
- id
Factor with 20 levels (
1–20). Cluster identifier (e.g., hospital). Each cluster contains 15 subjects.- group
Character. Treatment arm:
"placebo"(clusters 1–10) or"drug"(clusters 11–20).- age
Numeric. Continuous covariate drawn from \(N(50,\,10^2)\).
- y1
Integer (0/1). First binary outcome.
- y2
Integer (0/1). Second binary outcome.
Details
Data were generated with set.seed(2024) using logistic models
with cluster-specific random intercepts
\(u_{j1},\,u_{j2} \sim N(0,\,0.25)\):
$$
P(y_1 = 1) = \text{logit}^{-1}(-0.50 + 0.75\,\text{drug}
+ 0.10\,\text{age}/10 + u_{j1})
$$
$$
P(y_2 = 1) = \text{logit}^{-1}(-0.50 + 0.80\,\text{drug}
+ 0.05\,\text{age}/10 + u_{j2})
$$
where drug is 1 for the drug arm and 0 for placebo.
See data-raw/generate_examples.R for the full script.
Examples
head(bglmm_data)
#> id group age y2 y1
#> 1 1 placebo 41.27538 0 1
#> 2 1 placebo 49.95309 1 1
#> 3 1 placebo 54.95375 1 1
#> 4 1 placebo 69.72819 1 1
#> 5 1 placebo 38.03138 1 0
#> 6 1 placebo 51.30438 1 0
table(bglmm_data$group, bglmm_data$id)
#>
#> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
#> drug 0 0 0 0 0 0 0 0 0 0 15 15 15 15 15 15 15 15 15 15
#> placebo 15 15 15 15 15 15 15 15 15 15 0 0 0 0 0 0 0 0 0 0