rbbinom function

Sampling of beta-binomial data

rbbinom() samples beta-binomial data according to Menssen and Schaarschmidt (2019).

rbbinom(n, size, prob, rho)

Arguments

• n: defines the number of clusters ($i$)
• size: integer vector defining the number of trials per cluster ($n_i$)
• prob: probability of success on each trial ($\pi$)
• rho: intra class correlation ($\rho$)

Returns

a data.frame with two columns (succ, fail)

Details

For beta binomial data with $i=1, ... I$ clusters, the variance is

with $\rho$ as the intra class correlation coefficient

For the sampling $(a+b)$ is defined as

where $a=\pi (a+b)$ and $b=(a+b)-a$. Then, the binomial proportions for each cluster are sampled from the beta distribution

and the number of successes for each cluster are sampled to be

In this parametrization $E(\pi_i)=\pi=a/(a+b)$ and $E(y_i)=n_i \pi$. Please note, that $1+ (n_i-1) \rho$ is a constant if all cluster sizes are the same and hence, in this special case, also the quasi-binomial assumption is fulfilled.

Examples

# Sampling of example data
set.seed(234)
bb_dat1 <- rbbinom(n=10, size=50, prob=0.1, rho=0.06)
bb_dat1

set.seed(234)
bb_dat2 <- rbbinom(n=3, size=c(40, 50, 60), prob=0.1, rho=0.06)
bb_dat2

References

Menssen M, Schaarschmidt F.: Prediction intervals for overdispersed binomial data with application to historical controls. Statistics in Medicine. 2019;38:2652-2663. tools:::Rd_expr_doi("10.1002/sim.8124")