predint (version 2.2.1)

rnbinom: Sampling of negative binomial data

Description

rnbinom() samples negative-binomial data. The following description of the sampling process is based on the parametrization used by Gsteiger et al. 2013.

Usage

rnbinom(n, lambda, kappa, offset = NULL)

Value

rnbinom() returns a data.frame with two columns: y as the observations and offset as the number of offsets per observation.

Arguments

n

defines the number of clusters ($I$)

lambda

defines the overall Poisson mean ($\lambda$)

kappa

dispersion parameter ($\kappa$)

offset

defines the number of experimental units per cluster ($n_i$)

Details

The variance of the negative-binomial distribution is $$var(Y_i)=n_i\lambda (1+\kappa n_i\lambda ).$$ Negative-biomial observations can be sampled based on predefined values of $\kappa$, $\lambda$ and $n_i$:
Define the parameters of the gamma distribution as $a=\frac{1}{\kappa }$ and $b_i=\frac{1}{\kappa n_i\lambda }$. Then, sample the Poisson means for each cluster $${\lambda }_i\sim Gamma(a,b_i).$$ Finally, the observations $y_i$ are sampled from the Poisson distribution $$y_i\sim Pois({\lambda }_i)$$

References

Gsteiger, S., Neuenschwander, B., Mercier, F. and Schmidli, H. (2013): Using historical control information for the design and analysis of clinical trials with overdispersed count data. Statistics in Medicine, 32: 3609-3622. tools:::Rd_expr_doi("10.1002/sim.5851")

Examples

# Sampling of negative-binomial observations
# with different offsets
set.seed(123)
rnbinom(n=5, lambda=5, kappa=0.13, offset=c(3,3,2,3,2))