rnbinom {predint}

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)

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)

Value

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

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. 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))