rqpois function

Sampling of overdispersed Poisson data with constant overdispersion

rqpois() samples overdispersed Poisson data with constant overdispersion from the negative-binomial distribution such that the quasi-Poisson assumption is fulfilled. The following description of the sampling process is based on the parametrization used by Gsteiger et al. 2013.

rqpois(n, lambda, phi, offset = NULL)

Arguments

• n: defines the number of clusters ($I$)
• lambda: defines the overall Poisson mean ($\lambda$)
• phi: dispersion parameter ($\Phi$)
• offset: defines the number of experimental units per cluster ($n_i$)

Returns

a data.frame containing the sampled observations and the offsets

Details

It is assumed that the dispersion parameter ($\Phi$) is constant for all $i=1, ... I$ clusters, such that the variance becomes

For the sampling $\kappa_i$ is defined as

where $a_i=1/\kappa_i$ and $b_i=1/(\kappa_i n_i \lambda)$. Then, the Poisson means for each cluster are sampled from the gamma distribution

and the observations per cluster are sampled to be

Please note, that the quasi-Poisson assumption is not in contradiction with the negative-binomial distribution, if the data structure is defined by the number of clusters only (which is the case here) and the offsets are all the same $n_h = n_{h´} = n$.

Examples

# set.seed(123)
qp_dat1 <- rqpois(n=10, lambda=50, phi=3)
qp_dat1

# set.seed(123)
qp_dat2 <- rqpois(n=3, lambda=50, phi=3)
qp_dat2

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")