rqpois {predint}

Sampling of overdispersed Poisson data with constant overdispersion

Description

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.

Usage

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)

Details

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

var(y_i) = \Phi n_i \lambda

For the sampling \kappa_i is defined as

\kappa_i=(\Phi-1)/(n_i \lambda)

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

\lambda_i \sim Gamma(a_i, b_i)

and the observations per cluster are sampled to be

y_i \sim Pois(\lambda_i).

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.

Value

a data.frame containing the sampled observations and the offsets

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

# 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