We would like to thank D. Liu and S. Menjoge. Their letter has raised some statistical issues regarding the Poisson model with overdispersion correction and analysis of time-to-first event.
For the Poisson model with overdispersion correction, they state that this model “can also be viewed as equivalent to each individual having their own rate of exacerbations and the rate varying across the population following a gamma distribution” and provide two references for this statement. Unfortunately neither reference actually supports this view. In the first, McCullagh and Nelder 1 specifically state that a mixture of a Poisson …