Analysis of mortality rates via marginal extended quasi-likelihood.

We use a mixed Poisson regression model with extra variation to analyse mortality data cross-classified by age and geographic region. We use estimates of dispersion parameter and fixed effects parameters, obtained by maximizing a marginal quasi-likelihood function, to estimate mortality rates in an empirical Bayes manner. This is a modification of an earlier method by Tsutakawa that used the likelihood function and is computationally impractical for routine use. In order to apply the extended quasi-likelihood function, a linear variance function (of the mean) is used in place of a quadratic one used previously. We illustrate the method with male lung cancer deaths in the state of Missouri.