Mixed Model for Analyzing Geographic Variability in Mortality Rates

Abstract

A mixed model is proposed for the analysis of geographic variability in mortality rates. In addition to demographic parameters and random geographic parameters, the model includes additional random-effects parameters to adjust for extra-Poisson variability. The model uses a gamma-Poisson distribution with a random scale parameter having an inverse gamma prior. An empirical Bayes approach is used to estimate relative risks for geographic regions and annual rates for demographic groups within each region. Lung cancer in Missouri is used to motivate and illustrate the procedure. Observed disease-specific death rates of specific age/sex groups, within regional units such as counties or cities, are generally quite unreliable for all but the largest units. The amount of information available from any one unit is generally limited. But modeling the variability between and within units can improve estimates, as demonstrated frequently in empirical Bayes examples. A numerical comparison with the fixed effects multiplicative Poisson model demonstrates the considerable flexibility the random effects model has in showing how geographic effects change over different age/sex groups. Computing maximum likelihood estimates of hyper-parameters requires a fair amount of work, since the solution is iterative and requires numerical integration. Expressions are provided to facilitate computation for similar problems.

Key Words:

• Mortality statistics
• Random effects
• Gamma-Poisson
• Empirical Bayes
• Lung cancer