A variance components approach to categorical data models with heterogeneous cell populations: analysis of spatial gradients in lung cancer mortality rates in North Carolina counties.

A mixed categorical-continuous variable model is proposed for the analysis of mortality rates. This model differs from other available models, such as weighted least squares and loglinear models, in that the within-cell populations are assumed to be heterogeneous in their levels of mortality risk. Heterogeneity implies that, in addition to the sampling variance considered in other available models, there will be a second component of variance due solely to within-cell heterogeneity. Maximum likelihood procedures are presented for the estimation of the model parameters. These procedures are based on the assumption that the distribution function for each cell death count is the negative binomial probability function. This assumption is shown to be equivalent to assuming a mixture of Poisson processes with the differential risk levels among individuals within each cell being governed by a two-parameter gamma distribution. The model is applied to data on lung cancer mortality for 1970-1975 for the 100 counties of North Carolina. The analysis shows that, though a gradient in lung cancer mortality rates exist in space, the gradient is restricted to specific demographic categories identified by race, age and sex.