On the accommodation of disease rate correlations in aggregate data studies of disease risk factors

Prentice and Sheppard (1995, Biometrika 82, 113-125) proposed a method for estimating relative risks associated with poorly measured exposures using disease rates from multiple populations and exposure and confounding factor data from sample surveys of persons in each population. The method involved an assumption of independence of disease rates across populations, conditional on exposures and confounding factors. Here, this assumption is relaxed by allowing dependencies among the disease rates within a partition of the populations, perhaps defined on the basis of geographic proximity or cultural similarity. Such dependencies could, for example, derive from unmeasured risk factors that are shared among neighboring populations. Dependencies within an element of the partition are modeled by allowing a common correlation between the disease rates of contiguous populations and by inducing correlations between the rates for noncontiguous populations using a multivariate lognormal assumption. Estimating equations are proposed for relative risk parameter estimation, and robustness and efficiency properties are assessed through simulations. The relaxed estimation procedure is shown to yield useful efficiency gains when moderate or strong disease rate dependencies are present, especially when disease rate variances are large relative to binomial variance.