Interval Estimation for Age-Adjusted Rate Ratios Using Bayesian Convolution Model

Spatial correlation raises challenges in estimating confidence intervals for region specific event rates and rate ratios between geographic units that are nested. Methods have been proposed to incorporate spatial correlation by assuming various distributions for the structure of autocorrelation patterns. However, the derivation of these statistics based on approximation may have to condition on the distributional assumption underlying the data generating process, which may not hold for certain situations. This paper explores the feasibility of utilizing a Bayesian convolution model (BCM), which includes an uncorrelated heterogeneity (UH) and a conditional autoregression (CAR) component to accommodate both uncorrelated and correlated spatial heterogeneity, to estimate the 95% confidence intervals for age-adjusted rate ratios among geographic regions with existing spatial correlations. A simulation study is conducted and a BCM method is applied to two cancer incidence datasets to calculate age-adjusted rate/ratio for the counties in the State of Kentucky relative to the entire state. In comparison to three existing methods, without and with spatial correlation, the Bayesian convolution model-based estimation provides moderate shrinkage effect for the point estimates based on the neighbor structure across regions and produces a wider interval due to the inclusion of uncertainty in the spatial autocorrelation parameters. The overall spatial pattern of region incidence rate from BCM approach appears to be like the direct estimates and other methods for both datasets, even though "smoothing" occurs in some local regions. The Bayesian Convolution Model allows flexibility in the specification of risk components and can improve the accuracy of interval estimates of age-adjusted rate ratios among geographical regions as it considers spatial correlation.