Abstract
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.
Highlights
The ratio of age-adjusted rates is a common measure in public health for comparing rates between certain population groups or geographic units
The Bayesian convolution model (BCM) method is implemented to analyze the Kentucky male lung cancer and oral cancer incidence data acquired from the NCI SEER program, with the goal of obtaining the model-based age adjusted rate and county-to-state rate ratios (RR) with associated credible intervals by properly taking into consideration the spatial correlation patterns
Both the Spatial method and BCM consider the spatial correlation for estimating a confidence interval (CI) for RR
Summary
The ratio of age-adjusted rates is a common measure in public health for comparing rates between certain population groups or geographic units. The rate ratio comparing rates in a set of geographic units with an area considered to be “standard” is especially of interest to public health policy stakeholders on program planning and resource allocation. The key aspect of RR estimation between geographic units is the accommodation of spatial correlation, and the overlap of each region with. Bayesian Intervals of Rate Ratios the overall study region. Failing to account for spatial correlation leads to an underestimated variability in the point estimate with lower statistical power. The approximation method based on well-known statistical distributions (Gamma and F interval) [1, 2] has been proposed to address the correlation between subregion and overall regions. Zhu et al [3] developed a method to incorporate the spatial autocorrelation across regions into the confidence interval (CI) by assuming the structure of specific autocorrelation patterns which follows an exponential distribution
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