Estimating Individual-Level Risk in Spatial Epidemiology Using Spatially Aggregated Information on the Population at Risk

Abstract

We propose a novel alternative to case-control sampling for the estimation of individual-level risk in spatial epidemiology. Our approach uses weighted estimating equations to estimate regression parameters in the intensity function of an inhomogeneous spatial point process, when information on risk-factors is available at the individual level for cases, but only at a spatially aggregated level for the population at risk. We develop data-driven methods to select the weights used in the estimating equations and show through simulation that the choice of weights can have a major impact on efficiency of estimation. We develop a formal test to detect non-Poisson behavior in the underlying point process and assess the performance of the test using simulations of Poisson and Poisson cluster point processes. We apply our methods to data on the spatial distribution of childhood meningococcal disease cases in Merseyside, U.K. between 1981 and 2007.

A New Estimation Approach for Combining Epidemiological Data From Multiple Sources

“…We also apply the methods proposed by Prentice and Sheppard (1995) and Diggle et al (2010). For both methods, we first divide W into 100 equal subsquare regions, W k : k = 1, …, 100.…”

“…The unweighted version of the estimator is used due to its ease of implementation as well as its good performance (Prentice and Sheppard, 1995). For Diggle et al (2010), we assume that the summary measures ∫ W k λ 0 ( s ) Z ( s ) d s are also available, for k = 1, ⋯, 100. These summary measures are then combined with the case events in N 1 to estimate β .…”

“…These summary measures are then combined with the case events in N 1 to estimate β . Diggle et al (2010)’s method requires that the complete set of Z (·) must be known for the cases. As a result, N 2 cannot be used.…”

“…The methods proposed in Wakefield (2004) and Haneuse and Wakefield (2007, 2008a,b) concerned binary risk factors, but we may also be interested in continuous risk factors (e.g., exposure to traffic) in analyses. Diggle et al (2010) developed procedures for combining individual-level disease data and spatially aggregated information on a population at risk. They required spatially aggregated information for all risk factors under consideration, which may not be generally possible.…”

Continuous Inference for Aggregated Point Process Data

“…One possible explanation for this is because point level information is often not available for economic or confidentiality reasons; another possible explanation is convenience, e.g. if the desired data are collected routinely alongside other information (Beale et al ., ; Diggle et al ., ). To be absolutely clear about our distinction between discrete and aggregated data, we note that it is possible to fit a discrete model and to obtain spatially or spatiotemporally continuous inference via spatial prediction.…”