Use of space-time models to investigate the stability of patterns of disease

Abstract

Background: The use of Bayesian hierarchical spatial models has become widespread in disease mapping and ecologic studies of health-environment associations. In this type of study, the data are typically aggregated over an extensive time period, thus neglecting the time dimension. The output of purely spatial disease mapping studies is therefore the average spatial pattern of risk over the period analyzed, but the results do not inform about, for example, whether a high average risk was sustained over time or changed over time.

Objective: We investigated how including the time dimension in disease-mapping models strengthens the epidemiologic interpretation of the overall pattern of risk.

Methods: We discuss a class of Bayesian hierarchical models that simultaneously characterize and estimate the stable spatial and temporal patterns as well as departures from these stable components. We show how useful rules for classifying areas as stable can be constructed based on the posterior distribution of the space-time interactions. We carry out a simulation study to investigate the sensitivity and specificity of the decision rules we propose, and we illustrate our approach in a case study of congenital anomalies in England.

Results: Our results confirm that extending hierarchical disease-mapping models to models that simultaneously consider space and time leads to a number of benefits in terms of interpretation and potential for detection of localized excesses.

Keywords: Bayesian hierarchical models; congenital anomalies; disease mapping; mixture models; space-time interactions; stable disease patterns.

Figure 1

Grid of variable-size squares covering England (lilac), and squares considered for the simulation study (green).

Figure 2

(A) Risk profiles of the unmodified squares compared with those modified under each variance case, represented on the probability scale. (B–D) ORs on the logarithmic scale (risk pattern profiles, M₈ case): (B) 10 most “atypical” estimated profiles in the reference case (expanded scale); (C and D) estimated risk profiles for 10 randomly selected areas classified as “atypical” using rule 1 in the medium-variance (C) and high-variance (D) cases for the M₈ scenario.

Figure 3

Box plots of the posterior median of the empirical standard deviations of the space time interactions when we modeled ν_it as a mixture of two normals: M₂₀ (A), M₈ (B), and M₁ (C) scenarios. (D) Box plot of the empirical standard deviations using an exchangeable normal model for the space–time interactions.

Figure 4

ROC curves (A and B) and curves of false-negative and false-positive rates (C and D) associated with rule 1 (A and C) and rule 2 (B and D) for the M₈ scenario.

Figure 5

Maps of unadjusted (A) and adjusted (B) spatial risks for the case study. Overimposed with blue borders are the areas classified as “atypical” using rule 1.

Figure 6

Estimated main time trend in the case study (A), and estimated risk profiles of the clusters of “atypical” areas according to rules 1 (B) and 2 (C) in the case study.