Uncorrected Proof 2007-06-19 ✐ Shekhar • Xiong: GIS — Entry 118 — 2007/6/19 — 11:03 — page 1 — LE-T E X ✐ ✐ ✐ Spatial Uncertainty in Medical Geography: a Geostatistical Perspective 1 Spatial Uncertainty in Medical Geography: a Geostatistical Perspective PIERRE GOOVAERTS 1 BioMedware Inc, Ann Arbor, USA 2 Synonyms 3 Health geographics; Spatial epidemiology; Theory of ran- 4 dom functions 5 Definition 6 Medical geography is defined as the branch of Human 7 Geography concerned with the geographic aspects of 8 health, disease and health care [1]. Data available for the 9 study of spatial patterns of disease incidence and mortal- 10 ity, as well as the identification of potential causes, fall 11 within two main categories: individual-level data or aggre- 12 gated data; see Fig. 1. Although individual humans repre- 13 sent the basic unit of spatial analysis, case data are often 14 aggregated to a sufficient extent to prevent the disclosure 15 or reconstruction of patient identity [2]. The information 16 available thus takes the form of disease rates, e. g. num- 17 ber of deceased or infected patients per 100,000 habi- 18 tants, aggregated within areas that can span a wide range 19 of scales, such as census units or counties. Analysis of 20 aggregated data is frequently hampered by the presence of 21 noise caused by unreliable extreme rates computed from 22 sparsely populated geographical entities or for diseases 23 with a low frequency of occurrence. Ignoring the uncer- 24 tainty attached to rate estimates can lead to misallocation 25 of resources to investigate unreliable clusters of high risk, 26 while areas of real concern might go undetected. Smooth- 27 ing methods have been developed to improve the reliability 28 of these estimates by borrowing information from neigh- 29 boring entities [3]. Etymologically, the term “geostatistics” 30 designates the statistical study of natural phenomena. It has 31 recently been extended to health science to incorporate the 32 size and shape of administrative units, as well as the spatial 33 dependence of data, into the filtering of noisy rates and the 34 quantification of the corresponding uncertainty [4,5]. 35 Historical Background 36 The idea that place and location can influence health is 37 a very old and familiar concept in medical geography. One 38 of the first demonstrations of the power of mapping and 39 analyzing health data was provided by Dr. John Snow’s 40 study of the cholera epidemic that ravaged London in 41 1854. Using maps showing the locations of water pumps 42 and the homes of people who died of cholera, Snow was 43 able to deduce that one public pump was the source of 44 the cholera outbreak [6]. Since then, the field of medi- 45 cal geography has come a long way, replacing paper maps 46 with digital maps in what is now called Geographic Infor- 47 mation Systems (GIS). Similarly, descriptive speculation 48 about disease has given place to scientific analysis of spa- 49 tial patterns of disease including hypothesis testing, multi- 50 level modeling, regression and multivariate analysis [3]. 51 Notwithstanding the contributions of many others, includ- 52 ing Gandin, Matern, Yaglom, or Krige, Dr. Georges Math- 53 eron formalized the discipline of geostatistics as it is 54 known today. The early developments of geostatistics in 55 the 1960s’ aimed to improve the evaluation of recover- 56 able reserves in mining deposits [7]. Its field of applica- 57 tion expanded considerably to encompass nowadays most 58 fields of geoscience (e. g. geology, geochemistry, geohy- 59 drology, soil science) and a vast array of disciplines that 60 all deal with the analysis of space-time data, such as 61 oceanography, hydrogeology, remote sensing, agriculture, 62 and environmental sciences. Yet, the use of geostatistics 63 in medical geography is still in its infancy. Transferring to 64 health science methods originally developed for the analy- 65 sis of earth properties presents several methodological and 66 technical challenges that arise from the fact that health data 67 are typically aggregated over irregular spatial supports and 68 consist of a numerator and a denominator (i. e. rates). 69 The first initiative to tailor geostatistical tools to the analy- 70 sis of disease rates must be credited to Oliver et al.’s study 71 on the risk of childhood cancer in the West Midlands of 72 England [8]. A similar approach, called Poisson kriging, 73 was developed more recently in the field of marine ecolo- 74 gy and generalized to the analysis of cancer mortality rates 75 and cholera incidence data [5,9,10]. Poisson kriging was 76 combined with stochastic simulation to generate multiple 77 realizations of the spatial distribution of cancer mortali- 78 ty risk, allowing the propagation of uncertainty through 79 the detection of cancer clusters and outliers [11]. Complex 80 random field models that require distributional assump- 81 tions and computationally intensive parameter estimation 82 using Markov Chain Monte Carlo (MCMC) techniques 83 were also developed [12,13]. A limitation of all these stud- 84 ies is the assumption that the size and shape of geographi- 85 cal units, as well as the distribution of the population with- 86 in those units, are uniform, which is often inappropriate. 87 The critical issue of change of support has just started 88 being addressed in the literature. For example, geostatis- 89 tics was used for mapping the number of low birth weight 90 (LBW) babies at the Census tract level, accounting for 91 county-level LBW data and covariates measured over dif- 92 ferent spatial supports, such as a fine grid of ground-level 93 particulate matter concentrations or tract population [14]. 94 Scientific Fundamentals 95 A visual inspection of the cervix cancer mortality map in 96 Fig. 1 conveys the impression that rates are particularly 97 high in the centre of the study area, as well as in a few 98 Please note that the pagination is not final; in the print version an entry will in general not start on a new page. TS1 Please note that this figure will be printed in gray in the final version. Editor’s or typesetter’s annotations (will be removed before the final T E X run)