title: Nonparametric intensity bounds for the delineation of spatial clusters.
abstract: BACKGROUND
  There is considerable uncertainty in the disease rate estimation for aggregated area maps, especially for small population areas. As a consequence the delineation of local clustering is subject to substantial variation. Consider the most likely disease cluster produced by any given method, like SaTScan, for the detection and inference of spatial clusters in a map divided into areas; if this cluster is found to be statistically significant, what could be said of the external areas adjacent to the cluster? Do we have enough information to exclude them from a health program of prevention? Do all the areas inside the cluster have the same importance from a practitioner perspective?
  
  
  RESULTS
  We propose a method to measure the plausibility of each area being part of a possible localized anomaly in the map. In this work we assess the problem of finding error bounds for the delineation of spatial clusters in maps of areas with known populations and observed number of cases. A given map with the vector of real data (the number of observed cases for each area) shall be considered as just one of the possible realizations of the random variable vector with an unknown expected number of cases. The method is tested in numerical simulations and applied for three different real data maps for sharply and diffusely delineated clusters. The intensity bounds found by the method reflect the degree of geographic focus of the detected clusters.
  
  
  CONCLUSIONS
  Our technique is able to delineate irregularly shaped and multiple clusters, making use of simple tools like the circular scan. Intensity bounds for the delineation of spatial clusters are obtained and indicate the plausibility of each area belonging to the real cluster. This tool employs simple mathematical concepts and interpreting the intensity function is very intuitive in terms of the importance of each area in delineating the possible anomalies of the map of rates. The Monte Carlo simulation requires an effort similar to the circular scan algorithm, and therefore it is quite fast. We hope that this tool should be useful in public health decision making of which areas should be prioritized.
authors.affiliation: Statistics Department, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil.
authors.forename: Fernando L P
authors.initials: FL
authors.lastname: Oliveira
authors.forename: Luiz H
authors.initials: LH
authors.lastname: Duczmal
authors.forename: André L F
authors.initials: AL
authors.lastname: Cançado
authors.forename: Ricardo
authors.initials: R
authors.lastname: Tavares
mesh_terms: D001499:Bayes Theorem; D001938:Brazil / Q000453:epidemiology; D001943:Breast Neoplasms / Q000453:epidemiology; D014355:Chagas Disease / Q000453:epidemiology; D003627:Data Interpretation, Statistical; D004812:Epidemiologic Methods; D005260:Female; D005843:Geography; D006708:Homicide / Q000706:statistics & numerical data; D006801:Humans; D016013:Likelihood Functions; D009010:Monte Carlo Method; D011159:Population Surveillance / Q000379:methods*; D012306:Risk; D017062:Small-Area Analysis; D013029:Space-Time Clustering; D018709:Statistics, Nonparametric; D014481:United States / Q000453:epidemiology