title: From spatial ecology to spatial epidemiology: modeling spatial distributions of different cancer types with principal coordinates of neighbor matrices.
abstract: BACKGROUND
  Epidemiology and ecology share many fundamental research questions. Here we describe how principal coordinates of neighbor matrices (PCNM), a method from spatial ecology, can be applied to spatial epidemiology. PCNM is based on geographical distances among sites and can be applied to any set of sites providing a good coverage of a study area. In the present study, PCNM eigenvectors corresponding to positive autocorrelation were used as explanatory variables in linear regressions to model incidences of eight most common cancer types in Finnish municipalities (n = 320). The dataset was provided by the Finnish Cancer Registry and it included altogether 615,839 cases between 1953 and 2010.
  
  
  RESULTS
  PCNM resulted in 165 vectors with a positive eigenvalue. The first PCNM vector corresponded to the wavelength of hundreds of kilometers as it contrasted two main subareas so that municipalities located in southwestern Finland had the highest positive site scores and those located in midwestern Finland had the highest negative scores in that vector. Correspondingly, the 165(th) PCNM vector indicated variation mainly between the two small municipalities located in South Finland. The vectors explained 13 - 58% of the spatial variation in cancer incidences. The number of outliers having standardized residual > |3| was very low, one to six per model, and even lower, zero to two per model, according to Chauvenet's criterion. The spatial variation of prostate cancer was best captured (adjusted r (2) = 0.579).
  
  
  CONCLUSIONS
  PCNM can act as a complementary method to causal modeling to achieve a better understanding of the spatial structure of both the response and explanatory variables, and to assess the spatial importance of unmeasured explanatory factors. PCNM vectors can be used as proxies for demographics and causative agents to deal with autocorrelation, multicollinearity, and confounding variables. PCNM may help to extend spatial epidemiology to areas with limited availability of registers, improve cost-effectiveness, and aid in identifying unknown causative agents, and predict future trends in disease distributions and incidences. A large advantage of using PCNM is that it can create statistically valid reflectors of real predictors for disease incidence models with only little resources and background information.
authors.affiliation: Department of Nursing Science, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Finland ; Department of Biology, University of Eastern Finland, Kuopio, Finland.
authors.forename: Ari
authors.initials: A
authors.lastname: Voutilainen
authors.affiliation: Research Centre for Comparative Effectiveness and Patient Safety, University of Eastern Finland, Kuopio, Finland ; School of Pharmacy, University of Eastern Finland, Kuopio, Finland.
authors.forename: Anna-Maija
authors.initials: AM
authors.lastname: Tolppanen
authors.affiliation: Department of Nursing Science, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Finland.
authors.forename: Katri
authors.initials: K
authors.lastname: Vehviläinen-Julkunen
authors.affiliation: Department of Acute and Tertiary Care, School of Nursing, University of Pittsburgh, Pittsburgh, PA, USA.
authors.forename: Paula R
authors.initials: PR
authors.lastname: Sherwood
keywords: Cancer incidence; Finland; Principal coordinates of neighbor matrices; Spatial epidemiology