1. Approaching complex health-related phenomena through spatial modeling Approaching complex health-related phenomena through spatial modeling Explaining cancer incidences with spatial vectors based on geographical distances Ari Voutilainen Katri Vehviläinen-Julkunen University of Eastern Finland Paula R. Sherwood University of Pittsburgh State of Science on Nursing Research, Washington DC, September 18-20, 2014

2. Modeling complex phenomena is always challenging. Besides challenges arising from the substance, there are many statistical challenges due to… AUTOCORRELATION as measurements located near each other (in space or time!) resembles each other more (or less!) than those which are far away from each other. COLLINEARITY as explanatory variables are connected with each other. CONFOUNDERS which create artificial (statistical) connections between the response and explanatory variables.

3. A solution to deal with these statistical challenges is to use them as a source of information. P RINCIPAL C OORDINATES OF N EIGHBOR M ATRICES by Borcard & Legendre, 2002 PCNM is a particular case of Moran’s eigenvector maps where the spatial weighting matrix is defined with distances between study locations. PCNM models spatial relationships among sites in decreasing order of spatial scale. PCNM can be applied to any set of sites providing a good coverage of a geographical sampling area. PCNM variables are rotated so that they do not correlate with each other. Sample locations can be randomly or systematically assigned.

4. The number of municipalities in Finland is 320 of which 17 locate solely on islands without a bridge to the mainland. These 17 municipalities were excluded due to their very small population and restricted connections with other municipalities. For each municipality, a geometrical location was determined on the basis of the latitudes and longitudes.

5. Executing the PCNM analysis 1.A 2-dimensional matrix of Euclidean distances was conducted using the geographical locations of the municipalities as initial values. 2.A truncated connectivity matrix (W) was constructed according to the rule by Dray et al., 2006. 3.Eigenvectors were extracted from the centered W. The PCNM resulted in 156 variables corresponding to positive eigenvectors. (Negative eigenvectors model negative spatial correlation and they may be useful in some instances, but not in the present context.)

6. Explaining cancer incidences Three datasets: 1.Response: Incidences of seven most common cancer types 2.Explanatory: 156 spatial variables from the PCNM analysis 3.Explanatory: 17 socio-demographic and environmental variables Variation partitioning with redundancy analysis (RDA) A: spatial variables only 2% B: spatially structured actual variables 24% C: not spatially structured actual variables 12% ABC

7. 26% of variation in cancer incidences was explained by the PCNM variables of which 92% was actually due to spatially structured actual explanatory variables, such as the area for residents, industry, traffic and service, net income, and migration rate. 36% of variation in cancer incidences was explained by the actual explanatory variables but only 33% of this was due to not spatially structured (local) variables. 63% of the modeled variation in cancer incidences was spatially structured

8. To conclude  The lack of knowledge about spatial structuring of the data may lead to…  models which are statistically invalid and  biased associations between and within the response and explanatory variables.  PCNM (with variation partitioning) can be used to achieve a better understanding of the spatial structure of both the response and explanatory variables.  PCNM variables can act as proxies for any kind of processes resulting in spatial structuration of the response variable.

9. Thank you for your attention! Nea Malila from the Finnish Cancer Registry is thanked for supplying and pre-arranging the cancer dataset. This work was financially supported by the Finnish Cultural Foundation.