Statistical analyses
To produce a precise smoothed map of prevalence based
on individual locational information, we estimated a geoadditive
model (24–27) by using a two-dimensional (latitude/
longitude) smooth term for the spatial effect and simple
regression coefficients for individual and contextual factors
(refer to the Appendix). To obtain easily interpretable information
on the magnitude of spatial variations, we propose
an indicator on the odds ratio scale, the interquartile
spatial odds ratio, defined as the odds ratio between an individual
residing in a location in the first quartile and one
from a location in the fourth quartile of spatial risk, as
estimated from the geoadditive model (Appendix).
To make inferences on the magnitude of spatial variations,
we estimated a multilevel logistic model (3, 4) with
individuals nested within administrative neighborhoods (refer
to the Appendix). The neighborhood variance r2u
indicated
the amount of variability between neighborhoods
regarding substance-related disorders. Using Moran’s I
statistic (Appendix), we sought spatial autocorrelation in
the neighborhood residuals of the model (41, 42). To investigate
whether spatial correlation decreased with increasing
distance, we computed Moran’s I separately for those