Expected numbers of cases for each block group were
computed by applying reference incidence rates for the
same years (as estimated from the four administrative
departments of the study area, plus the departments of
Doubs and Hérault) to the person-years of each area stratified
by gender and 5-year age classes.
Models were fitted to the grouped data with Poisson
regression analysis. Logarithms of observed and expected
cases were linked with a set covariate values in a linear
model that dealt with Poisson overdispersion. To build
flexible models, penalized regression splines (based on 25
knots) were used [20]. Since the dioxin concentration distribution
was right-skewed, a square root transformation
was applied to force the exposure data to follow a normal
distribution. Log-transformed industry × years, log-transformed
population density, socio-economic level, and
NO2 concentration were entered as continuous variables
in the models. Urbanisation (yes/no, by collapsing the 3
urban categories), and administrative departments
(department of Isère as reference category) were treated as
categorical variables.
Multivariate models were run. Dioxin exposure (variable
under scrutiny) and administrative departments (to
account for their heterogeneity) were forced into the models.
Then, the 5 remaining independent variables were
introduced as spline functions. To assess the smoothing
added value, we followed the ad hoc approach proposed
by Wood et al. [20]. If the estimated degrees of freedom
were close to 1 (and a linear function was therefore estimated),
and if the generalized cross validation (GCV)
score was higher than the GCV for the unsmoothed
model, then the original unsmoothed variable was preferred
to the spline-smoothed version. Finally, using
Akaike's information criterion for covariate selection, a
backward stepwise selection was applied.
Hierarchical Bayesian Poisson regression models were
also fitted to these geographical data to address the issue
of spatial autocorrelation [21].
The relative risk (RR) associated with dioxin exposure was
therefore computed as .
Under a high exposure scenario, we have a priori defined
x1 (the reference concentration) as the 2.5th percentile
(1.25 × 10-4 μg/m2/year), and x2 as the 90th percentile
(1.78 × 10-2 μg/m2/year) of the dioxin exposure distribution
within the modelled zones (Figure 2).
Models were run with R software (package mgcv) and
WinBUGS software [22,23].