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CPS1956 Areti B. et al.
a spatially structured term following an intrinsic conditional autoregressive
prior ∼ ( , ) where is the adjacency matrix specifying the
2

spatial neighbourhood. The temporal component and the age component

both follow a Gaussian random walk prior of order 1 (RW1) which is

implemented as an ICAR prior. The interacton terms and follow normal
,
,
iid priors, while the interaction term follows an age specific random walk
,
prior of order 1 (RW1). All model hyperparameters follow a weakly informative
half Normal prior. The analysis was carried out using integrated nested Laplace
approximations (INLA), which is an alternative to the traditional Markov chain
Monte carlo (McMC) methods for Bayesian inference specifically designed for
latent Gaussian models (Rue and Held 2005; Blangiardo et al. 2013). In the
context of spatio-temporal modelling, several Bayesian detection rules exist,
and a trade off between true and false positives is usually desired. A common
practice is to use Bayesian exceedance probabilities (Richardson et al. 2004;
Lawson 2013). These base the detection rule on a cut off value on the posterior
probability that the space-time interaction is above a reference threshold. The
choice of the reference threshold value and the cut off value depends on the
data, i.e. number of areas, time points and magnitude of expected cases
(Ugarte et al. 2009). In our work, we were interested in detecting unusual
behaviour both in terms of increasing or decreasing trend compared to the
national one and we chose the reference threshold to be 1, and cut off values
0.05 and 0.95. Unusual areas were detected in terms of space-time interactions
over the last 5 years of the time period, i.e. 2013-2017,
( Prob(exp( >1))<0.05 or Prob(exp( >1))>0.95 ).
,
,
National mortality rates were calculated as the population-weighted average
of age-specific mortality rates. Finally, mortality rates were converted to life
expectancy using life table methods (Preston, Heuveline and Guillot 2001)

3. Result
Under the detection rule that we specified, we found 21 areas to be
unusual over the last 5 years of the study period with an exceedance
probability below 0.05, suggesting a decreased slope compared to the
national one, and 32 areas with an exceedance probability above 0.95,
suggesting an increased slope respectively (Figure 1).

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