2.2. Statistical analysis

Standard mortality ratios (SMR) were calculated as the ratio between the observed cases and those expected by sex and cause. To calculate the number of expected cases, the total mortality rates for age group, sex and cause are multiplied by person-years per census tract for each age group and sex. We also calculated the 95% credibility intervals of the SMRs.

Following this, we calculated the smoothed relative risks (RRs) and their corresponding 95% credibility intervals. The RR determines whether an area has an equal (RR = 1), higher (RR>1) or lower (RR<1) occurrence of cases than that expected from the reference rates. The RRs were calculated via a Besag, York and Mollié generalized linear mixed model (GLMM) [17]. This model adjusts a spatial Poisson model with two types of random effects, an unstructured effect which accounts for unstructured heterogeneity, and a structured effect, the spatial term, which considers the contiguity between areas. In order to define the contiguity in between areas we have used the borders of the adjacent census tracts. The model used to analyse the geographical distribution of mortality is defined as follows:

Where O_i denotes the cases observed in the census tract i, E_i are the expected cases, λ_i is the expected death rate, α is the intercept, h_i is the non-spatial random effect y b_i the spatial random effect. The non-spatial random effect (heterogeneity) is assumed to be a normal distribution with a zero mean and constant variance. For the random effect that captures the spatial variability, we have used an intrinsic conditional autoregressive model (CAR) [18,19].

In order to analyse the association of deprivation with cancer mortality, the census tract deprivation index has been included as an explanatory variable in the model, taking the census tracts with the lowest deprivation as reference categories. As such, the model takes the following form:

Where e^β is the RR associated with the deprivation index.

Using Besag, York and Mollié models with explanatory variables, we have analysed the association of the deprivation index with all of the studied forms of cancer across all of Andalusia. We also used this model to analyse each of the eight Andalusian province capitals individually in order to evaluate the risk within every city separately.

To determine the goodness of fit of the models we have utilized the deviance information criterion (DIC), a generalization of the Akaike information criterion (AIC) [20], in which the models with lower DIC will provide better adjustment.

The tool used for Bayesian inference of the subsequent marginal distributions for models parameters was Integrated Nested Laplace Approximations (INLA) [21]. For this, we used the R-INLA library version 18.07.12 [22] available in the R statistical package version 3.6.0 [23].

In order to produce the maps, smooth RRs were divided into 9 classes following quantiles, with the aim of guaranteeing the homogeneity of all of the geographical areas and be able to interpret the geographical distribution of the RRs properly [24]. For this we used version 10.5 of the ArcMap software package.