# Association of socioeconomic deprivation with life expectancy and all-cause mortality in Spain, 2011-2013

### Study design, participants, data and setting

We conducted a population-based multilevel study to derive LE at birth by SSE in Spain. Population and mortality data were taken from the Spanish Statistical Office for the period 2011-2013 using census tract level, age, calendar year and gender (data transfer agreement from Spanish Statistical Office number 67/2020). EL at birth for the period 2011-2013 is essential for cancer control and for establishing temporal comparisons (i.e. trends) over time when new information from the national census is made available. public in Spain.

We used the census tract layer from the 2011 Spanish census, with 35,960 census tracts. The average size of census tracts is 14.04 km2 (8.42mi2), and the average population is 1,311 for the census tract, with the closest equivalent to US geographic levels being the census block groupten. To measure deprivation in each census tract, we used the Spanish Deprivation Index (SDI)11 created by principal component analysis12 using data from the 2011 Spanish census carried out by the Spanish Statistical Office (https://www.ine.es/dyngs/INEbase/en/categoria.htm?c=Estadistica_P&cid=1254735572981).

The IDS includes information from six indicators mainly related to employment and education: percentage of manual workers (employed or unemployed), percentage of casual workers (employed or unemployed), percentage of population with insufficient level of education (i.e. less than 8 years of secondary education), and percentage of main residences without internet access11. Although the index does not contain any direct income information, we found in a previous study that SDI and average per capita income are associated with the census tract level.13. We used SDI divided into quintiles (Q), where Q5 represents the 20% of census tracts that are the most deprived areas (lowest SES) and Q1 the 20% of census tracts that are the least deprived areas. disadvantaged (highest SES).

The internal review board of the Andalusian School of Public Health (CP17/00206), the provincial internal research review board of Granada and the biomedical ethics committee of the Ministry of Health of the Andalusian regional government (study 0072-N-18) approved the study protocol. The study is in accordance with the principles set out in the Declaration of Helsinki.

### statistical analyzes

We performed a descriptive analysis, where we first calculated crude mortality rates per 100,000 people for the entire period and by deprivation quintiles, age categories and sex in Spain. To calculate the mortality rates, we used the total population at risk for the period analyzed.

Death and population counts produced by the Spanish Statistical Office were only available for five-year age groups from 0 to > 85 (i.e. abbreviated). Therefore, we used a modified modeling approach described elsewhere14 to estimate smoothed mortality rates using a multivariate flexible Poisson mixed-effects model15. Death counts were modeled under the generalized linear model, accounting for Poisson error, using restricted cubic splines to capture the smoothed effect of age, and including the at-risk population as an offset16. Models were stratified by sex. The covariates considered in the model were age-restricted cubic splines (using the mean age of each age group), the quintile of the IDS, the interaction between IDS and age, and the ordinate originally for census tracts. The specification of the model is given by:

$$mathrm{ln}left(mathrm{cases_{age,SDI}}/mathrm{population_{age,SDI}}right)mathrm{_j }=upbeta _0 +mathrm{ f}_ {1}left(mathrm{age}right)+sum_{mathrm{i}=2}^{5}{upbeta }_{mathrm{i}}times mathrm{ Quintile, {SDI}}+mathrm{f}_{2}(mathrm{quintile , SDI_i }times mathrm{ age}) +mathrm{ Q_j}$$

(1)

where QI is the y-intercept for the j census tract, and f1 and F2 represent the age-restricted cubic splines and the interaction between age and SDI quintiles, respectively.

We used an adaptive data cross-validation approach to identify the best position and number of nodes for the centered mean age of 60 years. Node positions were set at 2, 12, 22, 32, 42, 52, 67, and 82 years based on the lowest cross-validated mean absolute error of a set of models with different node positions.17.

We included the census tract as a random intercept [Qj in (Eq. 1)] to account for non-spatial variability and improve model fit, since random effects approximate penalized smoothing splines, reducing overfitting18. From the fitted model, we predicted the smoothed mortality rates taking into account the random interception by age group and deprivation quintile, stratified by sex. We derived LE for persons ≥75 years of age by census tracts from life tables and presented it in choropleth maps. LE quintiles were calculated by dividing census tracts into five groups, where Q1 represents the 20% of census tracts with the lowest LE, and Q5 the 20% of census tracts with the highest LE . In addition, we calculated LEs at birth by province, by weighting the LE of all census tracts in the province with the population size of each census tract.

To assess the goodness of fit of the model, we compared predicted and observed mortality rates. We derived 95% confidence intervals for mortality rates using the Delta method19.

We used Stata v.16.1 (StataCorp, College Station, Texas, USA) and R v.4.1.0 (R Foundation for Statistical Computing, Vienna, Austria) for statistical analysis and mapping. Syntax files for calculating mortality tables and derived mortality tables are available on GitHub (https://github.com/migariane/Spanish_LifeTablesByDeprivation).

### Ethical approval and consent to participate

The internal review board of the Andalusian School of Public Health (CP17/00206), the provincial internal research review board of Granada and the biomedical ethics committee of the Ministry of Health of the Andalusian regional government (study 0072-N-18) approved the study protocol. The study is in accordance with the principles set out in the Declaration of Helsinki.