When mapping life expectancy, and investigating its local variation in time, there is a conflict between using large areas and/or mortality data from long periods of time to have low variance life expectancy estimates, and using small areas and single-year mortality data to explore the space–time variation of life expectancy in detail, without bias. Here a Bayesian model is proposed to smooth annual small-area life expectancy estimates and help deal with that trade-off. The specific area effect on life expectancy, together with its spatial and temporal dependencies are modeled through random effects, while the effect of covariates is modeled through a fixed effect component. By smoothing life expectancy estimates directly, instead of smoothing age-specific mortality rates first the way done in the literature, the model used is easier to implement and interpret. The approach is illustrated, by using it to explore how life expectancy at birth of males and of females, and their gap, varied in space and in time in the city of Barcelona between 2007 and 2018, and their relationship with covariates. It is found that, on average, life expectancy has been growing by 0.23 years per year for males and 0.15 years per year for females. The female life expectancy is becoming more spatially homogeneous than the male one, while the rate of life expectancy growth for males turns out to be more homogeneous than for females.

中文翻译：

---

预期寿命映射的贝叶斯时空模型；2007 年至 2018 年巴塞罗那的变化

在绘制预期寿命图并调查其局部时间变化时，使用大面积和/或长时间的死亡率数据来获得低方差的预期寿命估计值，与使用小面积和单年死亡率数据来估计预期寿命之间存在冲突。不带偏见地详细探索预期寿命的时空变化。这里提出了一个贝叶斯模型来平滑每年的小区域预期寿命估计并帮助处理这种权衡。特定区域对预期寿命的影响及其空间和时间依赖性通过随机效应建模，而协变量的影响通过固定效应分量建模。通过直接平滑预期寿命估计，而不是像文献中那样首先平滑特定年龄死亡率，使用的模型更易于实施和解释。该方法通过使用它来探索 2007 年至 2018 年间巴塞罗那市男性和女性出生时的预期寿命及其差距如何在空间和时间上发生变化，以及它们与协变量的关系。研究发现，男性的预期寿命平均每年增长 0.23 岁，女性每年平均增长 0.15 岁。女性的预期寿命在空间上变得比男性更加同质，而男性的预期寿命增长速度比女性更加同质。研究发现，男性的预期寿命平均每年增长 0.23 岁，女性每年平均增长 0.15 岁。女性的预期寿命在空间上变得比男性更加同质，而男性的预期寿命增长速度比女性更加同质。研究发现，男性的预期寿命平均每年增长 0.23 岁，女性每年平均增长 0.15 岁。女性的预期寿命在空间上变得比男性更加同质，而男性的预期寿命增长速度比女性更加同质。