### INTRODUCTION

### METHODS

### Data sources

### Statistical analysis

#### Spatial autocorrelation of mortality rates

#### Spatio-temporal model

*m*) =

_{ita}*β*

_{0}+

*β*_{1}

*X**+*

_{it}*γ*

_{1}

*+ (*

_{,i}*γ*

_{2}

*·*

_{,i}*t*+

*γ*

_{3}

*) + (*

_{,it}*γ*

_{4}

*·*

_{,i}*α*+

*γ*

_{5}

*) +*

_{,ia}*γ*

_{6}

*,*

_{,ta}*m*is the mortality rate in region

_{ita}*i*(= 1, …, 250 district), year

*t*(= 0, …, 13, renumbered sequentially from 2004–2017), and age group

*α*(= 0, …, 18, renumbered sequentially from 0, 1–4, 5–9, …, 80–84, and 85+);

*β*

_{0}is a fixed intercept;

*X**is a vector of covariates for region*

_{it}*i*and year

*t*, and

*β*_{1}is the associated vector of regression coefficients;

*γ*

_{1}

*is a region-level random intercept;*

_{,i}*γ*

_{2}

*and*

_{,i}*γ*

_{4}

*are region-level random slopes for year and age group, respectively;*

_{,i}*γ*

_{3}

*,*

_{,it}*γ*

_{5}

*, and*

_{,ia}*γ*

_{6}

*are random intercepts on the region-year level, the region-age group level, and the year-age group level, respectively.*

_{,ta}*γ*

_{1}

*,*

_{,i}*γ*

_{2}

*, and*

_{,i}*γ*

_{4}

*were each assumed to follow a conditional autoregressive (CAR) distribution1617 and these random effects allow for spatial variation beyond those already described by covariates at the overall level (*

_{,i}*γ*

_{1}

*), linear deviation from the overall time trend (*

_{,i}*γ*

_{2}

*), and linear deviation from the overall age group trend (*

_{,i}*γ*

_{4}

*). The spatial structure of the CAR prior was imposed through an adjacency matrix*

_{,i}**W**of size

*n*×

*n*, with

*n*being the number of regions. The diagonal entries of

**W**are 0, and the off-diagonal entries are specified such that

*w*= 1 if regions

_{ij}*i*and

*j*are neighbors and

*w*= 0 otherwise. In this study, spatial weights based on Queen contiguity, which defines neighbors as spatial regions sharing a common edge or a common vertex, were used.

_{ij}*γ*

_{3}

*and*

_{,it}*γ*

_{5}

*were assumed to follow ${\scriptscriptstyle N\left(0,\u2007{?}_{{\gamma}_{3}}^{2}\right)}$ and ${\scriptscriptstyle N\left(0,\u2007{?}_{{\gamma}_{5}}^{2}\right)}$, respectively. These random effects allow for non-linear region-level deviations in the year and age group trends that are not captured by other trend components (i.e., linear deviations are accounted for by*

_{,ia}*γ*

_{2}

*and*

_{,i}*γ*

_{4}

*).*

_{,i}*γ*

_{6}

*was assumed to follow a normal distribution, with the precision matrix specified as the Kronecker product of the structure matrices using a first-order random walk for each of year and age group (i.e., a type IV interaction in the Knorr-Held classification17), which allows for simultaneous smoothing over year and age groups. logGamma (1, 0.001) hyper-priors were specified for the logarithm of the precision of each random effect and normal (0, 1000) hyper-priors were used for the common intercept and slope.*

_{,ta}#### Calculation of life expectancy at birth

### RESULTS

##### Table 1

^{a}Change in mortality rates: the gap in age-standardized mortality rate per 100,000 population between 2004 and each year;

^{b}Gap in Max − Min: the gap in the difference between the maximum and minimum age-standardized mortality rate per 100,000 population between 2004 and each year.

##### Table 2

##### Table 3

*P*value < 0.001).

^{a}Observed: median life expectancy at birth at the district level calculated from the observational data of the National Health Information Database;

^{b}Modeled: median life expectancy at birth at the district level from the spatio-temporal model;

^{c}Diff: median difference between the observed and model-based life expectancies at birth at the district level;

^{d}Corr: correlation between the observed and model-based life expectancies at birth;

^{e}Corr2: correlation between the observed and model-based life expectancies at birth based on 7-year pooled data.

### DISCUSSION

**W**in the model, it was not considered whether there were obstacles (e.g., rivers, mountains) between regions. However, most of those regions are actually connected by bridges or tunnels. Second, there are many islands in the west and south of Korea, so it was not possible to create adjacency weights based on the Queen criterion (i.e., neighbors if they share a common edge or a common vertex) in those regions. Therefore, if the island regions were nearby on the map, they were considered adjacent regions. In fact, most islands are connected by highway or ship routes, so people can come and go. In the case of Ulleungdo island on the east coast, neighboring regions were defined based on four ship routes.