Lim, Kang, Kim, and Khang: Spatio-temporal Analysis of District-level Life Expectancy from 2004 to 2017 in Korea

### Background

Health indicators, such as mortality rates or life expectancy, need to be presented at the local level to improve the health of local residents and to reduce health inequality across geographic areas. The aim of this study was to estimate life expectancy at the district level in Korea through a spatio-temporal analysis.

### Methods

Spatio-temporal models were applied to the National Health Information Database of the National Health Insurance Service to estimate the mortality rates for 19 age groups in 250 districts from 2004 to 2017 by gender in Korea. Annual district-level life tables by gender were constructed using the estimated mortality rates, and then annual district-level life expectancy by gender was estimated using the life table method and the Kannisto-Thatcher method. The annual district-level life expectancies based on the spatio-temporal models were compared to the life expectancies calculated under the assumption that the mortality rates in these 250 districts are independent from one another.

### Results

In 2017, district-level life expectancy at birth ranged from 75.5 years (95% credible interval [CI], 74.0–77.0 years) to 84.2 years (95% CI, 83.4–85.0 years) for men and from 83.9 years (95% CI, 83.2–84.6 years) to 88.2 years (95% CI, 87.3–89.1 years) for women. Between 2004 and 2017, district-level life expectancy at birth increased by 4.57 years (95% CI, 4.49–4.65 years) for men and by 4.06 years (95% CI, 3.99–4.12 years) for women. To obtain stable annual life expectancy estimates at the district level, it is recommended to use the life expectancy based on spatio-temporal models instead of calculating life expectancy using observed mortality.

### Conclusion

In this study, we estimated the annual district-level life expectancy from 2004 to 2017 in Korea by gender using a spatio-temporal model. Local governments could use annual district-level life expectancy estimates as a performance indicator of health policies to improve the health of local residents. The approach to district-level analysis with spatio-temporal modeling employed in this study could be used in future analyses to produce district-level health-related indicators in Korea.

### INTRODUCTION

Health indicators, such as the mortality rate or life expectancy (LE) in subnational areas, provide information that is necessary to improve community health and to address local health problems in vulnerable geographic areas. Local governments in Korea are establishing regional health care plans at the district level (i.e., ‘si’, ‘gun’, ‘gu’) to improve the quality of health care services for local residents and thereby to improve the health of local residents.1 LE presented at the district level could be used as a performance indicator of health policies, and calculating the LE gaps across geographic areas at the district level each year could help achieve a long-term health equity policy.
The National Health Insurance Service (NHIS) in Korea is the mandatory health insurance scheme for the entire Korean population. The National Health Information Database (NHID) provided by the NHIS consists of sub-databases (DBs) including the eligibility DB, the healthcare utilization DB, the health screening DB, and the healthcare provider DB.2 The NHID DB has been used to monitor health status and health equity at the national and local levels for the entire Korean population. Several Korean studies have examined subnational life expectancies using the NHID DB.345678 Bahk et al.3 showed that the crude mortality rate and LE at birth across the national, provincial, and district levels calculated using the NHID DB were consistent with the corresponding results calculated using the Korean Statistical Information Service (KOSIS) data from Statistics Korea, indicating that the NHID DB was a good source for monitoring the mortality rate and LE with representation of the entire Korean population. Kim et al.4 presented town-level life expectancy and other mortality metrics using the NHID DB. Lim et al.5 used the NHID DB to measure differences in quality-adjusted life expectancy by income in Korea at the national and district levels. Bahk et al.6 presented LE for 253 electoral constituencies in Korea using the NHID DB. However, these studies on LE and mortality metrics at the local level in Korea have limitations because their analyses were based on the assumption that observations are independent from one another (i.e., that there is no spatial autocorrelation), despite similar mortality rates in adjacent regions. Similarly, mortality rates in adjacent years should not be assumed to be independent from one another.
Moreover, estimating LE at the local level in Korea may encounter difficulties because of the rarity of deaths and small populations, especially in rural areas, which lead to uncertainty in estimating mortality rates. A previous study reported that the minimum population required to calculate a stable LE was 5,000.9 In order to ensure the minimum population needed to calculate income-quintile specific LE in small areas, Bahk et al.3 used 6-year pooled data and Lim et al.5 used 7-year pooled data for the number of population and deaths in each region. As a result, it was impossible to estimate LE by year.
These issues could be addressed effectively within the framework of spatio-temporal modeling, which allows for dependence of mortality rates on both space and time and improves the robustness of mortality estimates in subnational populations. Studies on the estimation of LE and mortality metrics at the local level using spatio-temporal models have been recently conducted,1011121314 but, to the best of our knowledge, no such studies have been conducted in Korea. This study aimed to estimate the annual district-level LE at birth in Korea based on the estimated mortality rates from spatio-temporal models using the NHID DB.

### Data sources

We obtained aggregated data from the NHID provided by the NHIS on the numbers of deaths and population by gender (both sexes, men, women) over the course of 14 years (2004–2017), divided into 19 age groups (0, 1–4, 5–9, …, 80–84, and 85+ years), and 250 districts based on the administrative districts in Korea in 2017 (the most recent year available at the time of this study). As administrative district classification criteria have changed several times during the study period (2004–2017), we reclassified the districts by year according to this 2017 administrative district classification to maintain the consistency of administrative district classifications in the NHID DB. In particular, the Sejong Special Provincial Municipality, which was established in 2012, was reclassified using the previous administrative district (‘dong’ unit). These reclassification processes have been applied in the previous studies.3578
Because there is considerable variation in education levels among districts in Korea, a district-level covariate for the proportion of the population aged 25 years or older who have completed a 4-year college or higher (= the number of people over 25 years old who have graduated from a 4-year college or higher / the number of people over 25 years old) was used in the spatio-temporal model. The covariate was created using data from the Population and Housing Census of Korea, with the proportion of college graduates from 2004 to 2009 based on the 2005 census data, the proportion of college graduates from 2010 to 2014 based on the 2010 census data, and the proportion of college graduates from 2015 to 2017 based on the 2015 census data.

### Statistical analysis

#### Spatial autocorrelation of mortality rates

Fig. 1 shows the distribution of age-standardized mortality rates at the district level by gender in 2017. The age-standardized mortality rates show little evidence of complete spatial randomness. Age-standardized mortality rates in neighboring districts were similar and showed clustered patterns. The extent to which similar (or dissimilar) districts are clustered can be quantified by a measure, such as Moran's I spatial statistic,15 a measure of global spatial autocorrelation that measures how the mortality rate in one district is similar to others surrounding it: Moran's I spatial statistic is close to +1 when similar values are spatially clustered, 0 when mortality rates are completely randomly distributed (i.e., no spatial autocorrelation), and -1 when dissimilar values are next to each other. Moran's I spatial statistic for age-standardized mortality rates at the district level by gender in 2017 was 0.584 for men and 0.399 for women, respectively, supporting the need to calculate LE based on mortality rates at the district level estimated using models that allow spatial dependence. The distribution of age-standardized mortality rates at the district level for both sexes in 2017 is given in Supplementary Fig. 1. Moran's I spatial statistic for both sexes was 0.611.

### Age-standardized mortality rates per 100,000 population in 250 districts for men (left) and women (right) in Korea, 2017, shown in 10 color groups with ranges for the categories determined by the deciles of age-standardized mortality rates per 100,000 population.

#### Spatio-temporal model

The allocation of numbers of deaths into units grouped by gender, 19 age groups, and 250 districts can result in few deaths in some units, leading to highly variable estimates of mortality rates. To overcome this issue, we used a Bayesian hierarchical model to estimate mortality rates by sharing information across age groups and regions and over time. In this approach, mortality rates for each age group, region, and year are informed by data in that age group-region-year unit, as well as by those in the adjacent age groups, adjacent districts, and adjacent years. The extent to which the estimated mortality rates are affected by adjacent units depends on the number of deaths, with larger groups and those with higher mortality rates being mostly informed by their own data and smaller groups with lower mortality rates being affected by a combination of their own data and data in other units.
The following model13 was used to estimate mortality rates by age group, region, and year, and then LE was calculated based on the estimated mortality rates. All analyses were done separately by gender (men, women, and both sexes combined):
Deathsita ~ Poisson (mita · Populationita),
log(mita) = β0 + β1Xit + γ1,i + (γ2,i · t + γ3,it) + (γ4,i · α + γ5,ia) + γ6,ta,
where mita is the mortality rate in region 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+); β0 is a fixed intercept; Xit is a vector of covariates for region i and year t, and β1 is the associated vector of regression coefficients; γ1,i is a region-level random intercept; γ2,i and γ4,i are region-level random slopes for year and age group, respectively; γ3,it, γ5,ia, and γ6,ta are random intercepts on the region-year level, the region-age group level, and the year-age group level, respectively. γ1,i, γ2,i, and γ4,i 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 (γ1,i), linear deviation from the overall time trend (γ2,i), and linear deviation from the overall age group trend (γ4,i). The spatial structure of the CAR prior was imposed through an adjacency matrix 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 wij = 1 if regions i and j are neighbors and wij = 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. γ3,it and γ5,ia were assumed to follow $N0, ?γ32$ and $N0, ?γ52$, 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 γ2,i and γ4,i). γ6,ta 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.

#### Calculation of life expectancy at birth

LE at birth was calculated based on the life table method, using the mortality rates at the district level estimated from the spatio-temporal models. Separate life tables were established for each combination of gender (both sexes, men, and women), 250 districts, and 14 years. We employed the Kannisto-Thatcher method18 to expand the terminal age group 85+ to estimate the probability of dying for each of the 5-year age groups 85–89, 90–94, …, 120–124, 125+. The 95% credible intervals (CIs) for LE at birth were calculated based on the 2.5th and 97.5th percentiles of the posterior distribution of the estimated mortality rates.
All statistical analyses were performed using SAS version 9.4 (SAS Institute Inc., Cary, NC, USA) and R version 3.4.1 (www.r-project.org). The models for estimating mortality rates were implemented in the R-INLA software. Subsequent procedures for estimating LE at birth were performed using SAS. The maps were created using QGIS version 3.12.0.

### Ethics statement

The present study protocol was reviewed and approved by the National Health Insurance Service of Korea (NHIS-2020-1-257) and the Seoul National University Hospital Institutional Review Board (IRB No. E-2005-024-1121). The requirement for informed consent was exempted by the board.

### RESULTS

Table 1 summarizes the results for death at the national and district levels from 2004 to 2017. The first section shows the number of population, the number of deaths, and age-standardized mortality rates at the national level: for example, in 2017, 145,935 of 25,062,848 men died, and the age-standardized mortality rate per 100,000 population was 548 in men, which was higher than the corresponding rate of 290 in women. The age-standardized mortality rate at the national level decreased by 333 deaths per 100,000 population in men and by 185 deaths per 100,000 population in women between 2004 and 2017. Differences in the age-standardized mortality gap between men and women tended to increase over time. The second section shows the distribution of age-standardized mortality rates in districts: for example, in 2017, the mean (standard deviation) of age-standardized mortality rates in men was 583 (80) deaths per 100,000 population, and the lowest mortality rate in men was 350 deaths per 100,000 population, compared with 537, 585, and 642 deaths per 100,000 population in districts in the 25th, 50th, and 75th percentiles, respectively, and 767 deaths per 100,000 population in the district with the highest rate. The difference between the minimum and maximum age-standardized mortality rate in districts decreased by 306 deaths per 100,000 population in men and by 182 deaths per 100,000 population in women between 2004 and 2017. The last column in the second section shows Moran's I spatial statistic. From 2004 to 2017, Moran's I spatial statistic ranged from 0.552 to 0.623 for men and from 0.329 to 0.482 for women, indicating that there were geographic patterns of spatial clustering in age-standardized mortality rates across districts. The results for both sexes combined are provided in Supplementary Table 1.

#### National-level deaths, number of population, and age-standardized mortality rates, and district-level distribution of age-standardized mortality rates by gender in Korea, 2004–2017

Gender Year National-level deaths, population, and age-standardized mortality rate District-level age-standardized mortality rate per 100 000 population
No. of population No. of deaths Mortality rate per 100,000 Change in mortality ratesa Mean SD Min Q1 Q2 Q3 Max Max − Min Gap in Max − Minb Moran's I
Men 2004 23,852,969 129,193 880 935 126 544 846 950 1,023 1,268 723 0.587
2005 23,950,517 128,669 844 −36 898 120 552 824 910 983 1,223 671 −53 0.570
2006 24,042,773 128,300 810 −70 860 117 506 784 867 937 1,138 632 −91 0.614
2007 24,143,782 129,834 786 −94 833 114 478 753 839 917 1,122 645 −78 0.593
2008 24,260,696 130,452 752 −128 802 114 433 728 811 892 1,100 667 −57 0.623
2009 24,410,504 131,465 718 −162 768 111 439 694 776 851 1,030 592 −132 0.593
2010 24,483,859 136,014 711 −170 759 108 452 689 762 833 1,030 578 −146 0.576
2011 24,575,874 137,101 687 −194 732 102 425 668 741 804 997 572 −151 0.612
2012 24,697,966 141,395 679 −201 725 103 409 662 730 796 995 586 −137 0.580
2013 24,773,343 139,687 636 −244 677 92 394 622 685 734 927 533 −191 0.575
2014 24,849,161 141,392 613 −267 654 91 389 600 657 711 952 562 −161 0.552
2015 24,928,709 143,675 593 −287 635 91 371 579 633 696 921 550 −173 0.619
2016 25,008,619 144,000 567 −313 606 85 362 553 611 664 793 431 −292 0.618
2017 25,062,848 145,935 548 −333 583 80 350 537 585 642 767 417 −306 0.584
Women 2004 23,764,721 105,234 475 491 54 341 452 491 527 702 361 0.366
2005 23,872,078 106,140 459 −16 472 50 325 441 475 507 637 311 −50 0.369
2006 23,975,730 105,619 437 −38 451 47 317 420 449 481 608 291 −70 0.339
2007 24,083,415 106,982 423 −52 435 45 324 407 434 461 557 233 −128 0.436
2008 24,207,199 105,963 396 −79 410 44 287 380 413 438 542 256 −105 0.482
2009 24,353,874 106,292 377 −98 389 43 244 365 389 415 496 252 −109 0.411
2010 24,442,869 110,249 371 −104 384 41 236 356 386 411 491 255 −106 0.391
2011 24,548,415 111,401 356 −119 368 41 231 341 369 395 514 283 −78 0.443
2012 24,678,785 117,161 354 −121 366 40 217 344 370 390 479 262 −99 0.372
2013 24,772,837 115,945 333 −142 344 41 226 322 345 369 500 275 −86 0.337
2014 24,872,377 117,636 320 −155 330 34 230 311 333 351 409 179 −182 0.329
2015 24,965,447 122,121 313 −162 325 35 235 305 326 346 420 185 −177 0.415
2016 25,058,551 122,943 299 −176 308 32 217 288 310 329 412 195 −166 0.435
2017 25,135,239 126,095 290 −185 299 32 218 279 300 322 397 179 −182 0.399
SD = standard deviation, Q1 = 25th percentile, Q2 = 50th percentile, Q3 = 75th percentile.
aChange in mortality rates: the gap in age-standardized mortality rate per 100,000 population between 2004 and each year; bGap 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.
In 2017, the LE at birth was 78.9 years (95% CI, 77.9–80.0 years) for men and 85.6 years (95% CI, 84.8–86.3 years) for women. For men, a high LE at birth was observed in the west (Seoul, Gyeonggi, Sejong, and Daejeon), while a low LE at birth was mainly observed in the northeast (Gangwon and Gyeongbuk) and south (Jeonnam and Gyeongnam). For women, high LE at birth was observed particularly in Sejong, Seoul, and Jeju, while low LE at birth was observed in some regions in Chungbuk, Ulsan, and Gyeongnam. Among 250 districts, LE at birth for men ranged from a minimum of 75.5 years (95% CI, 74.0–77.0 years) in Jindo-gun, Jeonnam to a maximum of 84.2 years (95% CI: 83.4–85.0) in Suji-gu, Yongin-si, Gyeonggi. LE at birth for women ranged from a minimum of 83.9 years (95% CI, 83.2–84.6 years) in Sasang-gu, Busan to a maximum of 88.2 years (95% CI, 87.3 to 89.1 years) in Gwacheon-si, Gyeonggi (Fig. 2). The results of district-level LE at birth from 2004 to 2017 are presented in Table 2. The results for both sexes combined are given in Supplementary Fig. 2 and Supplementary Table 2.

#### Distribution of district-level life expectancies at birth based on the spatio-temporal model by gender, 2004–2017

Gender Year District-level life expectancy at birth
Mean SD Min Q1 Q2 Q3 Max Max − Min Gap in Max − Mina
Men 2004 74.4 1.7 71.1 73.0 74.0 75.3 80.3 9.2
2005 74.8 1.7 71.4 73.5 74.4 75.8 80.4 9.0 −0.3
2006 75.1 1.7 72.0 73.8 74.8 76.1 80.8 8.7 −0.5
2007 75.4 1.7 72.2 74.1 75.0 76.4 81.2 9.1 −0.2
2008 75.8 1.8 72.5 74.4 75.5 76.9 81.5 9.0 −0.3
2009 76.1 1.8 72.8 74.7 75.9 77.2 82.1 9.3 −0.0
2010 76.4 1.7 73.4 75.1 76.2 77.4 82.2 8.8 −0.5
2011 76.7 1.7 73.7 75.3 76.5 77.8 82.4 8.7 −0.6
2012 76.8 1.7 73.8 75.5 76.7 77.9 82.6 8.8 −0.4
2013 77.4 1.8 74.2 76.0 77.2 78.5 83.1 8.9 −0.4
2014 77.6 1.8 74.4 76.2 77.5 78.8 83.2 8.8 −0.4
2015 78.3 1.7 75.2 76.9 78.2 79.4 83.6 8.4 −0.8
2016 78.7 1.7 75.4 77.2 78.5 79.7 84.0 8.6 −0.6
2017 78.9 1.8 75.5 77.5 78.9 79.9 84.2 8.7 −0.6
Women 2004 81.5 0.9 79.3 80.9 81.4 82.0 84.5 5.2
2005 81.8 0.9 79.7 81.2 81.7 82.2 84.7 5.1 −0.2−0.5
2006 82.0 0.8 80.1 81.5 81.9 82.5 84.9 4.8 −0.4
2007 82.4 0.8 80.5 81.8 82.3 82.9 85.3 4.8 −0.3
2008 82.9 0.9 80.9 82.3 82.8 83.3 85.9 5.0 −0.1
2009 83.3 0.9 81.4 82.8 83.2 83.8 86.5 5.1 −0.7
2010 83.5 0.9 81.8 83.0 83.4 83.9 86.4 4.6 −0.8
2011 83.8 0.8 82.3 83.3 83.7 84.2 86.7 4.4 −0.8
2012 83.9 0.8 82.2 83.3 83.7 84.3 86.6 4.4 −1.0
2013 84.4 0.8 82.8 83.8 84.2 84.7 87.1 4.3 −0.9
2014 84.6 0.8 83.0 84.0 84.5 85.0 87.4 4.4 −0.6
2015 85.0 0.9 83.0 84.5 84.9 85.4 87.7 4.7 −0.7
2016 85.4 0.9 83.6 84.8 85.3 85.8 88.1 4.5 −0.9
2017 85.6 0.8 83.9 85.0 85.5 86.0 88.2 4.3
SD = standard deviation, Q1 = 25th percentile, Q2 = 50th percentile, Q3 = 75th percentile.
aGap in Max − Min: the gap in the difference between the maximum and minimum life expectancy at birth between 2004 and each year.
Between 2004 and 2017, district LE at birth increased by 4.57 years (95% CI, 4.49–4.65 years) for men (from 74.4 years [95% CI, 73.3–75.5 years] to 78.9 years [95% CI, 77.9–80.0 years]) and by 4.06 years (95% CI, 3.99–4.12 years) for women (from 81.5 years [95% CI, 80.7–82.4 years] to 85.6 years [95% CI, 84.8–86.3 years]) on average. LE at birth increased in all districts between 2004 and 2017, but the magnitude of those increases varied widely, from 2.42 years (95% CI, 2.35–2.44 years) in Yanggu-gun, Gangwon to 8.02 years (95% CI, 7.92–8.11 years) in Gangseo-gu, Busan for men, and from 2.87 years (95% CI, 2.81–2.90 years) in Gangjin-gun, Jeonnam to 5.70 years (95% CI, 5.60–5.78 years) in Sejong for women. For men, between 2004 and 2017, high increases in LE at birth were mainly observed in the southeast (Ulsan, Busan, Daegu, and nearby areas) and northwest (some areas of Gyeonggi and Sejong), while low increases in LE at birth were mainly observed in the north (Gangwon), east (Gyeongbuk), and southwest (near the border between Jeonnam and Jeonbuk). For women, high increases in LE at birth were mainly observed in the southeast (Busan, Gyeongnam, and Gyeongbuk) and northwest (Gyeonggi and Sejong), while low increases in LE at birth were mainly observed in band-shaped areas that cross the country from north to south (Fig. 3). The results for both sexes combined are given in Supplementary Fig. 3.

#### Change in life expectancy at birth in 250 districts between 2004 and 2017 for men (left) and women (right) in Korea, shown in 10 color groups with ranges for the categories determined by the deciles of changes in life expectancy at birth.

The gap in LE at birth between men and women decreased by 0.51 years (from 7.15 years in 2004 to 6.64 years in 2017). The gap between the lowest and highest LE at birth among districts decreased by 0.55 years (from 9.24 years to 8.69 years) for men and by 0.89 years (from 5.23 years to 4.34 years) for women between 2004 and 2017. The corresponding interquartile ranges increased by 0.12 years (from 2.28 years to 2.40 years) for men, but decreased by 0.09 years (from 1.08 years to 0.98 years) for women between 2004 to 2017. In 2017, very high LEs at birth, denoted by dots as outliers in the box plots, were observed in Suji-gu, Yongin-si, Gyeonggi; Bundang-gu, Seongnam-si, Gyeonggi; Seocho-gu, Seoul; Gangnam-gu, Seoul; Giheung-gu, Yongin-si, Gyeonggi; and Gwacheon-si, Gyeonggi for men, and observed in Gwacheon-si, Gyeonggi; Gangnam-gu, Seoul; Suji-gu, Yongin-si, Gyeonggi; Dongjak-gu, Seoul; Yongsan-gu, Seoul; Bundang-gu, Seongnam-si, Gyeonggi; Seocho-gu, Seoul; and Jung-gu, Seoul for women (Fig. 4). The results for both sexes combined are given in Supplementary Fig. 4.

#### Distribution of life expectancy at birth in 250 districts from 2004 to 2017 by gender in Korea; the bottom border, middle line, and top border of the boxes indicate the 25th, 50th, and 75th percentiles, respectively, across all districts; the dashed lines (whiskers) represent the full range across districts except outliers; and circles (outliers) represent the observations with the highest or lowest life expectancy at birth.

Table 3 shows a comparison of LE at birth at the district level, calculated from the observational data of NHID and from the spatio-temporal model. The absolute median differences between the observed and model-based LE at birth at the district level from 2004 to 2017 were less than 0.4 years for men and 0.3 years for women. The correlation coefficients between the observed and model-based LE at birth at the district level from 2004 to 2017 were 0.879 to 0.943 for men and 0.624 to 0.781 for women. The reason for the low correlation coefficients of LE at birth was that in some districts, LE at birth calculated from the observed mortality rates was unstable due to the small population numbers in each age group in the life table. For example, the observed and model-based LEs at birth at the district level in 2017 were quite different in some districts with small populations, such as Ongjin-gun, Imsil-gun, and Yanggu-gun (Fig. 5). To explore this issue, based on the finding of a previous study9 that the minimum population required for a stable LE was 5000, we calculated the LE at birth for 250 districts using 7-year pooled data for population and deaths (2004–2010 and 2011–2017), and the newly obtained correlation coefficients are in the last column in Table 3, showing that the observed and model-based LEs at birth were highly correlated. Thus, using LE obtained from spatio-temporal models, rather than LE calculated from the observed mortality rates, enables stable estimates of annual district-level LE to be obtained. The results for both sexes combined are given in Supplementary Table 3.

#### Annual comparison of median results between the observed and model-based life expectancies at birth at the district level by gender

Gender Year Median life expectancy at birth
Observeda Modeledb Diffc Corrd Corr2e
Men 2004 73.6 74.0 −0.4 0.930 0.992
2005 74.1 74.4 −0.3 0.943
2006 74.9 74.8 −0.1 0.925
2007 75.2 75.0 −0.2 0.933
2008 75.7 75.5 0.0 0.911
2009 76.1 75.9 −0.0 0.917
2010 76.3 76.2 −0.1 0.899
2011 76.7 76.5 0.1 0.917 0.991
2012 77.0 76.7 0.1 0.923
2013 77.6 77.2 0.3 0.892
2014 78.1 77.5 0.4 0.891
2015 78.6 78.2 0.2 0.913
2016 78.9 78.5 0.3 0.879
2017 79.3 78.9 0.3 0.905
Women 2004 81.2 81.4 −0.3 0.759 0.952
2005 81.4 81.7 −0.3 0.781
2006 81.8 81.9 −0.1 0.682
2007 82.2 82.3 −0.1 0.685
2008 82.8 82.8 −0.0 0.742
2009 83.2 83.2 −0.1 0.688
2010 83.4 83.4 −0.0 0.624
2011 83.9 83.7 0.0 0.770 0.944
2012 84.0 83.7 0.1 0.687
2013 84.6 84.2 0.2 0.653
2014 84.8 84.5 0.2 0.624
2015 85.1 84.9 0.1 0.662
2016 85.7 85.3 0.3 0.635
2017 85.9 85.5 0.3 0.632
All correlation coefficients in Corr and Corr2 are statistically significant (P value < 0.001).
aObserved: median life expectancy at birth at the district level calculated from the observational data of the National Health Information Database; bModeled: median life expectancy at birth at the district level from the spatio-temporal model; cDiff: median difference between the observed and model-based life expectancies at birth at the district level; dCorr: correlation between the observed and model-based life expectancies at birth; eCorr2: correlation between the observed and model-based life expectancies at birth based on 7-year pooled data.

### DISCUSSION

In this study, we estimated annual district-level LE using the NHID DB from 2004 to 2017 through spatio-temporal analysis. Compared to purely spatial analysis or time-series analysis, spatio-temporal analysis has the advantage of being able to simultaneously study the effects of space and time. Spatio-temporal models allow for various kinds of interactions and relationships (spatial dependencies, temporal dependencies, and space-time dependencies) that may be present in the data, thus avoiding inappropriate model fitting (e.g., by ignoring dependencies) that may lead to incorrect conclusions.
Estimating LE based on spatio-temporal modeling, as done in this study, is necessary for the following reasons. First, model-based LEs in districts with small populations are more stable than LEs calculated under the assumption of independent observations. Second, annual LEs can be calculated without pooling multi-year data to secure the minimum population number required for a stable LE in each geographic area. Third, since the mortality rates are similar in adjacent regions, it is statistically inappropriate to conduct an analysis assuming that the mortality rates in each area are independent of each other. This study is meaningful in that it is the first study, to the best of our knowledge, to estimate LE at the district level in Korea by addressing the above issues.
Table 2 and Fig. 4 present decreases in the gaps in LE across districts in Korea. These findings are in line with prior Korean studies, which also reported similar temporal decreases in mortality metrics across districts in Korea.1920 In addition, mortality inequalities by geographic deprivation index have decreased in Korea.2122 These temporal patterns in geographic mortality inequalities are in contrast with the increasing inequalities in mortality metrics (LE and age-adjusted mortality rates) by individual socioeconomic position indicators, such as income and education, in Korea.232425
Study results showed that the Moran’s I was greater in men than in women. The gender difference in the Moran's I means that geographical clustering in mortality is more pronounced in men than in women in Korea. In Korea as well as in many other countries, the magnitude of socioeconomic inequalities in mortality and life expectancy is greater in men than in women.57232425 If the geographic areas in Korea reflect socio-economic position and such geographic areas tend to cluster, it is expected that the magnitude of clustering in mortality would be greater in men than in women.
This study has certain limitations that should be acknowledged. First, when constructing the adjacency weight matrix 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.
Based on the results of this study, the annual district-level LE could be used as a performance indicator of the local government's health policies to improve the health of local residents, and information on the LE gap between districts will ultimately contribute to stimulating health-equity policies and projects at the district level. It is also expected that annually monitoring and evaluating LE gaps across regions at the district level will help achieve a long-term health equity policy.
The approach to district-level analysis with a spatio-temporal modeling employed in this study could be used in future analyses to produce district-level health-related indicators (e.g., healthy LE) in Korea, such as forecasts of future mortality and LE, or cause-specific mortality rates.

### Notes

Funding: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF- 2019R1I1A1A01063964). This research was also supported by a grant of the Korea Health Technology R&D Project through the Korea Health Industry Development Institute (KHIDI), funded by the Ministry of Health & Welfare, Republic of Korea (grant No. HI18C0446).

Disclosure: The authors have no potential conflicts of interest to disclose.

Author Contributions:

• Conceptualization: Khang YH.v

• Data curation: Kang HY.

• Formal analysis: Lim HK, Kim IH.

• Writing - original draft: Lim HK, Khang YH.

• Writing - review & editing: Lim HK, Khang YH, Kang HY, Kim IH.

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### SUPPLEMENTARY MATERIALS

#### Supplementary Table 1

National-level deaths, number of population, age-standardized mortality rates, and district-level distribution of age-standardized mortality rates for both sexes combined, 2004-2017
jkms-36-e8-s001.doc

#### Supplementary Table 2

Distribution of district-level life expectancies at birth based on the spatio-temporal model for both sexes combined, 2004–2017
jkms-36-e8-s002.doc

#### Supplementary Table 3

Annual comparison of median results between the observed and model-based life expectancies at birth at the district level for both sexes combined
jkms-36-e8-s003.doc

#### Supplementary Table 4

The observed and spatio-temporal model-based life expectancies at birth at the district level by gender in 2017
jkms-36-e8-s004.doc

#### Supplementary Fig. 1

Age-standardized mortality rates per 100,000 population in 250 districts for both sexes in Korea, 2017, shown in 10 color groups with ranges for the categories determined by the deciles of age-standardized mortality rates per 100,000 population.
jkms-36-e8-s005.doc

#### Supplementary Fig. 2

Life expectancy at birth in 250 districts for both sexes combined in Korea, 2017, shown in 10 color groups with ranges for the categories determined by the deciles of life expectancy at birth.
jkms-36-e8-s006.doc

#### Supplementary Fig. 3

Change in life expectancy at birth in 250 districts between 2004 and 2017 for both sexes combined in Korea, shown in 10 color groups with ranges for the categories determined by the deciles of changes in life expectancy at birth.
jkms-36-e8-s007.doc

#### Supplementary Fig. 4

Distribution of life expectancy at birth in 250 districts from 2004 to 2017 for both sexes combined in Korea; the bottom border, middle line, and top border of the boxes indicate the 25th, 50th, and 75th percentiles, respectively, across all districts; the dashed lines (whiskers) represent the full range across districts except outliers; and circles (outliers) represent the observations with the highest life expectancy at birth.
jkms-36-e8-s008.doc
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