Publications-Theses
Article View/Open
Publication Export
-
Google ScholarTM
NCCU Library
Citation Infomation
Related Publications in TAIR
題名 平均餘命之估計方法
A Study of Estimation Methods for Life Expectancy作者 賴東圻
Lai, Dong-Qi貢獻者 余清祥<br>楊曉文
Yu, Qing-Xiang<br>Yang, Xiao-Wen
賴東圻
Lai, Dong-Qi關鍵詞 平均餘命
地區不平等
核修勻
標準化死亡率
克里金空間插值法
Life Expectancy
Regional Inequality
Kernel Smoothing
Standardized Death Rate
Kriging Spatial Interpolation日期 2025 上傳時間 2-Oct-2025 10:57:21 (UTC+8) 摘要 平均餘命為評估某地區人口健康狀況與不平等的重要指標，常用於公共衛生政策、資源分配與國際比較。然而，平均餘命在人口較少地區，因為樣本數稀疏而造成死亡率震盪，致使估計數值經常有高度波動的現象。雖然平均餘命估計大多透過生命表編算，背後雖有理論基礎的支撐，但在樣本不多時仍會有不小震盪，錯估平均餘命而導致不當的資源配置。因此本研究比較不同平均餘命估計方法，包括死亡率修勻、標準化死亡率（Standardized Mortality Rate）、空間內插（如Ordinary Kriging）等方法，藉由電腦模擬與實證分析，系統性的評估哪些方法較為穩定。本文評估標準採用估計偏誤、變異與均方誤差（MSE）。結果顯示，不修勻的平均餘命估計方法適用於人口較多時（如10萬），但人口不足5萬會有較大的估計偏誤；5萬到20萬人口需加入修勻較能降低估計震盪，而SDR模型則可用於人數低於5萬的情境。另外，套用空間模型的平均餘命估計結果在死亡率均質時會優於單點估計，且納入模型的點愈多估計效果愈佳。但在死亡率異質下，隨著納入的點增加，估計上會產生較大的偏誤，均方誤差會高於單點的估計。換言之，不同估算方法各具優勢，適用情境應根據人口規模、資料特性與研究目的而選擇。建議未來在小區域健康指標估計與發布時，應納入修勻或空間統計方法，同時揭露估計不確定性與方法選擇依據，以強化數據透明度與決策可用性。
Life expectancy is a crucial indicator for assessing population health status and inequality, widely applied in public health policy, resource allocation, and international comparisons. However, in areas with small populations, sparse data often lead to large fluctuations in mortality rates, resulting in unstable and biased estimates of life expectancy. Although life expectancy estimation is typically based on the life table method with solid theoretical foundations, it still suffers from considerable variation in small samples, which may misguide health assessments and resource distribution. This study compares several approaches to estimating life expectancy, including mortality smoothing, standardized death rate (SDR) models, and spatial interpolation methods such as ordinary kriging. Through computer simulations and empirical analysis, we systematically evaluate the stability of these methods using bias, variance, and mean squared error (MSE) as performance criteria. The results indicate that unsmoothed life expectancy estimates are suitable when the population size is large (e.g., 100,000), but they exhibit substantial bias when the population is below 50,000. For populations between 50,000 and 200,000, smoothing techniques effectively reduce fluctuations, while SDR models perform better in areas with fewer than 50,000 people. Furthermore, spatial models improve estimation when mortality rates are homogeneous across regions, and performance increases as more locations are incorporated. However, in heterogeneous mortality settings, including more locations may introduce greater bias and lead to higher MSE compared to single-area estimates. In conclusion, different estimation methods have their respective strengths, and their applicability depends on population size, data characteristics, and research objectives. We recommend that future small-area health indicator estimation and dissemination incorporate smoothing or spatial statistical approaches, while also reporting uncertainty and methodological considerations to enhance transparency and policy relevance.參考文獻 一、 中文文獻： [1] 王信忠、余清祥、王子瑜（2017），「臺灣原住民族死亡率暨生命表編撰研究」，《人口學刊》，55，99-131。 [2] 王信忠、金碩、余清祥（2012），「小區域死亡率推估之研究」，《人口學刊》，45，77-110。 [3] 余清祥、王信忠、呂靖翎（2025），「平均餘命與標準化死亡率之相關分析」，《人口學刊》。 [4] 余清祥、連宏銘（1999），「台灣地區死亡率現況的實證研究」，《壽險季刊》，111，2-16。 [5] 林正祥、張怡陵（2020），「影響平均餘命增長之生命表特性及其相關死亡率模式分析」，《台灣公共衛生雜誌》，39(1)，74-89。 [6] 董宜禎、陳寬政、王德睦、吳郁婷（2015），「臺灣人口平均餘命之趨緩成長」，《人口學刊》，50，29-60。 [7] 溫啓邦、蔡善璞、鍾文慎（2005），「高雄市與臺北市居民平均餘命差距之分析」，《臺灣衛生研究》，44(2)，101-124。 [8] 羅悅之（2017），「台灣死因別死亡率之社會經濟不平等（1971-2012）：生態研究」，臺灣大學健康政策與管理所碩士論文。 二、 英文文獻： [1] Chen, L., Gao, Y., Zhu, D., Yuan, Y., & Liu, Y. (2019). Quantifying the Scale Effect in geospatial big data using semi-variograms. PLOS ONE, 14(11), e0225139. [2] Chiang, C. L. (1960). A stochastic study of the life table and its applications: I. Probability Distributions of the Biometric functions. Biometrics, 16(4), 618–635. [3] Chiang, C. L. (1972). On constructing current life tables. Journal of the American Statistical Association, 67(339), 538–541. [4] Cressie, N. (2015). Statistics for spatial data. John Wiley & Sons. [5] Debón, A., Martínez-Ruiz, F., & Montes, F. (2010). A geostatistical approach for dynamic life tables: The effect of mortality on remaining lifetime and annuities. Insurance: Mathematics and Economics, 47(3), 327-336. [6] Eayres, D., & Williams, E. S. (2004). Evaluation of methodologies for small area life expectancy estimation. Journal of Epidemiology & Community Health, 58(3), 243-249. [7] Eilers, P. H., & Marx, B. D. (1996). Flexible Smoothing with B-splines and penalties. Statistical Science, 11(2), 89–121. [8] Goovaerts, P. (2005). Geostatistical Analysis of disease data: estimation of cancer mortality risk from empirical frequencies using Poisson kriging. International Journal of Health Geographics, 4, 1-33. [9] Graunt, J. (1665). Natural and political observations mentioned in a following index, and made upon the bills of mortality (3rd ed., much enlarged). Printed by John Martyn and James Allestry. [10] Halley, E. (1693). VI. An estimate of the degrees of the mortality of mankind; drawn from curious tables of the births and funerals at the city of Breslaw; with an attempt to ascertain the price of annuities upon lives. Philosophical Transactions of the Royal Society of London, 17(196), 596–610. [11] Hsu, C. C., Tsai, D. R., Su, S. Y., Jhuang, J. R., Chiang, C. J., Yang, Y. W., & Lee, W. C. (2023). A stabilized kriging method for mapping disease rates. Journal of Epidemiology, 33(4), 201-208. [12] Malczewski, J. (2010). Exploring spatial autocorrelation of life expectancy in Poland with global and local statistics. GeoJournal, 75, 79-92. [13] Oliver, M. A., & Webster, R. (1990). Kriging: A method of interpolation for geographical information systems. International Journal of Geographical Information Systems, 4(3), 313–332. [14] Tsai, S. P., Hardy, R. J., & Wen, C. P. (1992). The standardized mortality ratio and life expectancy. American Journal of Epidemiology, 135(7), 824–831. [15] Tyagi, A., & Singh, P. (2013). Applying kriging approach on pollution data using GIS software. International Journal of Environmental Engineering and Management, 4(3), 185–190. [16] Wang, J. L. (2005). Smoothing hazard rates. Encyclopedia of biostatistics (Vol. 7, pp. 4986–4997). Wiley. [17] Yue, J. C., Lin, C. T., Yang, Y. L., Chen, Y. C., Tsai, W. C., & Leong, Y. Y. (2023). Selection effect modification to the Lee-Carter model. European Actuarial Journal, 13(1), 213-234. [18] Yue, J. C., Tu, M. H., & Leong, Y. Y. (2024). A spatial analysis of the health and longevity of Taiwanese people. The Geneva Papers on Risk and Insurance-Issues and Practice, 49(2), 384-399. 描述 碩士
國立政治大學
統計學系
112354005資料來源 http://thesis.lib.nccu.edu.tw/record/#G0112354005 資料類型 thesis dc.contributor.advisor 余清祥<br>楊曉文 zh_TW dc.contributor.advisor Yu, Qing-Xiang<br>Yang, Xiao-Wen en_US dc.contributor.author (Authors) 賴東圻 zh_TW dc.contributor.author (Authors) Lai, Dong-Qi en_US dc.creator (作者) 賴東圻 zh_TW dc.creator (作者) Lai, Dong-Qi en_US dc.date (日期) 2025 en_US dc.date.accessioned 2-Oct-2025 10:57:21 (UTC+8) - dc.date.available 2-Oct-2025 10:57:21 (UTC+8) - dc.date.issued (上傳時間) 2-Oct-2025 10:57:21 (UTC+8) - dc.identifier (Other Identifiers) G0112354005 en_US dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/159687 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 112354005 zh_TW dc.description.abstract (摘要) 平均餘命為評估某地區人口健康狀況與不平等的重要指標，常用於公共衛生政策、資源分配與國際比較。然而，平均餘命在人口較少地區，因為樣本數稀疏而造成死亡率震盪，致使估計數值經常有高度波動的現象。雖然平均餘命估計大多透過生命表編算，背後雖有理論基礎的支撐，但在樣本不多時仍會有不小震盪，錯估平均餘命而導致不當的資源配置。因此本研究比較不同平均餘命估計方法，包括死亡率修勻、標準化死亡率（Standardized Mortality Rate）、空間內插（如Ordinary Kriging）等方法，藉由電腦模擬與實證分析，系統性的評估哪些方法較為穩定。本文評估標準採用估計偏誤、變異與均方誤差（MSE）。結果顯示，不修勻的平均餘命估計方法適用於人口較多時（如10萬），但人口不足5萬會有較大的估計偏誤；5萬到20萬人口需加入修勻較能降低估計震盪，而SDR模型則可用於人數低於5萬的情境。另外，套用空間模型的平均餘命估計結果在死亡率均質時會優於單點估計，且納入模型的點愈多估計效果愈佳。但在死亡率異質下，隨著納入的點增加，估計上會產生較大的偏誤，均方誤差會高於單點的估計。換言之，不同估算方法各具優勢，適用情境應根據人口規模、資料特性與研究目的而選擇。建議未來在小區域健康指標估計與發布時，應納入修勻或空間統計方法，同時揭露估計不確定性與方法選擇依據，以強化數據透明度與決策可用性。 zh_TW dc.description.abstract (摘要) Life expectancy is a crucial indicator for assessing population health status and inequality, widely applied in public health policy, resource allocation, and international comparisons. However, in areas with small populations, sparse data often lead to large fluctuations in mortality rates, resulting in unstable and biased estimates of life expectancy. Although life expectancy estimation is typically based on the life table method with solid theoretical foundations, it still suffers from considerable variation in small samples, which may misguide health assessments and resource distribution. This study compares several approaches to estimating life expectancy, including mortality smoothing, standardized death rate (SDR) models, and spatial interpolation methods such as ordinary kriging. Through computer simulations and empirical analysis, we systematically evaluate the stability of these methods using bias, variance, and mean squared error (MSE) as performance criteria. The results indicate that unsmoothed life expectancy estimates are suitable when the population size is large (e.g., 100,000), but they exhibit substantial bias when the population is below 50,000. For populations between 50,000 and 200,000, smoothing techniques effectively reduce fluctuations, while SDR models perform better in areas with fewer than 50,000 people. Furthermore, spatial models improve estimation when mortality rates are homogeneous across regions, and performance increases as more locations are incorporated. However, in heterogeneous mortality settings, including more locations may introduce greater bias and lead to higher MSE compared to single-area estimates. In conclusion, different estimation methods have their respective strengths, and their applicability depends on population size, data characteristics, and research objectives. We recommend that future small-area health indicator estimation and dissemination incorporate smoothing or spatial statistical approaches, while also reporting uncertainty and methodological considerations to enhance transparency and policy relevance. en_US dc.description.tableofcontents 第一章、 緒論 1 第一節、 研究背景與動機 1 第二節、 研究目的 4 第二章、 文獻探討 5 第一節、 文獻回顧 5 第二節、 資料介紹 6 第三節、 研究方法 7 第三章、 傳統死亡率平均餘命估計方法模擬 13 第一節、 平均餘命估算公式之模擬比較（不修勻情境） 13 第二節、 平均餘命估算公式之模擬比較（核修勻情境） 16 第三節、 SDR迴歸模型估計方法 19 第四節、 平均餘命估計方法比較 23 第四章、 克里金插值估計方法 26 第一節、 空間資料模擬與設計原則 26 第二節、 鄰近點納入效果之影響 29 第三節、 半變異函數之估計與模型選擇 32 第四節、 死亡率同質性估計結果 36 第五節、 死亡率異質性估計結果 40 第五章、 結論與建議 46 第一節、 結論 46 第二節、 建議 47 參考文獻 49 附錄 52 一、 平均餘命估計公式 52 二、 不同估計方法之MSE比較（女性） 54 zh_TW dc.format.extent 3536265 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0112354005 en_US dc.subject (關鍵詞) 平均餘命 zh_TW dc.subject (關鍵詞) 地區不平等 zh_TW dc.subject (關鍵詞) 核修勻 zh_TW dc.subject (關鍵詞) 標準化死亡率 zh_TW dc.subject (關鍵詞) 克里金空間插值法 zh_TW dc.subject (關鍵詞) Life Expectancy en_US dc.subject (關鍵詞) Regional Inequality en_US dc.subject (關鍵詞) Kernel Smoothing en_US dc.subject (關鍵詞) Standardized Death Rate en_US dc.subject (關鍵詞) Kriging Spatial Interpolation en_US dc.title (題名) 平均餘命之估計方法 zh_TW dc.title (題名) A Study of Estimation Methods for Life Expectancy en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 一、 中文文獻： [1] 王信忠、余清祥、王子瑜（2017），「臺灣原住民族死亡率暨生命表編撰研究」，《人口學刊》，55，99-131。 [2] 王信忠、金碩、余清祥（2012），「小區域死亡率推估之研究」，《人口學刊》，45，77-110。 [3] 余清祥、王信忠、呂靖翎（2025），「平均餘命與標準化死亡率之相關分析」，《人口學刊》。 [4] 余清祥、連宏銘（1999），「台灣地區死亡率現況的實證研究」，《壽險季刊》，111，2-16。 [5] 林正祥、張怡陵（2020），「影響平均餘命增長之生命表特性及其相關死亡率模式分析」，《台灣公共衛生雜誌》，39(1)，74-89。 [6] 董宜禎、陳寬政、王德睦、吳郁婷（2015），「臺灣人口平均餘命之趨緩成長」，《人口學刊》，50，29-60。 [7] 溫啓邦、蔡善璞、鍾文慎（2005），「高雄市與臺北市居民平均餘命差距之分析」，《臺灣衛生研究》，44(2)，101-124。 [8] 羅悅之（2017），「台灣死因別死亡率之社會經濟不平等（1971-2012）：生態研究」，臺灣大學健康政策與管理所碩士論文。 二、 英文文獻： [1] Chen, L., Gao, Y., Zhu, D., Yuan, Y., & Liu, Y. (2019). Quantifying the Scale Effect in geospatial big data using semi-variograms. PLOS ONE, 14(11), e0225139. [2] Chiang, C. L. (1960). A stochastic study of the life table and its applications: I. Probability Distributions of the Biometric functions. Biometrics, 16(4), 618–635. [3] Chiang, C. L. (1972). On constructing current life tables. Journal of the American Statistical Association, 67(339), 538–541. [4] Cressie, N. (2015). Statistics for spatial data. John Wiley & Sons. [5] Debón, A., Martínez-Ruiz, F., & Montes, F. (2010). A geostatistical approach for dynamic life tables: The effect of mortality on remaining lifetime and annuities. Insurance: Mathematics and Economics, 47(3), 327-336. [6] Eayres, D., & Williams, E. S. (2004). Evaluation of methodologies for small area life expectancy estimation. Journal of Epidemiology & Community Health, 58(3), 243-249. [7] Eilers, P. H., & Marx, B. D. (1996). Flexible Smoothing with B-splines and penalties. Statistical Science, 11(2), 89–121. [8] Goovaerts, P. (2005). Geostatistical Analysis of disease data: estimation of cancer mortality risk from empirical frequencies using Poisson kriging. International Journal of Health Geographics, 4, 1-33. [9] Graunt, J. (1665). Natural and political observations mentioned in a following index, and made upon the bills of mortality (3rd ed., much enlarged). Printed by John Martyn and James Allestry. [10] Halley, E. (1693). VI. An estimate of the degrees of the mortality of mankind; drawn from curious tables of the births and funerals at the city of Breslaw; with an attempt to ascertain the price of annuities upon lives. Philosophical Transactions of the Royal Society of London, 17(196), 596–610. [11] Hsu, C. C., Tsai, D. R., Su, S. Y., Jhuang, J. R., Chiang, C. J., Yang, Y. W., & Lee, W. C. (2023). A stabilized kriging method for mapping disease rates. Journal of Epidemiology, 33(4), 201-208. [12] Malczewski, J. (2010). Exploring spatial autocorrelation of life expectancy in Poland with global and local statistics. GeoJournal, 75, 79-92. [13] Oliver, M. A., & Webster, R. (1990). Kriging: A method of interpolation for geographical information systems. International Journal of Geographical Information Systems, 4(3), 313–332. [14] Tsai, S. P., Hardy, R. J., & Wen, C. P. (1992). The standardized mortality ratio and life expectancy. American Journal of Epidemiology, 135(7), 824–831. [15] Tyagi, A., & Singh, P. (2013). Applying kriging approach on pollution data using GIS software. International Journal of Environmental Engineering and Management, 4(3), 185–190. [16] Wang, J. L. (2005). Smoothing hazard rates. Encyclopedia of biostatistics (Vol. 7, pp. 4986–4997). Wiley. [17] Yue, J. C., Lin, C. T., Yang, Y. L., Chen, Y. C., Tsai, W. C., & Leong, Y. Y. (2023). Selection effect modification to the Lee-Carter model. European Actuarial Journal, 13(1), 213-234. [18] Yue, J. C., Tu, M. H., & Leong, Y. Y. (2024). A spatial analysis of the health and longevity of Taiwanese people. The Geneva Papers on Risk and Insurance-Issues and Practice, 49(2), 384-399. zh_TW
