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| 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
楊曉文
Yu, Qing-Xiang
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: | 2025-10-02 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：
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| 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 |
| 顯示於類別: | [統計學系] 學位論文
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