生命表結構及其衍生性公式應用探討

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Title:	生命表結構及其衍生性公式應用探討
Other Titles:	To explore the structural characteristics of Life Table and its Derivatives
Authors:	張怡陵 CHANG, YI-LING
Contributors:	林正祥 LIN, CHENG-HSIANG 統計學系
Keywords:	生命表衍生性公式;遲緩衰老;混合模式;死亡壓縮;死亡變異;存活曲線矩形化 life table derivatives;rectangularity of the survival curves;senescence-slowing;hybrid model of mortality;variability in the distribution of ages at death
Date:	2019
Issue Date:	2019-03-21T09:09:40Z (UTC)
Abstract:	生命表的概念起源於人類壽命的研究，它是人口學、保險精算學和公共衛生學中特有的專題，其係用來描述人口死亡過程的一種模型，且類似於可靠性理論中的統計方法；人類壽命是一種隨機實驗，其生死具有偶然性，生命表系統地記錄了一定人口中大量個體的生死結果，其中許多函數都是隨機變數。本研究利用生命表函數所衍生性之數學公式來詮釋生命表某些重要性質，以一窺生命表奧妙特性，並利用台灣生命表資料進行驗證，就其變化趨勢深入探討；先闡明生命表之結構特性，再藉由其衍生性公式進行分析探討生命表函數中風險函數、存活機率及平均餘命間之關係。此外，進一步就死亡年齡變異、存活曲線矩形化間之關係及延遲老化模式進行探討。1950年以後生命表資料顯示存活曲線矩形化趨勢明顯，由於死亡年齡變異與存活曲線矩形化為反向關係，我們藉由1996-2016年資料，以固定矩形、移動矩形、四分位距、標準差等指標測量存活曲線矩形化趨勢，另以Gini係數和生命表熵作為死亡年齡變異的測度。結果顯示：存活曲線在1996-2016年間逐漸呈現矩形化的情況，且死亡年齡變異也呈下降狀態。與矩形化緊密關連的現象為死亡壓縮，它是指死亡率下降過程，青中年人口存活率上升，死亡年齡逐漸集中在某一高齡區間的現象，故運用與死亡年齡眾數有關的標準差和C50指標來探討壽命後期死亡年齡變異的情形，均顯示變異會隨年代遞增而變小，而2008年後的死亡年齡區間收斂速度有變快的趨勢；最後我們以年齡95歲為上限利用面積差異百分比來檢測矩形化，其結果顯示矩形化逐漸趨向壽命極限。另一方面，有些研究學者認為人類的平均餘命長短與延遲老化有密切的關係，有諸多模式探討相關議題，其中較為重要之混合模式顯示平均餘命增長變化主要是受到死亡率下降和遲緩衰老步調下降消長的影響，吾等利用台灣1998-2008年的資料探討平均餘命增長趨勢，其中的27%是受到死亡率下降的影響，而受到延遲老化的影響則為73%，顯示這些年來平均餘命受到遲緩衰老的影響遠較死亡率下降來的大，對於平均餘命的展延，遲緩衰老當扮演舉足重的角色。 The concept of life table originated from the study of human longevity. It was presented as a subject peculiar to demography, actuarial science and public health. It is a model used to describe the process of population death and is similar to the statistical method in reliability theory. Human life is a random experiment, its outcomes, survival and death, are subject to death. A life table systematically records the life and death of a number of individuals in a certain population. Thus the elements in the life table are random variables. This study uses the mathematical formula derived from the life table random variables to interpret some important properties of the life table. The life table data in Taiwan is applied to verify the trend of these properties. Firstly, we clarify the structural characteristics of the life table, and use its derivatives to investigate some combinations among the force of mortality, survival probability and life expectancy. Secondly, we inspect the inverse relation between variability in the distribution of ages at death, and the rectangularity of the survival curves. Finally, a flexible model of mortality related to proportional-hazards and senescence-slowing is used for taking an inside look of the subtle characteristics of the life expectancy increasing. Historical data of Taiwan life table after 1950s shows that the survival curve appeared rectangularity gradually, and the variability in the distribution of ages at death is declining. Based on the life table data in Taiwan from 1998 to 2008, a hybrid model of mortality used for analyzing the life expectancy increasing of the elderly. We find the trend influence life expectancy increasing, of which 27% were affected by the decline in mortality, while 73% were affected by senescence-slowing, indicating the latter plays a pivotal role influence the life expectancy.
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