台灣的存活曲線矩型化與壽命延長

Rectangularization of the Survival Curve and Longevity Extension in Taiwan

10.6191/jps.2009.1

王德睦(Te-Mu Wang)；李大正(Ta-Cheng Li)

死亡率 ； 存活曲線矩型化 ； 死亡壓縮 ； 壽命延長 ； mortality ； rectangularization of survival curve ； mortality compression ； longevity extension

人口學刊

38期（2009 / 06 / 01）

1 - 31

繁體中文

1920年以後，台灣的死亡率開始長期大幅度的下降。早期以嬰幼兒死亡率的下降較明顯，晚近嬰幼兒死亡率已降至很低的水準，主要的死亡年齡以老年為主。上述變遷趨勢使得台灣的存活曲線，在年輕的部分由快速下降轉為接近水平；而在老年的部分則由較為平緩的下降，轉為較快速的下降，呈現出存活曲線矩型化的趨勢。存活曲線矩型化隱含存在壽命極限的概念，然是否存在壽命極限仍有爭議，部分學者轉從死亡年齡的集中化（死亡壓縮）的角度來理解矩型化現象，並延伸討論有關壽命延長的現象。 本文以生命表中的存活函數(l(下標 x))與死亡函數(d(下標 x))為分析的基礎，探討1955-2005年間台灣的死亡壓縮以及存活曲線的水平化、垂直化及其蘊含之壽命延長等現象。我們以SD(M+)、C50以及死亡年齡的四分位差(IQR)等指標測量死亡壓縮程度，並分解出各年齡組死亡率變化對死亡壓縮的影響。其次以固定矩型、移動矩型以及Cheunget al.(2005)建議的β、θ、θ(上標 *)、M+4SD(M+)等指標來衡量水平化、垂直化與壽命延長程度。結果顯示：存活曲線矩型化的程度（包括水平化與垂直化）於1955-2005年間持續上升。死亡壓縮的現象自1970年起趨於平緩，而造成死亡壓縮的主要力量從嬰幼兒死亡率下降轉向中、高年死亡率下降。M+4SD(M+)以及M+kSD(M+)兩個指標顯示兩性近五十年來的壽命延長仍呈現緩升趨勢，然本文之研究結果仍不足以確定壽命延長是否有極限。

The overall mortality rate in Taiwan has experienced a lengthy and drastic decline since 1920. The decline was first triggered by a phenomenal decrease in the infant mortality rate and, when this rate began to rest at its current low level, the elderly mortality rate took its turn to fall. As a result of the sharp drop then leveling off in the youth sector and the mild decrease then plunge in the elderly sector, rectangularization of the survival curve ensued. Although rectangularization of the survival curve implies the concept of a longevity limit, the existence of such a limit is still under debate. To avoid controversy, some scholars turn to interpret the rectangularization from the angle of mortality compression at age of death and extend their discussion to the phenomenon of longevity extension. This paper, based on the analysis of life table survivors (l(subscript x)) and life table deaths (d(subscript x)), discusses several phenomena that appeared in Taiwan between 1955 and 2005. These phenomena include mortality compression, the horizontalization and verticalization of the survival curve, and the implied longevity extension. We use indexes, such as SD(M+) (standard deviation of age at death above M), C50 (the shortest age interval concentrating 50 percent of the life duration), and the interquartile range (IQR) of age at death, to measure the degree of mortality compression, and to decompose the influence of changing mortality rate on mortality compression by age group. Next, we apply fixed rectangle, moving rectangle and other indexes recommended by Cheung et al. (2005), such as β, θ, θ(superscript *) and M+4SD(M+), to measure the horizontalization of the survival curve, the verticalization of the survival curve and the degree of longevity extension. Our results show that (1) rectangularization of the survival curve (including both horizontalization and verticalization of the survival curve) steadily increased during 1955 to 2005; (2) the degree of mortality compression had lessened since 1970, and the underlying force behind the mortality compression had shifted from the decrease in the infant mortality rate to the decrease in the adult and elderly mortality rate; (3) the two indexes M+4SD(M+) and M+kSD(M+) indicate that the longevity limit for both genders is still expanding upward gradually.

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