應用APC模式建構台灣世代平均餘命

Abstract

平均餘命在公共衛生和社會科學都有廣泛的運用。目前計算平均餘命多數是基於年代，然而年代平均餘命有許多缺點。例如，世代平均餘命可以反映實際群體平均餘命的改善或惡化，但是年代平均餘命不行。因此世代平均餘命比年代平均餘命容易解釋。不過計算世代平均餘命時常面臨資料不完整而遭遇困難。本論文使用台灣1975年至2022年0歲至90歲的人口資料計算死亡率並建構死亡機率，進而推算台灣137個世代的平均餘命。為了克服台灣137個世代死亡率資料不完整的問題，本論文使用年齡、年代、世代模式、簡單線性迴歸與蒙地卡羅模擬來建構缺失的死亡機率。年齡、年代、世代模式由年齡、年代和世代效應組成。由於世代加上年齡等於年代，使用年齡、年代、世代模式會遭遇不可甄別問題。本論文採用總和為零的限制式與額外的限制式克服不可甄別問題。有了137個世代各年齡層的死亡率後，可以將其轉成死亡機率並用美國疾病管制與預防中心的方法計算世代平均餘命。本論文發現台灣男性和女性的世代平均餘命趨勢向上，但是兩者的世代平均餘命在2022年的有所下降。本論文使用概似比檢定比較年齡、年代、世代模式(三因子)、單因子模式和雙因子模式，從結果可以發現三因子模式表現最好。進一步比較年齡、年代、世代模式和年齡、世代效應模式的對稱平均絕對百分比誤差，年齡、年代、世代模式的對稱平均絕對百分比誤差較小。本論文提供具便利性的方法來推估世代平均餘命，未來可以結合其他領域進行應用。例如，在社會科學方面，可以用以評估公共政策的成效。在公共衛生方面，可以評估疫苗政策或篩檢政策的成效，了解政策能夠提升多少世代平均餘命，藉以評估政策的效益。

Life expectancy is widely used in public health and social sciences. In addition, life expectancy is mostly calculated based on the period of time. However, period-based life expectancy has many drawbacks. For example, cohort-based life expectancy can reflect improvements or deteriorations in the life expectancy of a real population, whereas period-based life expectancy cannot. Therefore, cohort-based life expectancy can be interpreted easily. Due to incomplete mortality data, calculating cohort-based life expectancy often encounters difficulties. Population data of ages between 0 to 90 from Taiwan, spanning from 1975 to 2022, is used to obtain mortality rates and probability of death. Then, life expectancy of 137 cohorts in Taiwan is estimated. To resolve the issue of incomplete mortality data for these 137 cohorts, age-period-cohort models, simple linear regression and Monte Carlo approach are employed. The age-period-cohort model consists of age, period, and cohort effects. Because of the perfect collinearity of age, period, and cohort, that is, given the age and calendar year, the birth year can be determined. This is the so-called non-identifiability problem. Non-identifiability problem is overcome by applying the sum-to-zero constraint and additional constraint. After all mortality rates for different age groups across 137 cohorts are obtained, it is possible to convert these into probability of death and construct cohort-based life expectancy using the method of the Centers for Disease Control and Prevention. The result shows that the trend of cohort-based life expectancy at birth for both males and females in Taiwan has been upward; however, it has declined in 2022. Likelihood ratio tests are conducted to compare age-period-cohort models (three-factor model), one-factor models, and two-factor models. The result indicates that three-factor models are the best. On further comparison of the symmetric mean absolute percentage error between age-period-cohort models and age-cohort models, the errors of age-period-cohort models are smaller. This study provides a convenient method for estimating cohort-based life expectancy. This method can be applied to many fields, such as social sciences and public health. For example, it can be used to evaluate the effectiveness of policies. Furthermore, it can also be used to understand how much cohort-based life expectancy increases due to these policies and evaluate whether the desired result of vaccination or disease screening has been achieved.