统计研究 ›› 2022, Vol. 39 ›› Issue (4): 134-146.doi: 10.19343/j.cnki.11–1302/c.2022.04.010

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长寿且健康了吗?——基于状态可转移概率模型的验证

崔晓东 周海花 朱英明 陈培文   

  • 出版日期:2022-04-25 发布日期:2022-04-24

Longevity with Health? Test Based on State-transition Probability Model

Cui Xiaodong Zhou Haihua Zhu Yingming Chen Peiwen   

  • Online:2022-04-25 Published:2022-04-24

摘要: 精准判断增龄趋势下所增加的寿命是否健康不仅事关老年人生活质量,也是诸多公共政策设计的基础。现有研究假设健康状态为非可逆的吸收态且满足时间齐性,更适用于身体功能不可康复或数据不充分情况下的粗略估计,本文结合中国老年健康影响因素跟踪调查(CLHLS)数据,基于Markov过程构建状态可转移的概率矩阵模型,利用分段常数转移强度和队列错位相乘克服纵贯数据不充分的局限,分年龄和性别计算寿命和健康寿命并考察健康模式和区域差异。模型的有效性通过递进生存率和寿命值与对照组的匹配关系得到了检验,结果发现,健康寿命在余寿中的比例随年龄递减,延长的寿命中更多的是不健康寿命;与2005—2008年相比,2014—2017年期间老年人寿命、健康寿命和不健康寿命均有增加,但健康寿命增长的速度未能匹配寿命增长速度;各地区老年人健康状况虽有差异,但均为残障期扩张模式。本文为老年健康变化的量化研究提供可对比方案,研究结论为诸如退休年龄设计、健康老龄规划及养老负担预测等提供基础数据。

关键词: 寿命, 健康寿命, 转移概率矩阵, 马尔科夫过程

Abstract: Accurate projections of the health of increased life expectancy in the aging trend are imperative for the life quality of the elderly and design of related public policies. Currently available models assume that all health states are static, chronic and irreversible, which is more suitable for rough estimation with insufficient data or the health conditions are unrecoverable. We develop an alternative method based on Markov process, using cross-sectional representative surveys to build multistate-transition probability matrix with the data of CLHLS, and to solve the homogeneous hypothesis due to insufficient data, adopt queue misalignment multiplication. Then we calculate the life expectancy (LE), healthy life expectancy (HLE) by age and sex and compare health models and regional differences. To test the validity of the model, the survival probability and life expectancy we estimate match the reference group results. Our results show that the proportion of healthy increased life in the increased life expectancy decreases with age, namely the increased life is dominated by unhealthy life; LE, HLE and unhealthy LE are increasing for the elderly in 2014—2017, but HLE growth has not kept up with the pace of LE; the elderly health differs between regions but maintains a general mode of disability expansion. This paper provides comparable schemes for the quantitative study of elderly health changes and the conclusion offers basic data for the design of retirement age, health elderly planning and prediction of elderly healthcare burdens.

Key words: Life Expectancy, Healthy Life Expectancy, Transition Probability Matrix, Markov Process