BACKGROUND
Healthy longevity (HL) is an important measure of the prospects for quality of life in ageing societies. Incidence-based (cf. prevalence-based) models describe transitions among age classes and health stages. Despite the probabilistic nature of those transitions, analyses of healthy longevity have focused persistently on means (``health expectancy''), neglecting variances and higher moments.

OBJECTIVE
Our goal is a comprehensive methodology to analyze HL in terms of any combination of health stages and age classes, or of transitions among health stages, or of values (e.g., quality of life) associated with health stages or transitions.

METHODS
We construct multistate Markov chains for individuals classified by age and health stage and use Markov chains with rewards to compute all moments of HL.

RESULTS
We present a new and straightforward algorithm to create the multistate reward matrices for occupancy, transitions, or values associated with occupancy or transitions. As an example, we analyze a published model for colorectal cancer. The possible definitions of HL in this simple model outnumber the stars in the visible universe. Our method can analyze any of them; we show four examples: longevity without abnormal cells, cancer-free longevity, and longevity with cancer before or after a critical age.



中文翻译：

---

基于发病率模型的健康长寿：比天空中的星星更多的健康（作者：Hal Caswell，Silke van Daalen）

背景
健康长寿（HL）是衡量老龄化社会生活质量前景的重要指标。基于发生率（参见基于流行率）的模型描述了年龄等级和健康阶段之间的转变。尽管这些转变具有概率性质，但对健康长寿的分析一直专注于均值（“健康预期”），而忽略了差异和更高的时刻。

目标
我们的目标是根据健康阶段和年龄等级的任意组合、健康阶段之间的转变或与健康阶段或转变相关的价值（例如，生活质量）来分析HL的综合方法。

方法
我们为按年龄和健康阶段分类的个人构建多状态马尔可夫链，并使用带奖励的马尔可夫链来计算 HL 的所有时刻。

结果
我们提出了一种新的、直接的算法来为占用、转换或与占用或转换相关的值创建多状态奖励矩阵。例如，我们分析了已发表的结直肠癌模型。在这个简单模型中，HL 的可能定义数量超过了可见宇宙中的恒星。我们的方法可以分析其中任何一个；我们展示了四个例子：没有异常细胞的长寿、无癌症的长寿和关键年龄之前或之后的癌症长寿。