We use the illness-death model (IDM) for chronic conditions to derive a new analytical relation between the transition rates between the states of the IDM. The transition rates are the incidence rate (i) and the mortality rates of people without disease (m0) and with disease (m1). For the most generic case, the rates depend on age, calendar time and in case of m1 also on the duration of the disease. In this work, we show that the prevalence-odds can be expressed as a convolution-like product of the incidence rate and an exponentiated linear combination of i, m0 and m1. The analytical expression can be used as the basis for a maximum likelihood estimation (MLE) and associated large sample asymptotics. In a simulation study where a cross-sectional trial about a chronic condition is mimicked, we estimate the duration dependency of the mortality rate m1 based on aggregated current status data using the ML estimator. For this, the number of study participants and the number of diseased people in eleven age groups are considered. The ML estimator provides reasonable estimates for the parameters including their large sample confidence bounds.

翻译：本研究采用针对慢性疾病的illness-death模型(IDM)，推导出IDM各状态间转移率之间的新型解析关系。转移率包括发病率(i)、未患病者死亡率(m0)及患病者死亡率(m1)。在最一般情形下，这些比率依赖于年龄、日历时间，而m1还受病程时长影响。本文证明患病优势比可表示为发病率与i、m0、m1指数线性组合的卷积型乘积。该解析表达式可作为最大似然估计(MLE)及其大样本渐近理论的基础。在模拟研究中（模拟某慢性疾病的横断面试验），我们基于聚合当前状态数据，采用最大似然估计量估算m1的病程依赖性。研究中考虑了11个年龄组的参试者总数及患病人数。最大似然估计量能够给出包含大样本置信区间在内的合理参数估计。