Division of Epidemiology and Biostatistics, School of Public Health, Faculty of Health Sciences, University of the Witwatersrand, Johannesburg, South Africa.
National Institute of Health Research, Causeway, Harare, Zimbabwe.
Stat Methods Med Res. 2021 May;30(5):1373-1392. doi: 10.1177/0962280221997507. Epub 2021 Apr 7.
There are numerous fields of science in which multistate models are used, including biomedical research and health economics. In biomedical studies, these stochastic continuous-time models are used to describe the time-to-event life history of an individual through a flexible framework for longitudinal data. The multistate framework can describe more than one possible time-to-event outcome for a single individual. The standard estimation quantities in multistate models are transition probabilities and transition rates which can be mapped through the Kolmogorov-Chapman forward equations from the Bayesian estimation perspective. Most multistate models assume the Markov property and time homogeneity; however, if these assumptions are violated, an extension to non-Markovian and time-varying transition rates is possible. This manuscript extends reviews in various types of multistate models, assumptions, methods of estimation and data features compatible with fitting multistate models. We highlight the contrast between the frequentist (maximum likelihood estimation) and the Bayesian estimation approaches in the multistate modeling framework and point out where the latter is advantageous. A partially observed and aggregated dataset from the Zimbabwe national ART program was used to illustrate the use of Kolmogorov-Chapman forward equations. The transition rates from a three-stage reversible multistate model based on viral load measurements in WinBUGS were reported.
科学领域有很多使用多状态模型的，包括生物医学研究和健康经济学。在生物医学研究中，这些随机连续时间模型用于通过灵活的纵向数据框架来描述个体的事件时间生命史。多状态框架可以为单个个体描述多个可能的事件时间结果。多状态模型中的标准估计量是转移概率和转移率，从贝叶斯估计的角度来看，可以通过柯尔莫哥洛夫- Chapman 向前方程将其映射。大多数多状态模型假设马尔可夫性质和时间同质性；但是，如果违反了这些假设，则可以扩展到非马尔可夫和时变转移率。本文扩展了各种类型的多状态模型、假设、估计方法和与拟合多状态模型兼容的数据特征的综述。我们强调了多状态建模框架中频率派（最大似然估计）和贝叶斯估计方法之间的对比，并指出后者的优势。津巴布韦国家 ART 项目的部分观察和聚合数据集用于说明柯尔莫哥洛夫- Chapman 向前方程的使用。基于 WinBUGS 中病毒载量测量的三阶段可逆多状态模型的转移率报告。
