复发竞争风险、纵向标志物与健康状态的联合动态模型及统计推断
Joint Dynamic Models and Statistical Inference for Recurrent Competing Risks, Longitudinal Marker, and Health Status
AI总结：
本文针对纵向研究中复发竞争风险、纵向标志物与健康状态过程的关联建模问题，提出基于计数过程和连续时间马尔可夫链的联合动态随机模型，并开发半参数与似然推断方法，以支持个性化干预和精准医疗。
摘要：
考虑在纵向生物医学、公共卫生、工程、经济或社会科学研究中，一个受试者或单元在可能随机的时长内被监测。随时间推移，该单元经历竞争性复发事件，且一个纵向标志物在离散状态空间上发生转移。此外，其“健康或表现”状态也在离散状态空间上转移，其中某些状态可能是吸收态。一个协变量向量也将与该单元相关联。如果存在吸收态，该单元所关注的是其健康状态过程的吸收时间，这可被视为该单元的寿命。除了受其协变量向量影响外，复发竞争风险过程、纵向标志物过程和健康状态过程之间可能存在关联，即每个过程的时间演化与其他过程相关联。为了获得更真实的模型并提高推断性能，提出了这些组成部分的联合动态随机模型，并开发了统计推断方法。该联合模型通过计数过程和连续时间马尔可夫链构建，具有促进“个性化”干预的潜力。例如，这可以促进精准医疗在医学环境中的实施和采用。当可获得这些单元的样本时，开发了模型参数的半参数和基于似然的推断方法。模型参数估计量的有限样本性质和大样本性质，包括有限维和无限维参数，均通过解析推导或模拟研究获得。
英文摘要：
Consider a subject or unit in a longitudinal biomedical, public health, engineering, economic, or social science study which is being monitored over a possibly random duration. Over time this unit experiences competing recurrent events and a longitudinal marker transitions over a discrete state-space. In addition, its ``health or performance'' status also transitions over a discrete state-space with some states possibly absorbing states. A vector of covariates will also be associated with this unit. If there are absorbing states, of interest for this unit is its time-to-absorption of its health status process, which could be viewed as the unit's lifetime. Aside from being affected by its covariate vector, there could be associations among the recurrent competing risks processes, the longitudinal marker process, and the health status process in the sense that the time-evolution of each process is associated with the other processes. To obtain more realistic models and enhance inferential performance, a joint dynamic stochastic model for these components is proposed and statistical inference methods are developed. This joint model, formulated via counting processes and continuous-time Markov chains, has the potential of facilitating `personalized' interventions. This could enhance, for example, the implementation and adoption of precision medicine in medical settings. Semi-parametric and likelihood-based inferential methods for the model parameters are developed when a sample of these units is available. Finite-sample and asymptotic properties of estimators of model parameters, both finite- and infinite-dimensional, are obtained analytically or through simulation studies.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
