多状态模型是复杂的随机模型，侧重于由多个重要事件的时间和连续发生所定义的路径。特别是所谓的疾病死亡模型对于研究与其他可能的疾病、健康状况或死亡竞争的疾病相关概率特别有用。它们可以看作是竞争风险模型的概括，广泛用于众多高死亡风险的人群、如老年人或癌症患者，估算疾病发生率。前述疾病死亡模型的主要优点是，它们可以处理具有顺序发生且可能有非终止竞争事件的情况，而竞争风险模型则难以做到。我们提出了一种使用Cox比例风险模型的疾病死亡模型，基线危险函数采用Weibull函数，应用该模型进行复发髋部骨折研究。数据来自PREV2FO队列，包括2008-2015年间年龄65岁及以上、经骨质疏松性髋部骨折住院并康复出院的34491名患者。我们采用贝叶斯方法来近似该模型的每个参数的后验分布，从而得出累积发病率和转换概率。我们还将这些结果与竞争风险规格进行比较。后验转移概率显示男性死亡的概率更高，且随着年龄的增长而增加。女性更有可能复发并在复发后较少死亡。自由事件时间显示能够减少死亡风险。尽管对于常见的转换，疾病死亡模型和竞争风险模型估计相同，但疾病死亡模型从复发到死亡的转换提供了额外的信息。我们说明了多状态模型，特别是疾病死亡模型，当涉及到包含多个事件的生存场景、竞争疾病或死亡是必须考虑的事件时，特别有用。疾病死亡模型通过转移概率提供了从非终止健康状态到吸收状态（如死亡）的过渡额外信息，这意味着与竞争风险模型相比，更深入地了解了所涉及的实际问题。© 2023. The Author(s).

Multi-state models are complex stochastic models which focus on pathways defined by the temporal and sequential occurrence of numerous events of interest. In particular, the so-called illness-death models are especially useful for studying probabilities associated to diseases whose occurrence competes with other possible diseases, health conditions or death. They can be seen as a generalization of the competing risks models, which are widely used to estimate disease-incidences among populations with a high risk of death, such as elderly or cancer patients. The main advantage of the aforementioned illness-death models is that they allow the treatment of scenarios with non-terminal competing events that may occur sequentially, which competing risks models fail to do.We propose an illness-death model using Cox proportional hazards models with Weibull baseline hazard functions, and applied the model to a study of recurrent hip fracture. Data came from the PREV2FO cohort and included 34491 patients aged 65 years and older who were discharged alive after a hospitalization due to an osteoporotic hip fracture between 2008-2015. We used a Bayesian approach to approximate the posterior distribution of each parameter of the model, and thus cumulative incidences and transition probabilities. We also compared these results with a competing risks specification.Posterior transition probabilities showed higher probabilities of death for men and increasing with age. Women were more likely to refracture as well as less likely to die after it. Free-event time was shown to reduce the probability of death. Estimations from the illness-death and the competing risks models were identical for those common transitions although the illness-death model provided additional information from the transition from refracture to death.We illustrated how multi-state models, in particular illness-death models, may be especially useful when dealing with survival scenarios which include multiple events, with competing diseases or when death is an unavoidable event to consider. Illness-death models via transition probabilities provide additional information of transitions from non-terminal health conditions to absorbing states such as death, what implies a deeper understanding of the real-world problem involved compared to competing risks models.© 2023. The Author(s).