论文标题
相类型分布在经常性事件中的某些应用
Some applications of phase-type distributions in recurrent events
论文作者
论文摘要
在本文中，在后续时间内可能发生多个事件的复发事件是通过相类型分布建模的。我们将有限状态的连续时间马尔可夫工艺与多州用于复发事件的患者。重复发生的数量直到时间$ t $，每个州停留的时间以及死亡的时间至关重要。假定死亡的时间具有具有可解释参数的相型分布（在马尔可夫链环境中定义）。基础的连续时间马尔可夫链具有一个吸收状态（死亡）和瞬态状态，以反映康复和疾病阶段。获得了一个微分方程的系统，以计算各种过渡次数的概率，预期时间留在疾病阶段以及从阶段到另一个阶段过渡的可能性。该模型已通过真实和模拟数据集进行了校准。自举技术已用于构建参数的置信区间。
In this paper, the recurrent events that can occur more than one over the follow-up time have been modeled by phase-type distributions. We use the finite-state continuous-time Markov process with multi states for patients with recurrent events. The number of recurrences until time $t$, the time stay for every state and the time till death are of importances. The time till death is assumed to have a phase-type distribution (which is defined in a Markov chain environment) with interpretable parameters. The underlying continuous-time Markov chain has one absorbing state (death) and transient states to reflect recovery and disease stages. A system of differential equations is obtained to calculate the probability of various number of transitions, the conditional expected time to stay in a disease stage and the probability of transition from a stage to another. The model has been calibrated via a real and simulated datasets. The bootstrap techniques have been used to construct the confidence intervals for the parameters.
