标题： 将出生-死亡过程拟合到面板数据中并应用于细菌DNA指纹识别 显示英文标题

标题： Fitting birth-death processes to panel data with applications to bacterial DNA fingerprinting

摘要： 连续时间线性出生-死亡-迁入（BDI）过程在生态学和流行病学中经常被用来模拟感兴趣种群的随机动态。在临床环境中，多个出生-死亡过程可以描述个体患者的疾病轨迹，从而估计个体协变量对过程出生率和死亡率的影响。这种估计通常是通过分析在不等时间点收集的患者数据来完成的，这在生物统计文献中被称为面板数据。将线性BDI过程拟合到面板数据是一个非平凡的优化问题，因为出生率和死亡率可以是与感兴趣协变量相关的许多参数的函数。我们提出了一种新颖的期望-最大化（EM）算法，用于将带有协变量的线性BDI模型拟合到面板数据。我们推导了某些BDI过程统计量的联合生成函数的闭式表达式，并利用此生成函数将EM算法的E步以及Fisher信息的计算减少到一维积分。这种分析技术产生了一个计算效率高且稳健的优化算法，我们在一个开源的R包中实现了它。我们将该方法应用于结核分枝杆菌的DNA指纹分析，这是导致结核病的病原体，以研究IS6110拷贝数的患者内时间演变，这是一个在估计结核分枝杆菌感染流行病学簇时经常使用的遗传标记。我们的分析揭示了三种主要结核分枝杆菌谱系之间IS6110出生-死亡率的先前未记录的差异，这对使用IS6110进行结核分枝杆菌DNA指纹分析的流行病学家具有重要意义。 显示英文摘要

摘要： Continuous-time linear birth-death-immigration (BDI) processes are frequently used in ecology and epidemiology to model stochastic dynamics of the population of interest. In clinical settings, multiple birth-death processes can describe disease trajectories of individual patients, allowing for estimation of the effects of individual covariates on the birth and death rates of the process. Such estimation is usually accomplished by analyzing patient data collected at unevenly spaced time points, referred to as panel data in the biostatistics literature. Fitting linear BDI processes to panel data is a nontrivial optimization problem because birth and death rates can be functions of many parameters related to the covariates of interest. We propose a novel expectation--maximization (EM) algorithm for fitting linear BDI models with covariates to panel data. We derive a closed-form expression for the joint generating function of some of the BDI process statistics and use this generating function to reduce the E-step of the EM algorithm, as well as calculation of the Fisher information, to one-dimensional integration. This analytical technique yields a computationally efficient and robust optimization algorithm that we implemented in an open-source R package. We apply our method to DNA fingerprinting of Mycobacterium tuberculosis, the causative agent of tuberculosis, to study intrapatient time evolution of IS6110 copy number, a genetic marker frequently used during estimation of epidemiological clusters of Mycobacterium tuberculosis infections. Our analysis reveals previously undocumented differences in IS6110 birth-death rates among three major lineages of Mycobacterium tuberculosis, which has important implications for epidemiologists that use IS6110 for DNA fingerprinting of Mycobacterium tuberculosis.