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摘要翻译：
这本书从生物统计学的角度处理脂肪肝疾病。它以健康-疾病-死亡多状态模型的简单一般形式讨论疾病过程。利用极大似然方程和拟牛顿公式，用连续时间马尔可夫链估计速率转移矩阵，一旦得到，就可以通过对速率矩阵进行幂运算来估计概率转移矩阵。通过求解前向Kolmogorov微分方程也可以得到概率转移矩阵，其结果比对速率矩阵求幂更稳定。将疾病过程扩展为9个状态模型，以更详细的形式解释疾病过程各个详细阶段之间的过渡。概率转移矩阵用于估计每个阶段的患者数量，该矩阵与速率转移矩阵一起用于估计每个阶段患者的预期寿命。这些统计指标可以帮助卫生政策制定者和医疗保险管理者分配资源，对疾病的不同阶段进行调查和治疗，具有重要的价值。该方法具有很高的潜在价值，可用于制药公司进行的纵向研究，以评估用于治疗纤维化初始阶段患者的抗纤维化药物的效果。泊松回归模型也被用来将2型糖尿病、高胆固醇血症、肥胖症和高血压等高危协变量与疾病的进展速度和分期演变联系起来。对一般模型、扩展模型和协变量模型进行了人工假设实例说明，以证明数理统计指标。
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英文标题：
《Analysis of chronic diseases progression using stochastic modeling》
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作者：
Iman Mohammed Attia Ebd-Elkhalik Abo-Elreesh
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最新提交年份：
2021
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分类信息：
一级分类：Quantitative Biology 数量生物学
二级分类：Other Quantitative Biology 其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
This book handles the fatty liver disease from the bio-statistical point of view . It discusses the disease process in the simple general form of health-disease-death multi-states model . Continuous Time Markov Chains are used to estimate the rate transition matrix utilizing the MLE and Quasi-Newton formula , once obtained , the probability transition matrix can be estimated by exponentiation of the rate matrix . The probability transition matrix can also be obtained by solving the forward Kolmogorov differential equations , which yields more stable solution than exponentiation of rate matrix. The disease process is expanded in 9 states model to explain the transition among the detailed stages of the disease process , in more elaborate form. The probability transition matrix is used to estimate the number of patients in each stage , this matrix along with the rate transition matrix , both are used to estimate life expectancy of patients is each stage. These statistical indices are of great value as they can help the health policy makers and medical insurance managers to allocate the resources for investigating and treating patients in different stages of the disease . This method is of a high potential value to be used in longitudinal studies conducted by the pharmaceutical companies to evaluate the effect of anti-fibrotic drugs used to treat patients within the initial stages of fibrosis . Poisson regression model is also used to relate the high risk covariates such as type 2 diabetes, hypercholesterolemia , obesity and hypertension with the rate of progression and evolution of the stages of the disease over time. The general model , the expanded model and the model with covariates are illustrated by artificial hypothetical examples to demonstrate the mathematical statistical indices .
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PDF链接：
https://arxiv.org/pdf/2111.06892
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