|Abstract: ||慢性病的病程研究具有基本的重要性，因為藉由這些研究，研究人員可以更了解病程發展的機制，進而發展出更有效的治療方法，以改善患者的病況或延長其壽命。在文獻中，此類疾病常被表示成多態半馬可夫模型 (Multi-State Semi-Markov model)，以便從數學的觀點來從事此類研究。 此一模型大致可分為兩部份，一為如何定義病人的健康狀態，作為病程發展的標記，另一則為狀態轉移機制。狀態的定義通常來自醫學專家長期的臨床觀察，轉移機制則是由臨床收集的資料決定。在NSC-98-2218-E-004-002 計畫中(執行期限: 98/10/01-99/07/31，先期成果發表於上傳論文中)，我們考慮慢性B型肝炎自然進程(病患未經治療下病程發展)，將之以多態半馬可夫模型表示後，以獲得之資料將轉移機制表示成相對應的非線性規劃問題，並求取多個局部最佳解 (local optimal solutions) 以增進模型精確度。本計畫分兩階段延續先前研究，第一階段經由資料收集與分析，探討在不同治療方式下，轉移機制將如何改變，進而影響病程發展，並建立相關數學模型。第二階段將利用前述計畫與第一階段之成果，開發一以離散事件模擬法 (Discrete Event Simulation) 且具擴充性之模擬軟體，用以研究存活機率及不同治療方式的經濟效益，提供病患重要醫療資訊及健保給付參考。在第一階段的工作，於建模過程中，轉移機制中的機率分布參數 (parameters of probability distributions) 可藉由解答所對應的非線性規劃問題來決定。如同自然進程之研究，此類問題存在許多局部最佳解 (local optimal solution)。由於此類問題在數學上具有非凸性 (non-convexity)，全域最佳解 (global optimal solution) 通常很難求得。然而，從模型的角度而言，並非所有的局部最佳解所對應到的模型都具有足夠的準確度來表達病程隨著時間的發展。為解決此一困難，在本計畫中，此階段工作將沿用前期計畫 (NSC-98-2218-E-004-002) 的Trust-Tech method (本案主持人博士論文相關研究) 及建構中數值表現較優之Trust-Tech solver 來解答多種治療方式參數估計的問題。此一方法的優點在於以系統化且非隨機方式，求取多個局部最佳解甚至全域最佳解。如此一來，目標函數值較優的局部最佳解 (或全域最佳解)可用以建構準確度較佳的模型。第二階段的工作在於整合分析結果，由整體模型角度，考量病程前後期轉移有相關性下，模擬病程之發展。醫學發現，慢性B型肝炎前程狀態轉移時間長短與後程發展相關 (例如，病患發展成為肝硬化與其發生B型肝炎e抗原血清轉換 (HBeAg Seroconversion) 的年紀及處於e抗原陽性的時間長短相關)。就我們所知，此一現象尚未被放入相關建模文獻中。由於模型建立時，病程之發展為未知，因此，要表達病程前後發展相關性較為困難。本計畫利用離散事件模擬法，將此相關性推遲至模擬過程中才予以實現，並提供可擴充性佳之軟體架構，考量不同轉移分支時序有相關性時，病程發展之模擬。此外，我們將利用建立之模型與模擬方法，探討存活分析與治療方式經濟效益分析之應用問題。藉由分析文獻和醫院現有的臨床資料，本計畫希望建立一較準確的慢性B型肝炎在不同治療方式下的進程模型，並開發一離散事件模擬法為本的模擬軟體，在考量病程前後期轉移有相關性的情況下，從事存活機率及經濟效益分析。未來，此一研究中採用的研究方法與開發之軟體，將作為我們下一階段推廣此類研究於其他慢性病的基礎。|
The progression of chronic diseases is usually described as occurrence of successive discrete events. Studying the underlying dynamics, which specify the order of occurrence of these events and their interrelations, is of fundamental importance since it can provide a better understanding to the development of these diseases. Frequently, researchers can benefit from the dynamics-related information to design better clinic protocols to extend or improve patients’ lives. In our previous project (NSC-98-2218-E-004-002), we study the natural course of chronic hepatitis B virus infection. The disease progression is represented as a multi-state Semi-Markov model. The transition mechanism of the model is formulated as associated nonlinear programming problems. Through locating multiple local optimal solutions of the formulated problems, we seek to improve the traditional annual incidence rate based model, which does not provide the information of how transition rates may vary with time, with a more accurate mathematical model. In this continuing project, we extend our work in two stages. In the first stage, we consider modeling the progression of this disease under various treatment policies. Through clinic data collection and literature survey, we study the problem of how transition mechanisms will change under drug interventions and their effects on the disease progression. In the second stage, based on the data analysis in the prior stage, our goal is to develop a Discrete Event Simulation (DES) based tool to study patients’ survival probabilities and the cost-effectiveness of different treatment policies. This aims to assist patients with important medical information and also serves important reference for the policy planning for national health insurance. In the first stage, the parameters of probability distributions, which characterize the state transitions in the developed model, can be determined by solving the corresponding nonlinear programming problems (parameter estimation problems.) Similar to the study in the case of natural course, one key issue is that due to the non-convexity, these types of problems might possess multiple local optimal solutions and the global optimal solutions are usually difficult to be identified. However, an arbitrary local optimal solution may not be a satisfactory parameter for its resulting model doesn’t provide accurate information when it is applied in related applications. To overcome such difficulty, in our development, we again adopt the optimization paradigm (termed Trust-Tech method) applied in the work of our previous project (NSC-98-2218-E-004-002.) This paradigm has the advantages to systematically and deterministically identify multiple local optimal solutions or even the global optimal solutions to nonlinear programming problems. With this paradigm, the obtained global optimal solutions or high-quality local optimal solutions provide better options to the parameter estimation such that the resulting model can accurately represent the progression of chronic hepatitis B virus under various treatments. Our major focus in the second stage is to simulate the progression of this disease from the viewpoints of an integrated model. Especially, we consider the correlation among transitions which occur at sequential time instants. In the literature, it has been pointed out that the disease progression of hepatitis B virus infection at the later phases is correlated with its progression at the earlier phases. (For instance, it has been reported in the literature that the development of cirrhosis is correlated with the patients’ age when HBeAg seroconvertation occurs and their persistence of HBeAg positive state.) However, such correlation receives little attention and to the best of our knowledge, it has not been included in the relevant work. Since how the disease will progress is unknown at the stage of model development, it is difficult to describe such correlation in advance. To overcome this difficulty, we apply Discrete Event Simulation method in our study such that the correlation is only realized at the phase of disease progression simulation. Based on the developed model and this simulation method, we may simulate the progression of hepatitis B virus infection and may explore applications such as survival analysis and cost-effectiveness analysis of various treatments. Through literature survey and clinic data analysis, our goal can be briefly summarized as “ to provide more accurate progression models of chronic hepatitis B virus infection under drug interventions” and “to develop a DES based simulator to conduct the survival and cost-effectiveness analysis under the scenario of correlated transitions.” The research methods and developed tools will serve as the foundation to study other chronic diseases in our following research.