陳秀熙臺灣大學：流行病學研究所吳慧敏Wu, Hui-MinHui-MinWu2007-11-272018-06-292007-11-272018-06-292005http://ntur.lib.ntu.edu.tw//handle/246246/56216過去在非時間同質性多階段模式的探討與方法學發展方面的研究較為缺乏，更鮮有同時對資料的異質性問題進行考慮的研究。然而在決策分析領域中對此類模式應用的需求卻與日俱增。因此，本論文目的即在於 (1) 發展非時間同質性多階段馬可夫模式，並將共變項的作用考慮進來，並應用於大腸直腸癌自然病史進展之模式估計。 (2) 發展SAS巨集程式以簡化前述(1)模式之估計過程。 (3) 應用貝氏分析方法發展結合隨機效應之馬可夫模式以分析乳癌高危險群(具乳癌家族病史)婦女篩檢計畫。 (4) 應用前述(1)及(2)所發展之非時間同質性多階段馬可夫模式於大腸直腸癌篩檢政策之決策分析。 (5) 應用前述(3)所發展之貝氏隨機效應馬可夫模式於個人層次之乳癌篩檢決策分析。 因此，本論文可分為四個主要部份。在本論文的第一部分，我們發展了數個可適用於非時間同質性的多階段馬可夫模式，並同時考慮共變項對疾病自然史進展的影響。此外，將原本複雜的估計程式開發成為SAS巨集程式，以增加該模式的可用性。並於文中成功應用該巨集於大腸直腸癌三階段自然病史(正常à大腸腺腫à侵襲癌)的實例估計，並同時示範在不考慮及考慮共變項(如性別)下對自然病史進展的影響。此SAS巨集程式可適用於數個疾病進展階段與數個共變項。 在本論文的第二部份，我們則發展以貝氏分析方法進行多階段馬可夫模式的估計，並將來自不同層級(如家庭層次、個人層次)的異質性以隨機效應方式納入模式中。應用此模式分析乳癌高危險群(具乳癌家族病史)婦女篩檢計畫的結果顯示在家庭層次及個人層次均有統計上顯著之異質性。 在本論文的第三部份，我們示範如何將由第一部份所發展之非時間同質性馬可夫模式應用於大腸直腸癌篩檢政策之決策分析，比較新發展出的糞便DNA試驗相較於其他傳統篩檢方法是否具成本效益。 在本論文的第四部份，我們示範如何利用在第二部份所發展之貝式隨機效應多階段馬可夫模式進行個人層次之乳癌篩檢決策分析。結果顯示乳癌篩檢的效益會受到是否考慮不同層次隨機效應的影響，也就是當我們忽視資料中所存在的隨機效應時，可能會造成乳癌篩檢效益估計的偏差，而影響決策分析的結果。 整體而言，從方法學觀點而言，本論文有二個主要的貢獻： (1) 發展非時間同質性馬可夫模式及其SAS巨集程式。 (2) 以貝氏分析方法發展隨機效應之馬可夫模式。 而從應用的觀點而言，前述二個方法皆可應用到決策分析以解決不同層次來源的異質性。Non-homogeneous multi-state models with or without taking heterogeneity into account are barely addressed and developed. In the face of increasingly attention paid to decision analysis application of this technique and method is urgently needed. Therefore, this thesis aims at (1) developing nonhomogeneous Markov models incorporating covariates associated with colorectal cancer; (2) developing SAS macro program for model proposed in (1) for the ease of use; (3) applying Bayesian model in conjunction with random-effect Markov model to data on screening for females of relatives with breast cancer; (4) applying the non-homogeneous Markov model in (1)-(2) to decision making for colorectal cancer screening regimes given the perspective of policy level; (5) applying Bayesian approach with random-effect Markov model in (3) to decision making for breast cancer screening regime given the perspective of individual level. In the first part of this thesis, a series of nonhomogeneous Markov models incorporating covariates were developed and a SAS macro program for estimating the transition parameters in such models using SAS IML was also developed. The program was successfully applied to an example of a three-state disease model for the progression of colorectal cancer from normal (disease free), to adenoma (pre-invasive disease), and finally to invasive carcinoma, with or without adjusting for covariates. This macro program can be generalized to other k-state models with s covariates. In the second part of this thesis, we applied Bayesian approach to using random-effect parameters corresponding to different hierarchical levels (such as family or subject) to capture the heterogeneity resulting from different sources. This model has been applied to a breast cancer screening for women with relatives suffering from breast cancer and has found statistically significant random effect across family level and also subject level. In the third part of this thesis, we illustrated how to apply the non-homogeneous Markov model to decision-making of colorectal cancer screening with stool DNA test compared with other screening methods given population level. In the forth part of this thesis, we illustrated how to apply the Bayesian approach obtained three-state Markov model with random-effect to decision-making of breast cancer screening. The results suggest that the efficacy of breast cancer screening was also affected by whether to incorporate the random effect. This also implies making no allowance for random effect may yield biased effectiveness of decision analysis, which, in turn, affects the results of cost-effectiveness analysis. In conclusion, from the aspect of methodology, there are two major contributions resulting from this thesis including (1) Non-homogeneous Markov model was developed and implemented with SAS Macro program. (2) Markov model with random effect is developed by using Bayesian approach and implemented with acyclic graphic model using WinBugs program. From the aspect of application, the two methodologies mentioned above can be applied to decision analysis to tackle different sources of uncertainty involved in decision-making process.Table of Contents Chapter 1 Introduction 1 1.1. Backgrounds 1 1.1.1. Is the effectiveness of cancer screening always demonstrated by randomized controlled trial? 1 1.1.2. Quantitative decision-making model 2 1.1.3. Quantitative model for modeling the disease process 3 1.1.4. Non-homogeneous and exponential regression stochastic model in multi-state process 5 1.1.5. Individualized risk prediction and cancer screening 6 1.2. Aims 8 Chapter 2 Literature Review 9 2.1. Multi-state Model and Two-state Model with Covariate 9 2.1.1. Pike model 11 2.1.2. Gail model 14 2.2. Markov Models in the Disease Natural History 16 2.3. Markov Models in Decision Making for Evaluation of Cancer Screening 18 2.4. Bayesian Approach 19 2.5. Summary of Framework on Model Specification and Application to Decision-making 20 Chapter 3 Materials and Methods 22 3.1. Part I-- Non-homogeneous Markov Models with Covariates 22 3.1.1. Model formulation 22 3.1.2. Empirical data for sample runs 29 3.1.3. Developing SAS macro program for nonhomogeneous Markov models incorporating covariates 37 3.2. Part II-- Random-effect Markov model 38 3.2.1. Model formulation 38 3.2.2. Empirical data for sample runs 47 3.3. Part III --Application of Non-homogeneous Markov Model to Decision Making for Colorectal Cancer Screening Regimes 49 3.3.1. Model specification 49 3.3.2. Base-case estimates 57 3.3.3. Cost-effectiveness analysis 61 3.4 Part IV --Application of Bayesian Approach to Individualized Decision Making for Breast Cancer Screening Among Women with Positive Family History of Breast Cancer 65 3.4.1. Level of uncertainty in decision analysis 67 3.4.2. Prior, posterior, and predictive distribution of transition probabilities 67 Chapter 4 Results 71 4.1. Part I-- Non-homogeneous Markov Models with Covariates 71 4.1.1. Non-homogeneous Markov models with covariates—Results of sample runs 71 4.1.2. Developing SAS macro program for nonhomogeneous Markov models incorporating covariates 75 4.2. Part II-- Random-effect Markov Model 77 4.2.1. Basic screening findings 77 4.2.2. Data structure 79 4.2.3. Estimated results 80 4.3. Part III-- Application of Non-homogeneous Markov Model to Decision Making for Colorectal Cancer Screening Regimes 91 4.3.1. Base-case 91 4.3.2. Sensitivity analysis 95 4.4. Part IV --Application of Bayesian Approach to Individualized Decision Making for Breast Cancer Screening Among Women with Positive Family History of Breast Cancer 100 Chapter 5 Discussions 104 5.1. Part I-- Non-homogeneous Markov Models with Covariates 104 5.2. Part II-- Random Effect Markov Model 107 5.3. Part III --Application of Non-homogeneous Markov Model to Decision Making for Colorectal Cancer Screening Regimes 108 5.4. Part IV --Application of Bayesian Approach to Individualized Decision Making for Breast Cancer Screening Among Women with Positive Family History of Breast Cancer 113 Appendix 116 A.1. Three-state model without covariate 116 A.2. Three-state model with covariates 119 A.3. Publication 120 Reference List 121 List of Tables Table 3.1 Data for the three-state model 36 Table 3.2 Base-case estimates and ranges used in sensitivity analysis 63 Table 4.1 Distribution of screening attendance in TAMCAS program 78 Table 4.2 Screening findings of each screening rounds in TAMCAS program 78 Table 4.3 Distribution of detection mode of breast cancer cases in TAMCAS program 79 Table 4.4 Distribution of family size* by detection mode in TAMCAS program 80 Table 4.5 The list of Markov models built up in random effect section. 83 Table 4.6 Results of multi-state Markov models with random effects. 84 Table 4.7 Model fitting of random effect model 86 Table 4.8 Results of Random effect model with one covariate, age at first pregnancy (AP). 89 Table 4.9 Model fitting of random effect model with one covariate, age at first pregnancy (AP). 90 Table 4.10 Simulated results for screening regimes to prevent CRC* 93 Table 4.11 The posterior distribution and the corresponding beta distribution for simulation. 102 Table 4.12 The descriptive statistics of simulating samples for women with first full term pregnancy before and after 30 years old. 103 List of Figures Figure 2.1 Examples of models corresponding to two types of model 11 Figure 2.2 Model for rate of breast tissue ageing. 13 Figure 2.3 The overall framework for model specification. 21 Figure 3.1 A k-state progressive Markov model 23 Figure 3.2 A non-standard case-cohort design for adenoma and colorectal cancer. 31 Figure 3.3 A three-state Markov model for colorectal cancer. 32 Figure 3.4 A three-state Markov model for disease natural history. 39 Figure 3.5 Example of multi-level structure of correlated data. 41 Figure 3.6 The acyclic graphic model for estimating the random effect and fixed effect of multi-state process. 44 Figure 3.7 Markov process for disease natural history and prognosis of colorectal cancer (CRC).* 54 Figure 3.8 Transition matrix of Markov process for disease natural history and prognosis of colorectal cancer.* 55 Figure 3.9 Screening procedure for stool DNA testing every 3, 5, and 10 years, annual fecal occult blood testing, sigmoidoscopy every 5 years, and colonoscopy every 10 years.* 56 Figure 3.10 Framework for Markov decision analysis on the comparison of two decisions between “Screening” and “No screening”. 66 Figure 3.11 The acyclic graphic model for estimating the random effect on subject level and fixed effect (AP) 69 Figure 4.1 Analysis of colorectal cancer data set: Output of the SAS program for the three state Markov model. 73 Figure 4.2 Analysis of colorectal cancer data set: Output of the SAS program for the three-state Markov model with one covariate. 74 Figure 4.3 History of iterations and Kernel density for parameters of model M3. 88 Figure 4.4 Comparison of observed and predicted cumulative colorectal cancer incidence. 92 Figure 4.5 One-way sensitivity analyses for DNA3 against No Screening 97 Figure 4.6 Two-way sensitivity analysis varying sensitivity of stool DNA testing and cost of stool DNA testing 991432456 bytesapplication/pdfen-US馬可夫模式貝氏分析決策分析成本效益分析Markov modelBayesian approachDecision analysisCost-effectiveness analysis[SDGs]SDG3thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/56216/1/ntu-94-F89842006-1.pdf