# 臺灣博碩士論文加值系統

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 目的： 應用半參數的方法來估計多狀態隨機模式轉移的狀況並沒有被深入的研究。因此本研究主要的目的在於發展半參數隨機過程模型來評估相關共變數如何影響三階段疾病轉移。 方法： 在病理學上本研究利用隨機過程加入比例風險形式(proportional hazard form)及部分概式函數(partial likelihood)來處理危險因子不同狀態的轉移。我們將部分概式函數(partial likelihood)推廣至適應非馬可夫假設及使用隨機效用(random effect)模式解決不同狀態間轉移之相關性。另外，我們也採用了半馬可夫(semi-Markov)的方法來將三階段隨機模式以解除馬可夫鏈停留時間分佈(Embedded Markov Chain holding time distribution) 來表現，同時考慮競爭死因(competing risk)之問題。最後，我們也發利用排列的方法和區間設限的方法來處理因隱沒狀態(hidden state)轉移而產生的問題。 兩個例子： 1.Adenoma-invasive carcinoma-death是完全知道轉移時間的資料 2.Normal-the PCDP-clinical of breast cancer是有hidden state的資料。 結論： 本研究發展半參數隨機過程模型來估計危險因子如何影響三階段疾病轉移，並考慮不同困難度下其模式之適應性。
 Backgorund: The application of semiparametric method to multi- state stochastic process, particularly interval-censored data with hidden transition, has not been fully addressed. Objectives: The aim of this study was to develop a semiparametric stochastic model for assessing the effects of covariate on three-state disease progression. Methods: The three-state stochastic process plus the proportional hazard model and partial likelihood method was applied to assess the effect of covariates on different state transitions. Two thorny issues including the relaxation of Markov assumption and the correlation between different state transitions were also tackled by the extension of partial likelihood and the application of the random-effect model. The semi-Markov method was also proposed to model the covariate effect by the embedded Markov chain and holding time distribution taking competing risk problems into account. The permuted method and interval-censored method were adopted to tackle interval-censored data with hidden state transitions in three-state stochastic process. Illustrations: Two illustrations were given in this study, including adenoma-invasive carcinoma-death for data with the exact transition time known and normal-the PCDP-clinical progression of breast cancer phase for interval-censored with hidden state transitions. Conclusion: The present study proposed the semiparametric stochastic model for assessing the effects of covariates on three-state disease progression taking interval-censored data type and other issues into account.
 Abstract 中文摘要 Introduction Brief Review for previous studies on interval-censored data Method 1.Model specification 2.Semi-parametric model for data without hidden transition 3.Random effect model for correlation between the transition from sate 0 to state 1 and the transition between state 1 state 2 4.The Semi-parametric model for hidden transition Two Examples Discussion Reference
 Chen HH, Duffy SW, Tabar L. A Markov chain method to estimate the tumour progression rate from preclinical to clinical phase, sensitivity and positive predictive value for mammography in breast cancer screening. The Statistician 1996; 45: 307-317.Chen HH. Duffy SW, Tabar L, Day NE. Markov chain models for progression of breast cancer. Part II: prediction of outcomes for different screening regimes. Journal of Epidemiology and Biostatistics 1997; 2: 25-35.Chen THH, Yen MF, Lai MS, Koong, SL, Wang CY, Wong JM, Prevost TC, Duffy SW. Evaluation of a Selective Screening for Colorectal Carcinoma: The Taiwan Mulitcenter Cancer Screening (TAMCAS) Project. Cancer 1999; 86: 1116-28.Chen THH, Kuo HS, Yen MF, Lai MS, Tabar L, Duffy SW. Estimation of sojourn time in chronic disease screening without data on interval cases. Biometrics 2000; 56(1): 167-172.Cox DR. Regression models and life tables (with discussion). Journal of the Royal Statistical Society, B, 1972; 74: 187-220.Duffy SW, Chen HH, Tabar L, Day NE. Estimation of mean sojourn time in breast cancer screening using a Markov chain model of both entry and exit from the preclinical detectable phase. Statistics in Medicine 1995; 14: 1531-1543.Farrington CP. Interval censored survival data: A generalized linear modeling approach. Statistics in Medicine 1996; 15: 283-292.Finkelstein DM. A proportional hazards model for interval-censored failure time data. Biometrics 1986; 42: 845-854.Finkelstein DM, Wolfe RA. A semiparametric model for regression analysis of interval-censored failure time data. Biometrics 1985; 41: 933-945.Lai MS, Yen MF, Kuo HS, Koong SL, Tony HH Chen, Duffy SW. Efficacy of breast-cancer screening for female relatives of breast-cancer-index cases: Taiwan multicentre cancer screening (TAMCAS). Int J Cancer 1998; 78: 21-26.Lindsey JC, Ryan LM. Tutorial in biostatistics methods for interval-censored data. Statistics in Medicine; 17: 219-238.Odell PM, Anderson KM, D’Agostino RB. Maximum likelihood estimation for interval-censored data using a weibull-based accelerated failure time model. Biometrics 1992; 48: 951-959.Rücker G, Messerer D. Remission duration: Anexample of interval-censored observations. Statistics in Medicine 1988; 7: 1139-1145.Sargent DJ. A general framework for random effects survival analysis in the cox proportional hazards setting. Biometrics; 54: 1486-1497.Self SG, Grossman EA. Linear rank tests for interval-censored data with application to PCB levels in adipose tissue of transformer repair workers. Biometrics 1986; 42: 521-530.Smith PJ, Thompson TJ, Jereb JA. A model for interval-censored tuberculosis outbreak data. Statistics in Medicine 1997; 16: 485-496.
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