不同數值方法對於聯合模型參數估計的影響

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陳珮文(Pei-wen Chen) 查詢紙本館藏

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統計研究所

論文名稱

不同數值方法對於聯合模型參數估計的影響
(The impact of numerical methods on parameter estimation of the joint model)

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摘要(中)

在生物醫學研究的過程當中，除了事件時間之外還經常收集到長期追蹤資料 (longitudinal data)。一般最常使用比例風險模型 (proportional hazard model, Cox model) 推估時間相依共變數 (time-dependent covariate) 與存活時間的關聯性。然而，由於此方法需要病人的完整資訊，造成了資料收集之困難，所以將利用聯合模型 (joint model) 的概念來對資料做分析。此模型包含兩大部分：其一為長期追蹤資料，其二為存活資訊。在第一部分使用線性隨機效應模型 (linear random effect model) 處理長期追蹤資料，第二部分則是使用Cox模型描述共變數與存活時間之間的關係。結合這兩部分建構出聯合模型且利用EM演算法 (expectation maximize algorithm) 求得參數之最大概似估計值 (maximum likelihood estimate, MLE)。因在EM演算法中，許多積分並無封閉解，故必須使用數值積分，本研究之目的即是比較不同數值積分方法對於聯合模型參數估計值之影響。最後則藉由愛滋病和地中海果蠅資料驗證所估計參數之變化。

摘要(英)

Time-dependent covariates along with survival information are very common to be collected at the same time in many medical researches. For such kind of data, it is very popular to use Cox model to study the relationship between time-dependent covariates and the survival time. However, the partial likelihood requires the complete covariate information from the patients, which is usually not available in many medical researches. Joint model approach is a solution to analyze such kind of data. The longitudinal data is described by a linear random effects model, and the survival time is fitted by the Cox model. To derive the parameter estimates, EM algorithm is implemented to search for the maximum likelihood estimates. However, the expectation part in the EM algorithm involves multiple integration which has no closed-form and must be solved by the numerical integration. The purpose of this research is to compare different numerical integration methods for parameter estimation of the joint model. We demonstrate the properties of the estimation through studies of AIDS and medfly data.

關鍵字(中)

★ 長期追蹤資料
★ 比例風險模型
★ 聯合模型
★ 高斯積分

關鍵字(英)

★ longitudinal data
★ Cox model
★ joint model
★ Gaussian Quadrature

論文目次

第一章緒論 1
1.1 研究動機與背景 1
1.2 本文架構 5
第二章統計方法 6
2.1 聯合模型 6
2.1.1 定義符號與模型介紹 6
2.1.2 EM演算法之E-step 10
2.1.3 EM演算法之M-step 12
2.1.4 估計參數過程 13
2.2 數值積分方法整理 14
2.3 模擬積分 23
第三章模擬研究 30
3.1 模擬方法 30
3.1.1 生成資料演算法 33
3.1.2 牛頓法 34
3.2 模擬資料設計 35
3.3 模擬結果 36
第四章實例分析 42
4.1 果蠅實例分析 42
4.2 愛滋病實例分析 46
第五章結論與討論 51
參考文獻 53

參考文獻

[1]Boyle P., Broadie M. and Glasserman P. (1997) Monte Carlo methods for security pricing. Journal of Economic Dynamics and Control, 21, 1267-1321.
[2]Cox, D. R. (1972) Regression Models and Life-Tables. Journal of the Royal Statistical Society, 34, 187-220.
[3]Carey, J. R., Liedo, P., Muller, H. G., Wang, J. L. & Chiou, J. M. (1998) Relationship of age patterns of fecundity to mortality, longevity, and lifetime reproduction in a large cohort of Mediterranean fruit fly females. J. Gerontol.: Biol. Sci. 53, 245-51.
[4]Faure, H. (1982) Discrkpance de suites associkes B un systkme de numeration (en dimension s). Acta Arithmetica, XLI (1982), 337-351.
[5]Genz A. (1992) Numerical Computation of Multivariate Normal Probabilities. Journal of Computational and Graphical Statistics, 1(2), 141-149.
[6]Genz A. (1993) Comparison of Methods for the Computation of Multivariate Normal Probabilities. Computing Science and Statistics 25, pp. 400-405.
[7]Genz, A. (2004) Numerical computation of rectangular bivariate and trivariate normal and t-probabilities. Statistics and Computing, 14, 251–260.
[8]Halton, J. H., (1960) On the Efficiency of Certain Quasi-random Sequences of Points in Evaluating Multi-dimensional Integrals. Numerische Mathematik, Vol.2, P84-90.
[9]Hsieh, F., Tseng, Y. K. and Wang, J. L. (2006) Joint Modeling of Survival and Longitudinal Data: Likelihood Approach Revisited. Biometrics, 62, 1037-1043.
[10]Kaplan, E. L. and Meier, P. (1958) Nonparametric Estimation from Incomplete Observations. Journal of the American Statistical Association, 53, 457-481.
[11]Laird, N. M. and Ware, J. H. (1982) Random-effects models for longitudinal data. Biometrics, 38, 963-974.
[12]Lin, D. Y. and Ying, Z. (1993) Cox regression with incomplete covariate measurements. Journal of the American Statistical Association, 88(424), 1341-1349.
[13]Miwa, T., Hayter A. J., and Kuriki S. (2003) The evaluation of general non-centred orthant probabilities. Journal of The Royal Statistical Society Series B–Statistical Methodology, 65:223–234, 2003.
[14]Mi, X., Miwa T., and Hothorn T. (2009) Mvtnorm: New Numerical Algorithm for Multivariate Normal Probabilities. The R Journal Vol, 1, 37-39.
[15]Prentice, R. L. (1982) Covariate measurement errors and parameter estimation in a failure time regression model. Biometrika, 69, 331-342.
[16]Rizopoulos D., Verbeke G., Lesaffre E. (2009) Fully Exponential Laplace Approximations for the Joint Modeling of Survival and Longitudinal Data. Journal of the Royal Statistical Society B, 71, 637-654.
[17]Sobol, I. M.(1967) Distribution of points in a cube and approximate evaluation of integrals. Maths. Math. Phys. 7: 86–112 (in English).
[18]Tierney, L., Kass, R. and Kadane, J. (1989) Fully exponential Laplace approximations to expectations and variances of nonpositive functions. J. Am. Statist. Ass., 84, 710-753.
[19]Tsiatis, A. A., DeGruttola, V., and Wulfsohn, M. S. (1995) Modeling the relationship of survival to longitudinal data measured with error. Application to survival and CD4 counts in patients with AIDS. Journal of American Statistical Association, 90, 27-37.
[20]Tsiatis, A. A. and Davidian, M. (2004) Joint Modeling of Longitudinal and Time-to-Event Data: An Overview. Statistica Sinica, 14, 809-834.
[21]Tseng, Y. K., Hsieh F. and Wang, J. L. (2005) Joint modeling of accelerated failure time and longitudinal data. Biometrika, 92, 587-603.
[22]Tuffin, B. (2008) Randomization of Quasi-Monte Carlo Methods for Error Estimation: Survey and Normal Approximation, Monte Carlo Methods and Applications mcma. Volume 10, Issue 3-4, 617–628.
[23]Wulfsohn, M. S. and Tsiatis, A. A. (1997) A Joint Model for Survival and Longitudinal Data Measured with Error. Biometrics, 53, 330-339.
[24]Zeng, D. and Cai, J. (2005) Asymptotic Results for Maximum Likelihood Estimators in Joint Analysis of Repeated Measurements and Survival Time. The Annals of Statistics, 33(5), 2132-2163.

指導教授

曾議寬(Yi-kuan Tseng)

審核日期

2013-6-25

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