Random effects models for longitudinal data

Longitudinal Research with Latent Variables

Volumn , Issue , 2010, Pages 37-96

  Verbeke, Geert ^a   Molenberghs, Geert ^b   Rizopoulos, Dimitris ^c  

^a KU LEUVEN   (Belgium)

^b HASSELT UNIVERSITY   (Belgium)

^c ERASMUS MEDICAL CENTER   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84865726502     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-642-11760-2_2     Document Type: Chapter

References (160)

1. Aerts, M., Geys, H., Molenberghs, G., & Ryan, L. (2002). Topics in modelling of clustered data. London: Chapman & Hall.
2. Afifi, A., & Elashoff, R. (1966). Missing observations in multivariate statistics I: Review of the literature. Journal of the American Statistical Association, 61, 595-604.
3. Alonso, A., Geys, H., Molenberghs, G., & Vangeneugden, T. (2003). Validation of surrogate markers in multiple randomized clinical trials with repeated measurements. Biometrical Journal, 45, 931-945.
4. Alonso, A., & Molenberghs, G. (2007). Surrogate marker evaluation from an information theory perspective. Biometrics, 63, 180-186.
5. Alonso, A., Molenberghs, G., Geys, H., & Buyse, M. (2005). A unifying approach for surrogate marker validation based on Prentice's criteria. Statistics in Medicine, 25, 205-211.
6. Alonso, A., Molenberghs, G., Burzykowski, T., Renard, D., Geys, H., Shkedy, Z., Tibaldi, F., Abrahantes, J., & Buyse, M. (2004). Prentice's approach and the meta analytic paradigm: A reflection on the role of statistics in the evaluation of surrogate endpoints. Biometrics, 60, 724-728.
7. Altham, P. M. E. (1978). Two generalizations of the binomial distribution. Applied Statistics, 27, 162-167.
8. Andersen, P., Borgan, O., Gill, R., & Keiding, N. (1993). Statistical models based on counting processes. New York: Springer.
9. Arnold, B. C., & Strauss, D. (1991). Pseudolikelihood estimation: some examples. Sankhya: The Indian Journal of Statistics - Series B, 53, 233-243.
10. Bahadur, R. R. (1961). A representation of the joint distribution of responses to n dichotomous items. In H. Solomon (Ed.), Studies in item analysis and prediction, Stanford Mathematical Studies in the Social Sciences VI. Stanford, CA: Stanford University Press.
11. Beunckens, C., Sotto, C., & Molenberghs, G. (2007). A simulation study comparing weighted estimating equations with multiple imputation based estimating equations for longitudinal binary data. Computational Statistics and Data Analysis, 52, 1533-1548.
12. Brant, L. J., & Fozard, J. L. (1990). Age changes in pure-tone hearing thresholds in a longitudinal study of normal human aging. Journal of the Acoustical Society of America, 88, 813-820.
13. Breslow, N. E., & Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88, 9-25.
14. Brown, E., & Ibrahim, J. (2003). A Bayesian semiparametric joint hierarchical model for longitudinal and survival data. Biometrics, 59, 221-228.
15. Brown, E., Ibrahim, J., & DeGruttola, V. (2005). A flexible B-spline model for multiple longitudinal biomarkers and survival. Biometrics, 61, 64-73.
16. Burzykowski, T., Molenberghs, G., & Buyse, M. (2004). The validation of surrogate endpoints using data from randomized clinical trials: A case-study in advanced colorectal cancer. Journal of the Royal Statistical Society, Series A, 167, 103-124.
17. Burzykowski, T., Molenberghs, G., & Buyse, M. (2005). The evaluation of surrogate endpoints. New York: Springer.
18. Burzykowski, T., Molenberghs, G., Buyse, M., Geys, H., & Renard, D. (2001). Validation of surrogate endpoints in multiple randomized clinical trials with failure time end points. Applied Statistics, 50, 405-422.
19. Buyse, M., & Molenberghs, G. (1998). The validation of surrogate endpoints in randomized experiments. Biometrics, 54, 1014-1029.
20. Buyse, M., Molenberghs, G., Burzykowski, T., Renard, D., & Geys, H. (2000). The validation of surrogate endpoints in meta-analyses of randomized experiments. Biostatistics, 1, 49-67.
21. Cardiac Arrhythmia Suppression Trial (CAST) Investigators (1989). Preliminary report: effect of encainide and flecainide on mortality in a randomized trial of arrhythmia suppression after myocardial infraction. New England Journal of Medicine, 321, 406-412.
22. Catalano, P. J. (1997). Bivariate modelling of clustered continuous and ordered categorical outcomes. Statistics in Medicine, 16, 883-900.
23. Catalano, P. J., & Ryan, L. M. (1992). Bivariate latent variable models for clustered discrete and continuous outcomes. Journal of the American Statistical Association, 87, 651-658.
24. Chakraborty, H., Helms, R. W., Sen, P. K., & Cohen, M. S. (2003). Estimating correlation by using a general linear mixed model: Evaluation of the relationship between the concentration of HIV-1 RNA in blood and semen. Statistics in Medicine, 22, 1457-1464.
25. Chi, Y.-Y., & Ibrahim, J. (2006). Joint models for multivariate longitudinal and multivariate survival data. Biometrics, 62, 432-445.
26. Clayton, D. G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65, 141- 151.
27. Cover, T., & Tomas, J. (1991). Elements of information theory. New York: Wiley.
28. Cox, N. R. (1974). Estimation of the correlation between a continuous and a discrete variable. Biometrics, 30, 171-178.
29. Cox, D. R., & Wermuth, N. (1992). Response models for mixed binary and quantitative variables. Biometrika, 79, 441-461.
30. Cox, D. R., & Wermuth, N. (1994a). A note on the quadratic exponential binary distribution. Biometrika, 81, 403-408.
31. Cox, D. R., & Wermuth, N. (1994b). Multivariate dependencies: Models, analysis and interpretation. London: Chapman & Hall.
32. Dale, J. R. (1986). Global cross ratio models for bivariate, discrete, ordered responses. Biometrics, 42, 909-917.
33. Daniels, M. J., & Hughes, M. D. (1997). Meta-analysis for the evaluation of potential surrogate markers. Statistics in Medicine, 16, 1515-1527.
34. De Backer, M., De Keyser, P., De Vroey, C., & Lesaffre, E. (1996). A 12-week treatment for dermatophyte toe onychomycosis: Terbinafine 250mg/day vs. itraconazole 200mg/day-a doubleblind comparative trial. British Journal of Dermatology, 134, 16-17.
35. DeGruttola, V., & Tu, X. (1994). Modeling progression of CD-4 lymphocyte count and its relationship to survival time. Biometrics, 50, 1003-1014.
36. Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, Series B, 39, 1-38.
37. Diggle, P. J., Heagerty, P., Liang, K.-Y., & Zeger, S. L. (2002). Analysis of longitudinal data. New York: Oxford University Press.
38. Ding, J., & Wang, J.-L. (2008). Modeling longitudinal data with nonparametric multiplicative random effects jointly with survival data. Biometrics, 64, 546-556.
39. Dobson, A., &Henderson, R. (2003). Diagnostics for joint longitudinal and dropout time modeling. Biometrics, 59, 741-751.
40. Efron, B. (1986). Double exponential families and their use in generalized linear regression. Journal of the American Statistical Association, 81, 709-721.
41. Elashoff, R., Li, G., & Li, N. (2008). A joint model for longitudinal measurements and survival data in the presence of multiple failure types. Biometrics, 64, 762-771.
42. Fahrmeir, L., & Tutz, G. (2001). Multivariate statistical modelling based on generalized linear models. Heidelberg: Springer.
43. Faucett, C., Schenker, N., & Elashoff, R. (1998). Analysis of censored survival data with intermittently observed time-dependent binary covariates. Journal of the American Statistical Association, 93, 427-437.
44. Ferentz, A. E. (2002). Integrating pharmacogenomics into drug development. Pharmacogenomics, 3, 453-467.
45. Fieuws, S., & Verbeke, G. (2004). Joint modelling of multivariate longitudinal profiles: Pitfalls of the random-effects approach. Statistics in Medicine, 23, 3093-3104.
46. Fieuws, S., & Verbeke, G. (2006). Pairwise fitting of mixed models for the joint modelling of multivariate longitudinal profiles. Biometrics, 62, 424-431.
47. Fieuws, S., Verbeke, G., Boen, F., & Delecluse, C. (2006). High-dimensional multivariate mixed models for binary questionnaire data. Applied Statistics, 55, 1-12.
48. Fitzmaurice, G. M., & Laird, N. M. (1995). Regression models for a bivariate discrete and continuous outcome with clustering. Journal of the American Statistical Association, 90, 845-852.
49. Fitzmaurice, G. M., Laird, N. M., & Ware, J. H. (2004). Applied longitudinal analysis. New York: John Wiley & Sons.
50. Fleming, T. R., & DeMets, D. L. (1996). Surrogate endpoints in clinical trials: Are we being misled? Annals of Internal Medicine, 125, 605-613.
51. Folk, V. G., & Green, B. F. (1989). Adaptive estimation when the unidimensionality assumption of IRT is violated. Applied Psychological Measurement, 13, 373-389.
52. Follmann, D., &Wu, M. (1995). An approximate generalized linear model with random effects for informative missing data. Biometrics, 51, 151-168.
53. Forster, J. J., & Smith, P. W. (1998). Model-based inference for categorical survey data subject to non-ignorable non-response. Journal of the Royal Statistical Society, Series B, 60, 57-70.
54. Freedman, L. S., Graubard, B. I., & Schatzkin, A. (1992). Statistical validation of intermediate endpoints for chronic diseases. Statistics in Medicine, 11, 167-178.
55. Gail, M. H., Pfeiffer, R., van Houwelingen, H. C., & Carroll, R. J. (2000). On meta-analytic assessment of surrogate outcomes. Biostatistics, 1, 231-246.
56. Galecki, A. (1994). General class of covariance structures for two or more repeated factors in longitudinal data analysis. Communications in Statistics: Theory and Methods, 23, 3105-3119.
57. Genest, C., & McKay, J. (1986). The joy of copulas: bivariate distributions with uniform marginals. American Statistician, 40, 280-283.
58. Geys, H., Molenberghs, G., & Ryan, L. M. (1997). Pseudo-likelihood inference for clustered binary data. Communications in Statistics: Theory and Methods, 26, 2743-2767.
59. Geys, H., Molenberghs, G., & Ryan, L. (1999). Pseudolikelihood modeling of multivariate outcomes in developmental toxicology. Journal of the American Statistical Association, 94, 734- 745.
60. Gueorguieva, R. (2001). A multivariate generalized linear mixed model for joint modelling of clustered outcomes in the exponential family. Statistical Modelling, 1, 177-193.
61. Goldstein, H. (1979). The design and analysis of longitudinal studies. London: Academic Press.
62. Hartley, H. O., & Hocking, R. (1971). The analysis of incomplete data. Biometrics, 27, 7783-7808.
63. Harville, D. A. (1974). Bayesian inference for variance components using only error contrasts. Biometrika, 61, 383-385.
64. Harville, D. A. (1976). Extension of the Gauss-Markov theorem to include the estimation of random effects. The Annals of Statistics, 4, 384-395.
65. Harville, D. A. (1977). Maximum likelihood approaches to variance component estimation and to related problems. Journal of the American Statistical Association, 72, 320-340.
66. Hedeker, D., & Gibbons, R. D. (1994). A random-effects ordinal regression model for multilevel analysis. Biometrics, 50, 933-944.
67. Hedeker, D., & Gibbons, R. D. (1996). MIXOR: A computer program for mixed-effects ordinal regression analysis. Computer Methods and Programs in Biomedicine, 49, 157-176.
68. Henderson, R., Diggle, P., & Dobson, A. (2000). Joint modelling of longitudinal measurements and event time data. Biostatistics, 1, 465-480.
69. Henderson, C. R., Kempthorne, O., Searle, S. R., & Von Krosig, C. N. (1959). Estimation of environmental and genetic trends from records subject to culling. Biometrics, 15, 192-218.
70. Hougaard, P. (1986). Survival models for heterogeneous populations derived from stable distributions. Biometrika, 73, 387-396.
71. Hsieh, F., Tseng, Y.-K., & Wang, J.-L. (2006). Joint modeling of survival and longitudinal data: likelihood approach revisited. Biometrics, 62, 1037-1043.
72. Jennrich, R. I., & Schluchter, M. D. (1986). Unbalanced repeated measures models with structured covariance matrices. Biometrics, 42, 805-820.
73. Kenward, M. G., & Molenberghs, G. (1998). Likelihood based frequentist inference when data are missing at random. Statistical Science, 12, 236-247.
74. Krzanowski, W. J. (1988). Principles of multivariate analysis. Oxford: Clarendon Press.
75. Lagakos, S. W., & Hoth, D. F. (1992). Surrogate markers in AIDS: Where are we? Where are we going? Annals of Internal Medicine, 116, 599-601.
76. Laird, N. M., & Ware, J. H. (1982). Random effects models for longitudinal data. Biometrics, 38, 963-974.
77. Lang, J. B., & Agresti, A. (1994). Simultaneously modeling joint and marginal distributions of multivariate categorical responses. Journal of the American Statistical Association, 89, 625- 632.
78. Lange, K. (2004). Optimization. New York: Springer.
79. Lesko, L. J., & Atkinson, A. J. (2001). Use of biomarkers and surrogate endpoints in drug development and regulatory decision making: criteria, validation, strategies. Annual Review of Pharmacological Toxicology, 41, 347-366.
80. Liang, K.-Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13-22.
81. Liang, K.-Y., Zeger, S.L., & Qaqish, B. (1992). Multivariate regression analyses for categorical data. Journal of the Royal Statistical Society, Series B, 54, 3-40.
82. Lin, H., Turnbull, B., McCulloch, C., & Slate, E. (2002). Latent class models for joint analysis of longitudinal biomarker and event process data: Application to longitudinal prostate-specific antigen readings and prostate cancer. Journal of the American Statistical Association, 97, 53-65.
83. Lipsitz, S. R., Laird, N. M., & Harrington, D. P. (1991). Generalized estimating equations for correlated binary data: using the odds ratio as a measure of association. Biometrika, 78, 153- 160.
84. Little, R. J. A., & Rubin, D. B. (2002). Statistical analysis with missing data. New York: John Wiley & Sons.
85. Little, R. J. A., & Schluchter, M. D. (1985). Maximum likelihood estimation for mixed continuous and categorical data with missing values. Biometrika, 72, 497-512.
86. Liu, L. C., & Hedeker, D. (2006). A mixed-effects regression model for longitudinal multivariate ordinal data. Biometrics, 62, 261-268.
87. MacCallum, R., Kim, C., Malarkey, W., & Kiecolt-Glaser, J. (1997). Studying multivariate change using multilevel models and latent curve models. Multivariate Behavioral Research, 32, 215- 253.
88. Mancl, L. A., & Leroux, B. G. (1996). Efficiency of regression estimates for clustered data. Biometrics, 52, 500-511.
89. McCullagh, P., & Nelder, J. A. (1989). Generalized linear models. London: Chapman & Hall/CRC.
90. Michiels, B., Molenberghs, G., Bijnens, L., Vangeneugden, T., & Thijs, H. (2002). Selection models and pattern-mixture models to analyze longitudinal quality of life data subject to dropout. Statistics in Medicine, 21, 1023-1041.
91. Molenberghs, G., Burzykowski, T., Alonso, A., Assam, P., Tilahun, A., & Buyse, M. (2008). The meta-analytic framework for the evaluation of surrogate endpoints in clinical trials. Journal of Statistical Planning and Inference, 138, 432-449.
92. Molenberghs, G., Burzykowski, T., Alonso, A., Assam, P., Tilahun, A., & Buyse, M. (2009). A unified framework for the evaluation of surrogate endpoints in clinical trials. Statistical Methods in Medical Research, 00, 000-000.
93. Molenberghs, G., Geys, H., & Buyse, M. (2001). Evaluation of surrogate end-points in randomized experiments with mixed discrete and continuous outcomes. Statistics in Medicine, 20, 3023- 3038.
94. Molenberghs, G., & Kenward, M. G. (2007). Missing data in clinical studies. Chichester: John Wiley & Sons.
95. Molenberghs, G., & Lesaffre, E. (1994). Marginal modelling of correlated ordinal data using a multivariate Plackett distribution. Journal of the American Statistical Association, 89, 633-644.
96. Molenberghs, G., & Lesaffre, E. (1999). Marginal modelling of multivariate categorical data. Statistics in Medicine, 18, 2237-2255.
97. Molenberghs, G., & Verbeke, G. (2005). Models for discrete longitudinal data. New York: Springer.
98. Morrell, C. H., & Brant, L. J. (1991). Modelling hearing thresholds in the elderly. Statistics in Medicine, 10, 1453-1464.
99. Neuhaus, J. M., Kalbfleisch, J. D., & Hauck, W. W. (1991). A comparison of cluster-specific and population-averaged approaches for analyzing correlated binary data. International Statistical Review, 59, 25-30.
100. Ochi, Y., & Prentice, R. L. (1984). Likelihood inference in a correlated probit regression model. Biometrika, 71, 531-543.
101. Olkin, I., & Tate, R. F. (1961). Multivariate correlation models with mixed discrete and continuous variables. Annals of Mathematical Statistics, 32, 448-465 (with correction in 36, 343-344).
102. Oort, F. J. (2001). Three-mode models for multivariate longitudinal data. British Journal of Mathematical and Statistical Psychology, 54, 49-78.
103. Pearson, J. D., Morrell, C. H., Gordon-Salant, S., Brant, L. J., Metter, E. J., Klein, L. L., & Fozard, J. L. (1995). Gender differences in a longitudinal study of age-associated hearing loss. Journal of the Acoustical Society of America, 97, 1196-1205.
104. Pharmacological Therapy for Macular Degeneration Study Group (1997). Interferon α-IIA is ineffective for patients with choroidal neovascularization secondary to age-related macular degeneration. Results of a prospective randomized placebo-controlled clinical trial. Archives of Ophthalmology, 115, 865-872.
105. Pinheiro, J. C., & Bates, D. M. (2000). Mixed effects models in S and S-Plus. New York: Springer.
106. Prentice, R. L., &Zhao, L. P. (1991). Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses. Biometrics, 47, 825-839.
107. Potthoff, R. F., & Roy, S. N. (1964). A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika, 51, 313-326.
108. Prentice, R. (1982). Covariate measurement errors and parameter estimates in a failure time regression model. Biometrika, 69, 331-342.
109. Prentice, R. L. (1988). Correlated binary regression with covariates specific to each binary observation. Biometrics, 44, 1033-1048.
110. Prentice, R. L. (1989). Surrogate endpoints in clinical trials: definitions and operational criteria. Statistics in Medicine, 8, 431-440.
111. Proust-Lima, C., Joly, P., Dartigues, J. F., & Jacqmin-Gadda, H. (2009). Joint modelling of multivariate longitudinal outcomes and a time-to-event: A nonlinear latent class approach. Computational Statistics and Data Analysis, 53, 1142-1154.
112. Raab, G. M., & Donnelly, C. A. (1999). Information on sexual behaviour when some data are missing. Applied Statistics, 48, 117-133.
113. Regan, M. M., & Catalano, P. J. (1999a). Likelihood models for clustered binary and continuous outcomes: Application to developmental toxicology. Biometrics, 55, 760-768.
114. Regan, M. M., & Catalano, P. J. (1999b). Bivariate dose-response modeling and risk estimation in developmental toxicology. Journal of Agricultural, Biological and Environmental Statistics, 4, 217-237.
115. Regan, M. M., & Catalano, P. J. (2000). Regression models for mixed discrete and continuous outcomes with clustering. Risk Analysis, 20, 363-376.
116. Regan, M. M., & Catalano, P. J. (2002). Combined continuous and discrete outcomes. In M. Aerts, H. Geys, G. Molenberghs, & L. Ryan (Eds.), Topics in modelling of clustered data. London: Chapman & Hall.
117. Renard, D., Geys, H., Molenberghs, G., Burzykowski, T., & Buyse, M. (2002). Validation of surrogate endpoints in multiple randomized clinical trials with discrete outcomes. Biometrical Journal, 44, 1-15.
118. Rizopoulos, D., Verbeke, G., & Molenberghs, G. (2009a). Multiple-imputation-based residuals and diagnostic plots for joint models of longitudinal and survival outcomes. Biometrics, to appear. doi: 10.1111/j.1541-0420.2009.01273.x.
119. Rizopoulos, D., Verbeke, G., & Lesaffre, E. (2009b). Fully exponential Laplace approximation for the joint modelling of survival and longitudinal data. Journal of the Royal Statistical Society, Series B, 71, 637-654.
120. Rizopoulos, D., Verbeke, G., & Molenberghs, G. (2008). Shared parameter models under random effects misspecification. Biometrika, 95, 63-74.
121. Robins, J. M., Rotnitzky, A., & Scharfstein, D. O. (1998). Semiparametric regression for repeated outcomes with non-ignorable non-response. Journal of the American Statistical Association, 93, 1321-1339.
122. Robins, J. M., Rotnitzky, A., & Zhao, L. P. (1995). Analysis of semiparametric regression models for repeated outcomes in the presence of missing data. Journal of the American Statistical Association, 90, 106-121.
123. Roy, J., & Lin, X. (2000). Latent variable models for longitudinal data with multiple continuous outcomes. Biometrics, 56, 1047-1054.
124. Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys. New York: John Wiley & Sons.
125. Rubin, D. B., Stern, H. S., & Vehovar, V. (1995). Handling "don't know" survey responses: The case of the Slovenian plebiscite. Journal of the American Statistical Association, 90, 822-828.
126. Sammel, M. D., Ryan, L. M., & Legler, J. M. (1997). Latent variable models for mixed discrete and continuous outcomes. Journal of the Royal Statistical Society, Series B, 59, 667-678.
127. Schafer J. L. (1997). Analysis of incomplete multivariate data. London: Chapman & Hall.
128. Schafer, J. L. (2003). Multiple imputation in multivariate problems when the imputation and analysis models differ. Statistica Neerlandica, 57, 19-35.
129. Schatzkin, A., & Gail, M. (2002). The promise and peril of surrogate end points in cancer research. Nature Reviews Cancer, 2, 19-27.
130. Schemper, M., & Stare, J. (1996). Explained variation in survival analysis. Statistics in Medicine, 15, 1999-2012.
131. Self, S., & Pawitan, Y. (1992). Modeling a marker of disease progression and onset of disease. In N.P. Jewell, K. Dietz, & V.T. Farewell (Eds.), AIDS epidemiology: Methodological issues. Boston: Birkhauser.
132. Shah, A., Laird, N., & Schoenfeld, D. (1997). A random-effects model for multiple characteristics with possibly missing data. Journal of the American Statistical Association, 92, 775-779.
133. Shannon, C. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379-423 and 623-656.
134. Shock, N.W., Greullich, R. C., Andres, R., Arenberg, D., Costa, P. T., Lakatta, E. G., & Tobin, J. D. (1984). Normal human aging: The Baltimore Longitudinal Study of Aging. National Institutes of Health publication 84-2450.
135. Shih, J. H., & Louis, T. A. (1995). Inferences on association parameter in copula models for bivariate survival data. Biometrics, 51, 1384-1399.
136. Sivo, S. A. (2001). Multiple indicator stationary time series models. Structural Equation Modeling, 8, 599-612.
137. Song, X., Davidian, M., & Tsiatis, A. (2002). A semiparameteric likelihood approach to joint modeling of longitudinal and time-to-event data. Biometrics, 58, 742-753.
138. Tate, R. F. (1954). Correlation between a discrete and a continuous variable. Annals of Mathematical Statistics, 25, 603-607.
139. Tate, R.F. (1955). The theory of correlation between two continuous variables when one is dichotomized. Biometrika, 42, 205-216.
140. Thijs, H., Molenberghs, G., Michiels, B., Verbeke, G., &Curran, D. (2002). Strategies to fit patternmixture models. Biostatistics, 3, 245-265.
141. Therneau, T., & Grambsch, P. (2000). Modeling survival data: Extending the Cox Model. New York: Springer.
142. Thiébaut, R., Jacqmin-Gadda, H., Chêne, G., Leport, C., &Commenges, D. (2002). Bivariate linear mixed models using SAS PROC MIXED. Computer Methods and Programs in Biomedicine, 69, 249-256.
143. Thum, Y. M. (1997). Hierarchical linear models for multivariate outcomes. Journal of Educational and Behavioral Statistics, 22, 77-108.
144. Tibaldi, F. S, Cortĩnas Abrahantes, J., Molenberghs, G., Renard, D., Burzykowski, T., Buyse, M., Parmar, M., Stijnen, T., & Wolfinger, R. (2003). Simplified hierarchical linear models for the evaluation of surrogate endpoints. Journal of Statistical Computation and Simulation, 73, 643- 658.
145. Tseng, Y.-K., Hsieh, F., & Wang, J.-L. (2005). Joint modelling of accelerated failure time and longitudinal data. Biometrika, 92, 587-603.
146. Tsiatis, A., & Davidian, M. (2001). A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error. Biometrika, 88, 447-458.
147. Tsiatis, A., & Davidian, M. (2004). Joint modeling of longitudinal and time-to-event data: An overview. Statistica Sinica, 14, 809-834.
148. Tsiatis, A., DeGruttola, V., & Wulfsohn, M. (1995). Modeling the relationship of survival to longitudinal data measured with error: Applications to survival and CD4 counts in patients with AIDS. Journal of the American Statistical Association, 90, 27-37.
149. Van der Laan, M. J., & Robins, J. M. (2002). Unified methods for censored longitudinal data and causality. New York: Springer.
150. Verbeke, G., Lesaffre, E., & Spiessens, B. (2001). The practical use of different strategies to handle dropout in longitudinal studies. Drug Information Journal, 35, 419-434.
151. Verbeke, G., & Molenberghs, G. (2000). Linear mixed models for longitudinal data. New York: Springer.
152. Verbeke, G., Molenberghs, G., Thijs, H., Lesaffre, E., & Kenward, M. G. (2001). Sensitivity analysis for non-random dropout: A local influence approach. Biometrics, 57, 7-14.
153. Wang, Y., & Taylor, J. (2001). Jointly modeling longitudinal and event time data with application to acquired immunodeficiency syndrome. Journal of the American Statistical Association, 96, 895-905.
154. Wolfinger, R. D. (1998). Towards practical application of generalized linear mixed models. In B. Marx & H. Friedl (Eds.), Proceedings of the 13th International Workshop on Statistical Modeling (pp. 388-395). New Orleans, Louisiana, USA.
155. Wolfinger, R., & O'Connell, M. (1993). Generalized linear mixed models: A pseudo-likelihood approach. Journal of Statistical Computation and Simulation, 48, 233-243.
156. Wu, M., & Carroll, R. (1988). Estimation and comparison of changes in the presence of informative right censoring by modeling the censoring process. Biometrics, 44, 175-188.
157. Wulfsohn, M., & Tsiatis, A. (1997). A joint model for survival and longitudinal data measured with error. Biometrics, 53, 330-339.
158. Xu, J., & Zeger, S. (2001). Joint analysis of longitudinal data comprising repeated measures and times to events. Applied Statistics, 50, 375-387.
159. Yu, M., Law, N., Taylor, J., & Sandler, H. (2004). Joint longitudinal-survival-cure models and their application to prostate cancer. Statistica Sinica, 14, 835-832.
160. Zhao, L. P., Prentice, R. L., & Self, S. G. (1992). Multivariate mean parameter estimation by using a partly exponential model. Journal of the Royal Statistical Society B, 54, 805-811.