A Comparative Study of Approaches for Predicting Prostate Cancer from Longitudinal Data

References

• Altman , D. G. , De Stavola , B. L. ( 1994 ). Practical problems in fitting a proportional hazards model to data with updated measurements of the covariates . Statistics in Medicine 13 : 301 – 341 .
   PubMed Web of Science ®Google Scholar
• Brant , L. J. , Sheng , S. L. , Morrell , C. H. , Verbeke , G. N. , Lesaffre , E. , Carter , H. B. ( 2003 ). Screening for prostate cancer by using random-effects models . Journal of the Royal Statistical Society: Series A 166 : 51 – 62 .
   Web of Science ®Google Scholar
• Brant , L. J. , Sheng , S. L. , Morrell , C. H. , Zonderman , A. B. ( 2005 ). Data from a Longitudinal Study Provided Measurements of Cognition to Screen for Alzheimer's Disease . Journal of Clinical Epidemiology 58 ( 7 ): 701 – 707 .
   PubMedGoogle Scholar
• Bycott , P. , Taylor , J. ( 1998 ). A comparison of smoothing techniques for CD4 data measured with error in a time-dependent Cox proportional hazards model . Statistics in Medicine 17 : 2061 – 2077 .
   PubMed Web of Science ®Google Scholar
• Carter , H. B. , Pearson , J. D. , Metter , E. J. , Brant , L. J. , Chan , D. W. , Andres , R. , Fozard , J. L. , Walsh , P. C. ( 1992 ). Longitudinal evaluation of prostate-specific antigen levels in men with and without prostate disease . Journal of the American Medical Association 267 : 2215 – 2220 .
   PubMed Web of Science ®Google Scholar
• Cook , N. R. ( 2008 ). Statistical evaluation of prognostic versus diagnostic models: Beyond the ROC curve . Clinical Chemistry 54 ( 1 ): 17 – 23 .
   PubMed Web of Science ®Google Scholar
• D'Amico , A. V. , Whittington , R. , Malkowicz , S. B. , Weinstein , M. , Tomaszewski , J. E. , Schultz , D. , Rhude , M. , Rocha , S. , Wein , A. , Richie , J. P. ( 2001 ). Predicting prostate specific antigen outcome preoperatively in the prostate specific antigen era . Journal of Urology 166 : 2185 – 2188 .
   PubMed Web of Science ®Google Scholar
• De Gruttola , V. , Tu , X. M. ( 1994 ). Modeling progression of CD-4-lymphocyte count and its relationship to survival time . Biometrics 50 : 1003 – 1014 .
   PubMed Web of Science ®Google Scholar
• De Stavola , B. L. , Christensen , E. (1996). Multilevel models for longitudinal variables prognostic for survival. Lifetime Data Analysis 2:329–347.
   PubMedGoogle Scholar
• Fieuws , S. , Verbeke , G. ( 2006 ). Pairwise fitting of mixed models for the joint modelling of multivariate longitudinal profiles . Biometrics 62 ( 2 ): 424 – 431 .
   PubMed Web of Science ®Google Scholar
• Fieuws , S. , Verbeke , G. , Brant , L. J. ( 2003 ). Classification of longitudinal profiles using nonlinear mixed-effects models. Technical Report TR0356, Interuniversity Attraction Pole, IAP Statistics Network, Louvan-la-Neuve, Belgium, http://www.stat.ucl.ac.be/IAP/ .
   Google Scholar
• Fieuws , S. , Verbeke , G. , Maes , B. , Vanrenterghem , Y. ( 2008 ). Predicting renal graft failure using multivariate longitudinal profiles . Biostatistics 9 : 419 – 431 .
   PubMed Web of Science ®Google Scholar
• Guo , X. , Carlin , B. P. ( 2004 ). Separate and joint modeling of longitudinal and event time data using standard computer packages . The American Statistician 58 : 16 – 24 .
   Web of Science ®Google Scholar
• Henderson , R. , Diggle , P. , Dobson , A. ( 2000 ). Joint modelling of longitudinal measurements and event time data . Biostatistics 1 : 465 – 480 .
   PubMedGoogle Scholar
• Hogan , J. W. , Laird , N. M. ( 1997 ). Model-based approaches to analysing incomplete longitudinal and failure time data . Statistics in Medicine 16 : 259 – 272 .
   PubMed Web of Science ®Google Scholar
• Komárek , A. , Hansen , B. E. , Kuiper , E. M. M. , van Buuren , H. R. , Lesaffre , E. ( 2010 ). Discriminant analysis using a multivariate linear mixed model with a normal mixture in the random effects distribution . Statistics in Medicine 29 : 3267 – 3283 .
   PubMedGoogle Scholar
• Law , N. J. , Taylor , J. M. G. , Sandler , H. ( 2002 ). The joint modeling of a longitudinal disease progression marker and the failure process in the presence of cure . Biostatistics 3 : 547 – 563 .
   PubMed Web of Science ®Google Scholar
• Lin , H. , McCulloch , C. E. , Mayne , S. T. ( 2002 ). Maximum likelihood estimation in the joint analysis of time-to-event and multiple longitudinal variables . Statistics in Medicine 21 : 2369 – 2382 .
   PubMed Web of Science ®Google Scholar
• Lin , H. , Turnbull , B. W. , McCulloch , C. E. , Slate , E. H. ( 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 .
   Web of Science ®Google Scholar
• McIntosh , M. W. , Urban , N. ( 2003 ). A parametric empirical Bayes method for cancer screening using longitudinal observations of a biomarker . Biostatistics 4 : 27 – 40 .
   PubMed Web of Science ®Google Scholar
• Morrell , C. H. ( 1998 ). Likelihood ratio testing of variance components in the linear mixed-effects model using restricted maximum likelihood . Biometrics 54 : 1560 – 1568 .
   PubMed Web of Science ®Google Scholar
• Morrell , C. H. , Pearson , J. D. , Brant , L. J. ( 1997 ) Linear transformations of linear mixed-effects models . The American Statistician 51 : 338 – 343 .
   Web of Science ®Google Scholar
• Morrell , C. H. , Pearson , J. D. , Carter , H. B. , Brant , L. J. ( 1995 ). Estimating unknown transition times using a piecewise nonlinear mixed-effects model in men with prostate cancer . Journal of the American Statistical Association 90 : 45 – 53 .
   Web of Science ®Google Scholar
• Morrell , C. H. , Brant , L. J. , Sheng , S. L. ( 2007 ) Comparing approaches for predicting prostate cancer from longitudinal data. 2007 Proceedings of the American Statistical Association, Biometrics Section [CD-ROM], Alexandria, VA: American Statistical Association , pp. 127 – 133 .
   Google Scholar
• Morrell , C. H. , Brant , L. J. , Ferrucci , L. ( 2009 ). Model choice can obscure results in longitudinal studies . Journal of Gerontology: Medical Sciences 64A ( 2 ): 215 – 222 .
   Web of Science ®Google Scholar
• Muthén , B. ( 2001a ). Latent variable mixture modeling . In: Marcoulides , G. A. , Schumacker , R. E. , eds. New Developments and Techniques in Structural Equation Modeling . Mahwah , NJ : Lawrence Erlbaum Associates , pp. 1 – 33 .
   Google Scholar
• Muthén , B. ( 2001b ). Second-generation structural equation modeling with a combination of categorical and continuous latent variables: New opportunities for latent class/latent growth modeling . In: Collins , L. M. , Sayer , A. , eds. New Methods for the Analysis of Change . Washington , D.C. : APA , pp. 291 – 322 .
   Google Scholar
• Muthén , B. ( 2004 ). Latent variable analysis: Growth mixture modeling and related techniques for longitudinal data . In: Kaplan , D. , ed. Handbook of Quantitative Methodology for the Social Sciences . Newbury Park , CA : Sage Publications , pp. 345 – 368 .
   Google Scholar
• Muthén , B. , Shedden , K. (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics 55:463–469.
   PubMed Web of Science ®Google Scholar
• Pauler , D. K. , Finkelstein , D. M. ( 2002 ). Predicting time to prostate cancer recurrence based on joint models for non-linear longitudinal biomarkers and event time outcomes . Statistics in Medicine 21 : 3897 – 3911 .
   PubMed Web of Science ®Google Scholar
• Pauler , D. K. , Laird , N. M. ( 2002 ). Non-linear hierarchical models for monitoring compliance . Statistics in Medicine 21 : 219 – 229 .
   PubMed Web of Science ®Google Scholar
• Pearson , J. D. , Morrell , C. H. , Landis , P. K. , Brant , L. J. ( 1994 ). Mixed-effects regression models for studying the natural history of prostate disease . Statistics in Medicine 13 : 587 – 601 .
   PubMed Web of Science ®Google Scholar
• Shock , N. W. , Greulich , R. C. , Andres , R. , Lakatta , E. G. , Arenberg , D. , Tobin , J. D. ( 1984 ). Normal Human Aging: The Baltimore Longitudinal Study of Aging . NIH Publication No. 84–2450. Washington , D.C. : U.S. Government Printing Office .
   Google Scholar
• Skates , S. J. , Pauler , D. K. , Jacobs , I. J. ( 2001 ). Screening based on the risk of cancer calculation from Bayesian hierarchical changepoint and mixture models of longitudinal markers . Journal of the American Statistical Association 96 : 429 – 439 .
   Web of Science ®Google Scholar
• Slate , E. H. , Clark , L. C. ( 1999 ). Using PSA to detect prostate cancer onset: an application of Bayesian retrospective and prospective change-point identification. In: Gatsonis, C., Kass, R. E., Carlin, B., Carriquiry, A., Gelman, A., Verdinelli, I., West, M., eds. Case Studies in Bayesian Statistics IV, New York: Springer, pp. 511–533 .
   Google Scholar
• Slate , E. H. , Cronin , K. A. ( 1997 ). Change-point modeling of longitudinal PSA as a biomarker for prostate cancer. In: Gatsonis, C., Hodges, J. S., Kass, R. E., McCulloch, R. E., Rossi, P., Singpurwalla, N. D., eds. Case Studies in Bayesian Statistics III, New York: Springer, pp. 435–456 .
   Google Scholar
• Slate , E. H. , Turnbull , B. W. ( 2000 ). Statistical models for longitudinal biomarkers of disease onset . Statistics in Medicine 19 : 617 – 637 .
   PubMed Web of Science ®Google Scholar
• Thum , Y. M. , Bhattacharya , S. K. ( 2001 ). Detecting a change in school performance: A Bayesian analysis for a multilevel join point problem . Journal of Educational and Behavioral Statistics 26 : 443 – 468 .
   Web of Science ®Google Scholar
• Tsiatis , A. A. , De Gruttola , V. , Wulfsohn , M. S. ( 1995 ). Modeling the relationship of survival to longitudinal data measures with error. Applications to survival and CD4 counts in patients with AIDS . Journal of the American Statistical Association 90 : 27 – 37 .
   Web of Science ®Google Scholar
• Verbeke , G. , Lesaffre , E. ( 1996 ). A linear mixed-effects model with heterogeneity in the random-effects population . Journal of the American Statistical Association 91 : 217 – 221 .
   Web of Science ®Google Scholar
• Verbeke , G. , Molenberghs , G. ( 2000 ). Linear Mixed Models for Longitudinal Data . New York : Springer .
   Google Scholar
• Wang , Y. , Taylor , J. M. G. ( 2001 ). Jointly modeling longitudinal and event time data with application to acquired immunodeficiency syndrome . Journal of the American Statistical Association 96 : 895 – 905 .
   Web of Science ®Google Scholar
• Whittemore , A. S. , Lele , C. , Friedman , G. G. , Stamey , T. , Vogelman , J. H. , Orentreich , N. ( 1995 ). Prostate-specific antigen as predictor of prostate cancer in black men and white men . Journal of the National Cancer Institute 87 : 354 – 360 .
   PubMed Web of Science ®Google Scholar
• Wulfsohn , M. S. , Tsiatis , A. A. ( 1997 ). A joint model for survival and longitudinal data measured with error . Biometrics 53 : 330 – 339 .
   PubMed Web of Science ®Google Scholar