The Annals of Applied Statistics

Dynamic prediction for multiple repeated measures and event time data: An application to Parkinson’s disease

Jue Wang, Sheng Luo, and Liang Li

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In many clinical trials studying neurodegenerative diseases such as Parkinson’s disease (PD), multiple longitudinal outcomes are collected to fully explore the multidimensional impairment caused by this disease. If the outcomes deteriorate rapidly, patients may reach a level of functional disability sufficient to initiate levodopa therapy for ameliorating disease symptoms. An accurate prediction of the time to functional disability is helpful for clinicians to monitor patients’ disease progression and make informative medical decisions. In this article, we first propose a joint model that consists of a semiparametric multilevel latent trait model (MLLTM) for the multiple longitudinal outcomes, and a survival model for event time. The two submodels are linked together by an underlying latent variable. We develop a Bayesian approach for parameter estimation and a dynamic prediction framework for predicting target patients’ future outcome trajectories and risk of a survival event, based on their multivariate longitudinal measurements. Our proposed model is evaluated by simulation studies and is applied to the DATATOP study, a motivating clinical trial assessing the effect of deprenyl among patients with early PD.

Article information

Ann. Appl. Stat. Volume 11, Number 3 (2017), 1787-1809.

Received: July 2016
Revised: March 2017
First available in Project Euclid: 5 October 2017

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Area under the ROC curve clinical trial failure time latent trait model


Wang, Jue; Luo, Sheng; Li, Liang. Dynamic prediction for multiple repeated measures and event time data: An application to Parkinson’s disease. Ann. Appl. Stat. 11 (2017), no. 3, 1787--1809. doi:10.1214/17-AOAS1059.

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  • Blanche, P., Proust-Lima, C., Loubère, L., Berr, C., Dartigues, J.-F. and Jacqmin-Gadda, H. (2015). Quantifying and comparing dynamic predictive accuracy of joint models for longitudinal marker and time-to-event in presence of censoring and competing risks. Biometrics 71 102–113.
  • Brooks, D. J. (2008). Optimizing levodopa therapy for Parkinson’s disease with levodopa/carbidopa/entacapone: Implications from a clinical and patient perspective. Neuropsychiatric Disease and Treatment 4 39–47.
  • Brown, E. R. and Ibrahim, J. G. (2003). Bayesian approaches to joint cure-rate and longitudinal models with applications to cancer vaccine trials. Biometrics 59 686–693.
  • Chi, Y.-Y. and Ibrahim, J. G. (2006). Joint models for multivariate longitudinal and multivariate survival data. Biometrics 62 432–445.
  • Crainiceanu, C., Ruppert, D. and Wand, M. P. (2005). Bayesian analysis for penalized spline regression using WinBUGS. J. Stat. Softw. 14 1–24.
  • Denison, D. G. T., Mallick, B. K. and Smith, A. F. M. (1998). Automatic Bayesian curve fitting. J. R. Stat. Soc. Ser. B. Stat. Methodol. 60 333–350.
  • DiMatteo, I., Genovese, C. R. and Kass, R. E. (2001). Bayesian curve-fitting with free-knot splines. Biometrika 88 1055–1071.
  • Duane, S., Kennedy, A. D., Pendleton, B. J. and Roweth, D. (1987). Hybrid Monte Carlo. Phys. Lett. B 195 216–222.
  • Dunson, D. B. (2007). Bayesian methods for latent trait modelling of longitudinal data. Stat. Methods Med. Res. 16 399–415.
  • Elashoff, R. M., Li, G. and Li, N. (2007). An approach to joint analysis of longitudinal measurements and competing risks failure time data. Stat. Med. 26 2813–2835.
  • Escobar, M. D. (1994). Estimating normal means with a Dirichlet process prior. J. Amer. Statist. Assoc. 89 268–277.
  • Fox, J.-P. (2005). Multilevel IRT using dichotomous and polytomous response data. Br. J. Math. Stat. Psychol. 58 145–172.
  • Friedman, J. H. and Silverman, B. W. (1989). Flexible parsimonious smoothing and additive modeling. Technometrics 31 3–39.
  • Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. and Rubin, D. B. (2014). Bayesian Data Analysis, 3rd ed. CRC Press, Boca Raton, FL.
  • Gilks, W. R., Best, N. G. and Tan, K. K. C. (1995). Adaptive rejection Metropolis sampling within Gibbs sampling. Appl. Stat. 44 455–472.
  • Harrell, F. (2015). Regression Modeling Strategies: With Applications to Linear Models, Logistic and Ordinal Regression, and Survival Analysis. Springer, Berlin.
  • He, B. and Luo, S. (2016). Joint modeling of multivariate longitudinal measurements and survival data with applications to Parkinson’s disease. Stat. Methods Med. Res. 25 1346–1358.
  • Henderson, R., Diggle, P. and Dobson, A. (2000). Joint modelling of longitudinal measurements and event time data. Biostatistics 1 465–480.
  • Hoffman, M. D. and Gelman, A. (2014). The no-U-turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. J. Mach. Learn. Res. 15 1593–1623.
  • Ibrahim, J. G., Chu, H. and Chen, L. M. (2010). Basic concepts and methods for joint models of longitudinal and survival data. J. Clin. Oncol. 28 2796–2801.
  • Jacqmin-Gadda, H., Sibillot, S., Proust, C., Molina, J.-M. and Thiébaut, R. (2007). Robustness of the linear mixed model to misspecified error distribution. Comput. Statist. Data Anal. 51 5142–5154.
  • Lambert, P. and Vandenhende, F. (2002). A copula-based model for multivariate non-normal longitudinal data: Analysis of a dose titration safety study on a new antidepressant. Stat. Med. 21 3197–3217.
  • Lee, S.-Y. and Song, X.-Y. (2004). Evaluation of the Bayesian and maximum likelihood approaches in analyzing structural equation models with small sample sizes. Multivar. Behav. Res. 39 653–686.
  • Li, L., Greene, T. and Hu, B. (2016). A simple method to estimate the time-dependent receiver operating characteristic curve and the area under the curve with right censored data. Stat. Methods Med. Res. Published online on Nov. 28, 2016, DOI:10.1177/0962280216680239.
  • Liu, L. and Huang, X. (2009). Joint analysis of correlated repeated measures and recurrent events processes in the presence of death, with application to a study on acquired immune deficiency syndrome. J. R. Stat. Soc. Ser. C. Appl. Stat. 58 65–81.
  • Lunn, D. J., Thomas, A., Best, N. and Spiegelhalter, D. (2000). WinBUGS—A Bayesian modelling framework: Concepts, structure, and extensibility. Stat. Comput. 10 325–337.
  • Luo, S. and Wang, J. (2014). Bayesian hierarchical model for multiple repeated measures and survival data: An application to Parkinson’s disease. Stat. Med. 33 4279–4291.
  • McCulloch, C. E. and Neuhaus, J. M. (2011). Misspecifying the shape of a random effects distribution: Why getting it wrong may not matter. Statist. Sci. 26 388–402.
  • Molenberghs, G. and Verbeke, G. (2005). Models for Discrete Longitudinal Data. Springer, New York.
  • O’Brien, L. M. and Fitzmaurice, G. M. (2004). Analysis of longitudinal multiple-source binary data using generalized estimating equations. J. R. Stat. Soc. Ser. C. Appl. Stat. 53 177–193.
  • Proust-Lima, C., Amieva, H. and Jacqmin-Gadda, H. (2013). Analysis of multivariate mixed longitudinal data: A flexible latent process approach. Br. J. Math. Stat. Psychol. 66 470–486.
  • Proust-Lima, C., Dartigues, J.-F. and Jacqmin-Gadda, H. (2016). Joint modeling of repeated multivariate cognitive measures and competing risks of dementia and death: A latent process and latent class approach. Stat. Med. 35 382–398.
  • Proust-Lima, C., Séne, M., Taylor, J. M. G. and Jacqmin-Gadda, H. (2014). Joint latent class models for longitudinal and time-to-event data: A review. Stat. Methods Med. Res. 23 74–90.
  • Rizopoulos, D. (2011). Dynamic predictions and prospective accuracy in joint models for longitudinal and time-to-event data. Biometrics 67 819–829.
  • Rizopoulos, D., Verbeke, G. and Molenberghs, G. (2008). Shared parameter models under random effects misspecification. Biometrika 95 63–74.
  • Rizopoulos, D., Murawska, M., Andrinopoulou, E.-R., Molenberghs, G., Takkenberg, J. J. and Lesaffre, E. (2013). Dynamic predictions with time-dependent covariates in survival analysis using joint modeling and landmarking. arXiv preprint arXiv:1306.6479.
  • Rizopoulos, D., Hatfield, L. A., Carlin, B. P. and Takkenberg, J. J. M. (2014). Combining dynamic predictions from joint models for longitudinal and time-to-event data using Bayesian model averaging. J. Amer. Statist. Assoc. 109 1385–1397.
  • Ruppert, D. (2002). Selecting the number of knots for penalized splines. J. Comput. Graph. Statist. 11 735–757.
  • Ruppert, D., Wand, M. P. and Carroll, R. J. (2003). Semiparametric Regression. Cambridge Series in Statistical and Probabilistic Mathematics 12. Cambridge Univ. Press, Cambridge.
  • Sène, M., Taylor, J. M. G., Dignam, J. J., Jacqmin-Gadda, H. and Proust-Lima, C. (2016). Individualized dynamic prediction of prostate cancer recurrence with and without the initiation of a second treatment: Development and validation. Stat. Methods Med. Res. 25 2972–2991.
  • Shoulson, I. (1998). DATATOP: A decade of neuroprotective inquiry. Parkinson study group. Deprenyl and Tocopherol antioxidative therapy of Parkinsonism. Ann. Neurol. 44 S160–S166.
  • Stan Development Team (2016). Stan modeling language users guide and reference manual, version 2.14.0.
  • Stone, C. J., Hansen, M. H., Kooperberg, C. and Truong, Y. K. (1997). Polynomial splines and their tensor products in extended linear modeling. Ann. Statist. 25 1371–1470.
  • Sun, J., Park, D.-H., Sun, L. and Zhao, X. (2005). Semiparametric regression analysis of longitudinal data with informative observation times. J. Amer. Statist. Assoc. 100 882–889.
  • Taylor, J. M. G., Park, Y., Ankerst, D. P., Proust-Lima, C., Williams, S., Kestin, L., Bae, K., Pickles, T. and Sandler, H. (2013). Real-time individual predictions of prostate cancer recurrence using joint models. Biometrics 69 206–213.
  • Tseng, Y.-K., Hsieh, F. and Wang, J.-L. (2005). Joint modelling of accelerated failure time and longitudinal data. Biometrika 92 587–603.
  • Tsiatis, A. A. and Davidian, M. (2004). Joint modeling of longitudinal and time-to-event data: An overview. Statist. Sinica 14 809–834.
  • Van Houwelingen, H. C. (2007). Dynamic prediction by landmarking in event history analysis. Scand. J. Stat. 34 70–85.
  • Verbeke, G., Fieuws, S., Molenberghs, G. and Davidian, M. (2014). The analysis of multivariate longitudinal data: A review. Stat. Methods Med. Res. 23 42–59.
  • Vonesh, E. F., Greene, T. and Schluchter, M. D. (2006). Shared parameter models for the joint analysis of longitudinal data and event times. Stat. Med. 25 143–163.
  • Wand, M. P. (2000). A comparison of regression spline smoothing procedures. Comput. Statist. 15 443–462.
  • Wang, J. and Luo, S. (2017). Multidimensional latent trait linear mixed model: An application in clinical studies with multivariate longitudinal outcomes. Stat. Med. 36 3244–3256, DOI:10.1002/sim.7347.
  • Wang, J., Luo, S. and Li, L. (2017). Supplement to “Dynamic prediction for multiple repeated measures and event time data: An application to Parkinson’s disease.” DOI:10.1214/17-AOAS1059SUPP.
  • Wulfsohn, M. S. and Tsiatis, A. A. (1997). A joint model for survival and longitudinal data measured with error. Biometrics 53 330–339.
  • Xu, J. and Zeger, S. L. (2001). Joint analysis of longitudinal data comprising repeated measures and times to events. J. R. Stat. Soc. Ser. C. Appl. Stat. 50 375–387.
  • Yang, L., Yu, M. and Gao, S. (2016). Prediction of coronary artery disease risk based on multiple longitudinal biomarkers. Stat. Med. 35 1299–1314.

Supplemental materials

  • Web supplement: Web-based supporting materials. The web-based supporting materials include additional results and figures discussed in the main text, Stan code for the simulation study and a screenshot of the online calculator.