Top

BMC Medical Research Methodology

Published in:

Open Access 01-12-2017 | Research Article

Nonlinear joint models for individual dynamic prediction of risk of death using Hamiltonian Monte Carlo: application to metastatic prostate cancer

Authors: Solène Desmée, France Mentré, Christine Veyrat-Follet, Bernard Sébastien, Jérémie Guedj

Published in: BMC Medical Research Methodology | Issue 1/2017

Abstract

Background

Joint models of longitudinal and time-to-event data are increasingly used to perform individual dynamic prediction of a risk of event. However the difficulty to perform inference in nonlinear models and to calculate the distribution of individual parameters has long limited this approach to linear mixed-effect models for the longitudinal part. Here we use a Bayesian algorithm and a nonlinear joint model to calculate individual dynamic predictions. We apply this approach to predict the risk of death in metastatic castration-resistant prostate cancer (mCRPC) patients with frequent Prostate-Specific Antigen (PSA) measurements.

Methods

A joint model is built using a large population of 400 mCRPC patients where PSA kinetics is described by a biexponential function and the hazard function is a PSA-dependent function. Using Hamiltonian Monte Carlo algorithm implemented in Stan software and the estimated population parameters in this population as priors, the a posteriori distribution of the hazard function is computed for a new patient knowing his PSA measurements until a given landmark time. Time-dependent area under the ROC curve (AUC) and Brier score are derived to assess discrimination and calibration of the model predictions, first on 200 simulated patients and then on 196 real patients that are not included to build the model.

Results

Satisfying coverage probabilities of Monte Carlo prediction intervals are obtained for longitudinal and hazard functions. Individual dynamic predictions provide good predictive performances for landmark times larger than 12 months and horizon time of up to 18 months for both simulated and real data.

Conclusions

As nonlinear joint models can characterize the kinetics of biomarkers and their link with a time-to-event, this approach could be useful to improve patient’s follow-up and the early detection of most at risk patients.

Available only for authorised users

Tsiatis AA, Davidian M. Joint modeling of longitudinal and time-to-event data: an overview. Statistica Sinica. 2004; 14:809–34.

Wu L, Liu W, Yi GY, Huang Y. Analysis of longitudinal and survival data: joint modeling, inference methods, and issues. J Probab Stat. 2011;2012;17.

Rizopoulos D. Joint Models for Longitudinal and Time-to-Event Data: With Applications in R.Boca Raton: CRC Press; 2012.CrossRef

Rizopoulos D. Dynamic predictions and prospective accuracy in joint models for longitudinal and time-to-event data. Biometrics. 2011; 67(3):819–29.CrossRefPubMed

Rizopoulos D, Murawska M, Andrinopoulou ER, Molenberghs G, Takkenberg JJM, Lesaffre E. Dynamic predictions with time-dependent covariates in survival analysis using joint modeling and landmarking. arXiv preprint arXiv:1306.6479. 2013. https://arxiv.org/abs/1306.6479.

Proust-Lima C, Taylor JM. Development and validation of a dynamic prognostic tool for prostate cancer recurrence using repeated measures of posttreatment PSA: a joint modeling approach. Biostatistics. 2009; 10:535–49.CrossRefPubMedPubMedCentral

Brown ER, Ibrahim JG, DeGruttola V. A Flexible B-Spline Model for Multiple Longitudinal Biomarkers and Survival. Biometrics. 2005; 61(1):64–73.CrossRefPubMed

Mbogning C, Bleakley K, Lavielle M. Joint modelling of longitudinal and repeated time-to-event data using nonlinear mixed-effects models and the stochastic approximation expectation maximization algorithm. J Stat Comput Simul. 2015; 85(8):1512–28.CrossRef

Desmée S, Mentré F, Veyrat-Follet C, Guedj J. Nonlinear mixed-effect models for prostate-specific antigen kinetics and link with survival in the context of metastatic prostate cancer: a comparison by simulation of two-stage and joint approaches. AAPS J. 2015; 17(3):691–9.CrossRefPubMedPubMedCentral

10.

Stan Development Team. Stan Modeling Language User’s Guide and Reference Manual, Version 2.8.0. 2015. http://mc-stan.org/users/documentation/index.html.

11.

Neal RM, et al.MCMC using Hamiltonian dynamics. Handbook of Markov Chain Monte Carlo. 2011; 2:113–62.

12.

Hoffman MD, Gelman A. The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. J Mach Learn Res. 2014; 15(1):1593–623.

13.

Betancourt M, Girolami M. Hamiltonian Monte Carlo for hierarchical models. Current trends in Bayesian methodology with applications. 2015; 79:30.

14.

Betancourt M. A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv preprint arXiv:1701.02434. 2017. https://arxiv.org/abs/1701.02434.

15.

Blanche P, Proust-Lima C, Loubère L, Berr C, Dartigues JF, Jacqmin-Gadda H. Quantifying and comparing dynamic predictive accuracy of joint models for longitudinal marker and time-to-event in presence of censoring and competing risks. Biometrics. 2015; 71(1):102–13.CrossRefPubMed

16.

Mauguen A, Rachet B, Mathoulin-Pélissier S, Lawrence GM, Siesling S, MacGrogan G, et al.Validation of death prediction after breast cancer relapses using joint models. BMC Med Res Methodol. 2015; 15(1):1.CrossRef

17.

Tannock IF, Fizazi K, Ivanov S, Karlsson CT, Fléchon A, Skoneczna I, et al.Aflibercept versus placebo in combination with docetaxel and prednisone for treatment of men with metastatic castration-resistant prostate cancer (VENICE): a phase 3, double-blind randomised trial. Lancet Oncol. 2013; 14(8):760–8.CrossRefPubMed

18.

Delyon B, Lavielle M, Moulines E. Convergence of a stochastic approximation version of the EM algorithm. Ann Stat. 1999; 27:94–128.CrossRef

19.

Heagerty PJ, Zheng Y. Survival model predictive accuracy and ROC curves. Biometrics. 2005; 61(1):92–105.CrossRefPubMed

20.

Parast L, Cheng SC, Cai T. Landmark prediction of long-term survival incorporating short-term event time information. J Am Stat Assoc. 2012; 107(500):1492–501.CrossRefPubMedPubMedCentral

21.

Schoop R, Graf E, Schumacher M. Quantifying the predictive performance of prognostic models for censored survival data with time-dependent covariates. Biometrics. 2008; 64(2):603–10.CrossRefPubMed

22.

Graf E, Schmoor C, Sauerbrei W, Schumacher M. Assessment and comparison of prognostic classification schemes for survival data. Stat Med. 1999; 18(17-18):2529–45.CrossRefPubMed

23.

Blanche P, Latouche A, Viallon V. Time-dependent AUC with right-censored data: a survey. In: Risk Assessment and Evaluation of Predictions. New York: Springer: 2013. p. 239–51.

24.

Gerds TA, Schumacher M. Consistent estimation of the expected brier score in general survival models with right-censored event times. Biometrical J. 2006; 48(6):1029–40.CrossRef

25.

Blanche P. Package ’timeROC’: time-dependent ROC curve and AUC for censored survival data. Vienna: R Foundation for Statistical Computing; 2013.

26.

Desmée S, Mentré F, Veyrat-Follet C, Sébastien B, Guedj J. Using the SAEM algorithm for mechanistic joint models characterizing the relationship between nonlinear PSA kinetics and survival in prostate cancer patients. Biometrics. 2016; 73(1):305–12.CrossRefPubMed

27.

Tu H, Jacobs SC, Borkowski A, Kyprianou N. Incidence of apoptosis and cell proliferation in prostate cancer: Relationship with TGF- β1 and bcl-2 expression. Int J Cancer. 1996; 69(5):357–63.CrossRefPubMed

28.

Polascik TJ, Oesterling JE, Partin AW. Prostate specific antigen: a decade of discovery-what we have learned and where we are going. J Urol. 1999; 162(2):293–306.CrossRefPubMed

29.

Prague M, Commenges D, Drylewicz J, Thiébaut R. Treatment Monitoring of HIV-infected patients based on mechanistic models. Biometrics. 2012; 68(3):902–11.CrossRefPubMed

30.

Brilleman SL, Crowther MJ, May MT, Gompels M, Abrams KR. Joint longitudinal hurdle and time-to-event models: an application related to viral load and duration of the first treatment regimen in patients with HIV initiating therapy. Stat Med. 2016; 35(20):3583–94.CrossRefPubMed

31.

Wilbaux M, Tod M, De Bono J, Lorente D, Mateo J, Freyer G, et al.A joint model for the kinetics of CTC count and PSA concentration during treatment in metastatic castration-resistant prostate cancer. CPT: Pharmacometrics Syst Pharmacol. 2015; 4(5):277–85.

Title: Nonlinear joint models for individual dynamic prediction of risk of death using Hamiltonian Monte Carlo: application to metastatic prostate cancer
Authors: Solène Desmée
France Mentré
Christine Veyrat-Follet
Bernard Sébastien
Jérémie Guedj
Publication date: 01-12-2017
Publisher: BioMed Central
Published in: BMC Medical Research Methodology / Issue 1/2017
Electronic ISSN: 1471-2288
DOI: https://doi.org/10.1186/s12874-017-0382-9

Keynote webinar | Spotlight on sleep in brain health

Springer Medicine

Nonlinear joint models for individual dynamic prediction of risk of death using Hamiltonian Monte Carlo: application to metastatic prostate cancer

Abstract

Background

Methods

Results

Conclusions

Keynote webinar | Spotlight on sleep in brain health

Springer Medicine

Abstract

Background

Methods

Results

Conclusions

Please log in to get access to this content

Other articles of this Issue 1/2017

Validity and reliability of a Malay version of the brief illness perception questionnaire for patients with type 2 diabetes mellitus

Estimating parameters for probabilistic linkage of privacy-preserved datasets

Grey literature in systematic reviews: a cross-sectional study of the contribution of non-English reports, unpublished studies and dissertations to the results of meta-analyses in child-relevant reviews

Estimating a population cumulative incidence under calendar time trends

The impact of the lookback period and definition of confirmatory events on the identification of incident cancer cases in administrative data

Erratum to: Exploring functional data analysis and wavelet principal component analysis on ecstasy (MDMA) wastewater data