Joint modelling of longitudinal and repeated time-to-event data using nonlinear mixed-effects models and the stochastic approximation expectation–maximization algorithm

Mbogning, Cyprien; Bleakley, Kevin; Lavielle, Marc

doi:10.1080/00949655.2013.878938

Cited by 19 publications

(21 citation statements)

References 31 publications

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“…Then inference is performed by fitting the two processes simultaneously, a particularly challenging step when the biomarker kinetics are nonlinear. [18][19][20][21][22] In addition, to better assess the effect of a treatment in a population of interest, joint models can also be used at the individual level to rapidly identify patients most at risk of death and/or progression that could benefit from alternative therapies. To the best of our knowledge, such models have not yet been developed to support strategies of individualized therapy in cancer immunotherapies.…”

Section: Association Between Tumor Size Kinetics and Survival In Patimentioning

confidence: 99%

Association Between Tumor Size Kinetics and Survival in Patients With Urothelial Carcinoma Treated With Atezolizumab: Implication for Patient Follow‐Up

Tardivon

Desmée

Kerioui

et al. 2019

Clin Pharma and Therapeutics

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We characterized the association between tumor size kinetics and survival in patients with advanced urothelial carcinoma treated with atezolizumab (anti‐programmed death‐ligand 1, Tecentriq) using a joint model. The model, developed on data from 309 patients of a phase II clinical trial, identified the time‐to‐tumor growth and the instantaneous changes in tumor size as the best on‐treatment predictors of survival. On the validation dataset containing data from 457 patients from a phase III study, the model predicted individual survival probability using 3‐month or 6‐month tumor size follow‐up data with an area under the receptor‐occupancy curve between 0.75 and 0.84, as compared with values comprised between 0.62 and 0.75 when the model included only information available at treatment initiation. Including tumor size kinetics in a relevant statistical framework improves the prediction of survival probability during immunotherapy treatment and may be useful to identify most‐at‐risk patients in “real‐time.”

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Section: Association Between Tumor Size Kinetics and Survival In Patimentioning

confidence: 99%

Association Between Tumor Size Kinetics and Survival in Patients With Urothelial Carcinoma Treated With Atezolizumab: Implication for Patient Follow‐Up

Tardivon

Desmée

Kerioui

et al. 2019

Clin Pharma and Therapeutics

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“…For the estimation of the mechanistic joint model, we used the approach of penalized likelihood maximized with the Marquardt algorithm. It would be of interest to perform a simulation study to compare the algorithm with other algorithms for mechanistic joint models, for instance, methods that use the Laplace approximation, implemented in NONMEM software or the SAEM algorithm implemented in both Monolix software and NONMEM. However, in the case of more complex model with no analytical solution, numerical schemes are required, which would demand implementation of built‐in algorithms for ODEs numerical solutions in the programs for the estimation.…”

Section: Discussionmentioning

confidence: 99%

Multivariate joint frailty model for the analysis of nonlinear tumor kinetics and dynamic predictions of death

Król

Tournigand²,

Michiels

et al. 2018

Statistics in Medicine

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The Response Evaluation Criteria in Solid Tumors are used as standard guidelines for the clinical evaluation of cancer treatments. The assessment is based on the anatomical tumor burden: change in size of target lesions and evolution of nontarget lesions (NTL). Despite unquestionable advantages of this standard tool, Response Evaluation Criteria in Solid Tumors are subject to some limitations such as categorization of continuous tumor size or negligence of its longitudinal trajectory. In particular, it is of interest to capture its nonlinear shape and model it simultaneously with recurrent progressions of NTL and overall survival. We propose a multivariate nonlinear mechanistic joint frailty model for longitudinal data, recurrent events, and a terminal event. In the model, the tumor size trajectory is described using an ordinary differential equation that accounts for the natural growth and treatment-induced decline. We perform a simulation study to validate the method and apply the model to a phase III clinical trial in colorectal cancer. In the results of the analysis, we determine on which component, tumor size, NTL, or death the treatment acts mostly and perform dynamic predictions of death. We compare the model with other models that consider parametric functions or splines for the tumor size trajectory in terms of goodness of fit and predictive accuracy.

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“…In a NLMEM framework, the Stochastic Approximation Expectation-Maximization (SAEM) algorithm [18] implemented in Monolix (www.lixoft.eu) provides unbiased estimates for both longitudinal and survival parameters [8, 9]. As in other EM algorithms, this algorithm is an iterative process where each iteration is divided into a step where the complete likelihood conditional on observations is calculated (E-step), and a step where the complete likelihood is maximized (M-step).…”

Section: Methodsmentioning

confidence: 99%

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

Desmée

Veyrat‐Follet

Sébastien³

et al. 2017

BMC Med Res Methodol

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BackgroundJoint 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.MethodsA 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.ResultsSatisfying 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.ConclusionsAs 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.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-017-0382-9) contains supplementary material, which is available to authorized users.

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Joint modelling of longitudinal and repeated time-to-event data using nonlinear mixed-effects models and the stochastic approximation expectation–maximization algorithm

Cited by 19 publications

References 31 publications

Association Between Tumor Size Kinetics and Survival in Patients With Urothelial Carcinoma Treated With Atezolizumab: Implication for Patient Follow‐Up

Association Between Tumor Size Kinetics and Survival in Patients With Urothelial Carcinoma Treated With Atezolizumab: Implication for Patient Follow‐Up

Multivariate joint frailty model for the analysis of nonlinear tumor kinetics and dynamic predictions of death

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

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