Abstract
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.
Highlights
Joint models of longitudinal and time-to-event data are increasingly used to perform individual dynamic prediction of a risk of event
This approach can be made more flexible by using splines [3, 7], it does not handle models that are nonlinear in the parameters, i.e., nonlinear mixed-effect models (NLMEM), such as mechanistic models defined by differential equations
Traditional Markov Chain Monte Carlo (MCMC) are based on random walk which provides estimators with good properties of convergence, but in practice and especially in a high-dimensional context, this asymptotic behavior is of limited use because of finite computational resources
Summary
Joint models of longitudinal and time-to-event data are increasingly used to perform individual dynamic prediction of a risk of event. 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. Desmée et al BMC Medical Research Methodology (2017) 17:105 numerical difficulties have long limited the use of joint models, and of dynamic predictions, to linear models for the longitudinal processes. This approach can be made more flexible by using splines [3, 7], it does not handle models that are nonlinear in the parameters, i.e., nonlinear mixed-effect models (NLMEM), such as mechanistic models defined by differential equations. The Halmitonian Monte Carlo (HMC), implemented in Stan [10], uses the geometry of the parameters space to generate effective and rapid exploration of this space, and stronger guarantees on the convergence [11,12,13,14]
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