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Statistics in medicine
12 30, 2020;39 (30): 4853-4868.

Bayesian inference using Hamiltonian Monte-Carlo algorithm for nonlinear joint modeling in the context of cancer immunotherapy.

Marion Kerioui, Francois Mercier, Julie Bertrand, Coralie Tardivon, René Bruno, Jérémie Guedj, Solène Desmée
Author Information
  1. Marion Kerioui: Université de Paris, INSERM, IAME, F-75006 Paris, France. ORCID
  2. Francois Mercier: Biostatistics - Roche Innovation Center Basel, Basel, Switzerland. ORCID
  3. Julie Bertrand: Université de Paris, INSERM, IAME, F-75006 Paris, France.
  4. Coralie Tardivon: Université de Paris, INSERM, IAME, F-75006 Paris, France.
  5. René Bruno: Genentech/Roche - Service de Pharmacologie Clinique, Marseille, France.
  6. Jérémie Guedj: Université de Paris, INSERM, IAME, F-75006 Paris, France.
  7. Solène Desmée: Université de Tours, Université de Nantes, INSERM SPHERE, UMR 1246, Tours, France.
PMID: 33032368 DOI: 10.1002/sim.8756

Abstract

Treatment evaluation in advanced cancer mainly relies on overall survival and tumor size dynamics. Both markers and their association can be simultaneously analyzed by using joint models, and these approaches are supported by many softwares or packages. However, these approaches are essentially limited to linear models for the longitudinal part, which limit their biological interpretation. More biological models of tumor dynamics can be obtained by using nonlinear models, but they are limited by the fact that parameter identifiability require rich dataset. In that context Bayesian approaches are particularly suited to incorporate the biological knowledge and increase the information available, but they are limited by the high computing cost of Monte-Carlo by Markov Chains algorithms. Here, we aimed to assess the performances of the Hamiltonian Monte-Carlo (HMC) algorithm implemented in Stan for inference in a nonlinear joint model. The method was validated on simulated data where HMC provided proper posterior distributions and credibility intervals in a reasonable computational time. Then the association between tumor size dynamics and survival was assessed in patients with advanced or metastatic bladder cancer treated with atezolizumab, an immunotherapy agent. HMC confirmed limited sensitivity to prior distributions. A cross-validation approach was developed and identified the current slope of tumor size dynamics as the most relevant driver of survival. In summary, HMC is an efficient approach to perform nonlinear joint models in a Bayesian framework, and opens the way for the use of nonlinear models to characterize both the rapid dynamics and the intersubject variability observed during cancer immunotherapy treatment.

Keywords

Bayesian inference HMC algorithm cancer joint models nonlinear mixed effect models

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MeSH Term

Algorithms
Bayes Theorem
Humans
Immunotherapy
Markov Chains
Monte Carlo Method
Neoplasms
Nonlinear Dynamics
Journal Article Research Support, Non-U.S. Gov't
Article has an altmetric score of 6

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