Adaptive protocols based on predictions from a mechanistic model of the effect of IL7 on CD4 counts

Abstract

In human immunodeficiency virus–infected patients, antiretroviral therapy suppresses the viral replication, which is followed in most patients by a restoration of CD4+ T cells pool. For patients who fail to do so, repeated injections of exogenous interleukin 7 (IL7) are experimented. The IL7 is a cytokine that is involved in the T cell homeostasis and the INSPIRE study has shown that injections of IL7 induced a proliferation of CD4+ T cells. Phase I/II INSPIRE 2 and 3 studies have evaluated a protocol in which a first cycle of three IL7 injections is followed by a new cycle at each visit when the patient has less than 550 CD4 cells/μL. Restoration of the CD4 concentration has been demonstrated, but the long‐term best adaptive protocol is yet to be determined. A mechanistic model of the evolution of CD4 after IL7 injections has been developed, which is based on a system of ordinary differential equations and includes random effects. Based on the estimation of this model, we use a Bayesian approach to forecast the dynamics of CD4 in new patients. We propose four prediction‐based adaptive protocols of injections to minimize the time spent under 500 CD4 cells/μL for each patient, without increasing the number of injections received too much. We show that our protocols significantly reduce the time spent under 500 CD4 over a period of two years, without increasing the number of injections. These protocols have the potential to increase the efficiency of this therapy.

Modeling and characterization of inter-individual variability in CD8 T cell responses in mice

“…In immunology, Keersmaekers et al [25] have recently studied the differences between two vaccines with nonlinear mixed effects models and ordinary differential equation (ODE) models for T and B cells. Jarne et al [26] and Villain et al [27] A number of models of the CD8 T cell response based on ODEs have been proposed over the years.…”

“…In immunology, Keersmaekers et al [ 25 ] have recently studied the differences between two vaccines with nonlinear mixed effects models and ordinary differential equation (ODE) models for T and B cells. Jarne et al [ 26 ] and Villain et al [ 27 ] have used the same approach to investigate the effect of IL7 injections on HIV+ patients to stimulate the CD4 T cell response. None of these works aimed at identifying immunological heterogeneous processes or characterizing the between-individual variability in CD8 T cell responses, rather nonlinear mixed effects models have been used to characterize the average behavior of the cell populations and explain the data.…”

Effects of interventions and optimal strategies in the stochastic system approach to causality

“…A more complex observation scheme arise if the visit-times are also random; their law may be described by a counting process N (jumping at visit times), the compensator of which could depend on the past of Y, Z, A, C. If we restrict to cases where it depends only on past values of Z, A, C, this mechanism is ignorable for inference (Commenges, 2019b). Adapting visit-times may lead to efficient strategies (Villain et al, 2019), but we do not develop this possibility in this paper.…”

Parameter estimation in nonlinear mixed effect models based on ordinary differential equations: an optimal control approach

“…ODE models are standard in population dynamics, epidemiology, virology, pharmacokinetics, or genetic regulation networks analysis due to their ability to describe the main mechanisms of interaction between different biological components of complex systems, their evolution in time and to provide reasonable approximations of stochastic dynamics Perelson et al (1996); Lavielle and Mentré (2007); Wakefield and Racine-Poon (1995); Andraud et al (2012); Pasin et al (2019); M. Lavielle and Mentre (2011); Le et al (2015); Engl et al (2009); Wu et al (2014). Evidence of the relevance of ODEs resides for example in their joint use with control theory methods for the purpose of optimal treatment design Guo and Sun (2012); Agusto and Adekunle (2014); Zhang and Xu (2016); Pasin et al (2018); Villain et al (2019). In cases of experimental designs involving a large number of subjects and limited number of individual measurements, non-linear mixed-effect models may be more relevant than subject-by-subject model to gather information from the whole population while allowing between-individual variability.…”