I am involved in developing mechanistic models for HIV infection and the immune system, in collaboration with Mélanie Prague, Rodolphe Thiébaut, Ana Jarne and Laura Villain. The first topic is mainly in collaboration with Mélanie Prague, now researcher at INRIA, Bordeaux. We have developed models for interaction between HIV and the immune system. Based on these models, we have proposed an algorithm for dose monitoring.
Mechanistic models are also developed for estimating and understanding the effect of injection of Interleukin 7 on the restauration of the immune system in HIV infected patients. This was the topic of the PhD of Ana Jarne and now pursued in the PhD of Laura Villain. The clinical aim is to propose adaptive strategy of injection of IL7.
A program called NIMROD allows to make inference in these complex mechanistic models including random effects.
Stochastic system approach to causality
I develop an approach of causality based on dynamical systems, that I call the stochastic system approach. Causality is not a technical, but a philosophical concept. My approach is that causality can be grounded on the existence of physical laws, even if we can infer causal links without completely knowing them. Whatever the approach, the key assumption is that of "no unmeasured confounders". The potential outcomes formalism is not necessary. Technically and practically, the stochastic system approach amounts to build a dynamical system based on possibly stochastic differential equations. Thus this approach has a link with the topic of mechanistic models. The approach is promising for assessing treatment regimes and also in lifecourse epidemiology. This work is done in collaboration with Anne Gégout-Petit and Mélanie Prague.
Book: Dynamical Biostatistical models
A book on dynamical statistical models has been pusblished by Chapman & Hall in 2016. It encompasses the models for quantitative longitudinal data, life history events and the stochastic approach to causality, including mechanistic models.