Mechanistic models
I am involved in developing mechanistic models for HIV infection and the immune system, in collaboration with Mélanie Prague, Rodolphe Thiébaut and Ana Jarne. The first topic is mainly in collaboration with Mélanie Prague, now post-doc in Harvard. We have developed models for interaction between HIV and the immune system. Based on these models, we have proposed an algorithm for dose monitoring. The current work aims at analysing several studies simultaneously and identifying the effect of each drug in combination of antiretrovirals.
The other topîc is that of the PhD of Ana Jarne. Mechanistic models are developed for estimating and understanding the effect of injection of Interleukin 7 on the restauration of the immune system in HIV infected patients.
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 counterfactual approach 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.

Estimator choice based on information theory
Information theory allows to define a broad class of criteria for estimator choice in different situations (including prognosis), generalizing the Akaike information criterion. The crossentropy of estimators in different contexts can be estimated by crossvalidation and approximate formula can be developed for the leave-one-out crossvalidation.

(ANR funded project), 2011-2013.
Dynamical Biostatistical Models.
In a context where public health issues are increasingly important, where epidemiologists collect richer data through cohort studies, statistical models play an increasingly important role. In particular, dynamic models are used to model the risk of relevant events and can be used for prognosis. At the same moment, there is an important development of biostatistical models. The multi-state models are used to model the occurrence of several events, models for quantitative longitudinal data are used to model the evolution of biological markers or psychometric scores, joint models are used to model simultaneously both types of data. Two particular public health issues are dementia and hospital-acquired infections. In both cases several events may occur and must be taken into account in the analysis. For example, dementia occurring in elderly should be modelled simultaneously with death, which instantaneous risk may be greater than that of dementia. This is necessary to obtain unbiased estimates because the diagnosis of dementia is made at discrete time. This also allows calculating the expected time spent in dementia. In addition a joint model using psychometric tests can predict the onset of dementia, and thus at risk subjects could be treated early with better chances of success. For hospital-acquired infections, this dynamic aspect of prognosis is also crucial. Biostatistics teams in Bordeaux (directed by Daniel Commenges) and Leiden (Hein Putter) are specialists in these models. The project consists in continuing to develop some statistical aspects, in increasing the impact of this methodological effort in epidemiological practice, through collaboration with two teams of epidemiology, one devoted to the epidemiology of brain aging ( directed by Jean-François Dartigues, Bordeaux), the other to hospital-acquired infections (directed by Jean-François Timsit, Grenoble). The aim is to strengthen the link between sophisticated statistical developments and epidemiology as well as with clinical research. In addition, the project seeks to promote the dissemination of such methods by writing friendly and reliable software. This software, developed in the free language R,  will cover a range of multi-state and joint models, with the ability to easily switch from one model to another and compare the quality of estimators obtained by criteria such as Akaike criterion and its derivatives. This development must go hand in hand with writing a book describing the theory with applications and implementation of software.

Book: Dynamical Biostatistical models
A book on dynamical statistical models will be pusblished by Chapman & Hall in 2015. It will encompass the models for qunatitative longitudinal data, life history events and the stochastic approach to causality, including mechanistic models.