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## EPC Inria Xpop : population modelling for life sciences

*Joint Team with the Centre de Recherche Inria Saclay - Île-de-France,
See the webpage of the Inria team Xpop.*

### Members of the team

**Leader:**

Marc Lavielle, Directeur de Recherche Inria

**Permanent Researchers:**

Julie Josse, Partial time Professor, Ecole Polytechnique

Erwan Le Pennec, P rofessor, Ecole Polytechnique

Eric Moulines, Professor, Ecole Polytechnique

**PhD students:**

Nicola Brosse

Belhal Karimi

Geneviève Robin

Marine Zulian

**Assistant:**

Katia Evrat

### Research lines

**Markov Chain Monte Carlo algorithms**

While these Monte Carlo algorithms have turned into standard tools over the past decade, they still face diffculties in handling less regular problems such as those involved in deriving inference for high-dimensional models. One of the main problems encountered when using MCMC in this challenging settings is that it is diffcult to design a Markov chain that effciently samples
the state space of interest.
The Metropolis-adjusted Langevin algorithm (MALA) is a Markov chain Monte Carlo (MCMC) method for obtaining random samples from a probability distribution for which direct sampling is diffcult.
MALA and its extensions have demonstrated to represent very effcient alternative for sampling from high dimensional distributions. We therefore need to adapt these methods to general mixed effects models.

**Massive and missing data**

The ability to easily collect and gather a large amount of data from di-erent sources can be seen
as an opportunity to better understand many processes. It has already led to breakthroughs
in several application areas. However, due to the wide heterogeneity of measurements and
objectives, these large databases often exhibit an extraordinary high number of missing values.
Hence, in addition to scienti-c questions, such data also present some important methodological
and technical challenges for data analyst.

Missing values occur for a variety of reasons: machines that fail, survey participants who
do not answer certain questions, destroyed or lost data, dead animals, damaged plants, etc.
Missing values are problematic since most statistical methods can not be applied directly on a
incomplete data. Many progress have been made to properly handle missing values. However,
there are still many challenges that need to be addressed in the future, that are crucial for the
users.

**Population pharmacometrics**

Pharmacometrics involves the analysis and interpretation of data produced in pre-clinical and
clinical trials. Studies in pre-clinical and clinical pharmacology, pharmacokinetics, pharmacodynamics,
and toxicology typically involve collection of various types of experimental data in
individuals, groups and populations. Appropriate methods of analysis of such data requires an
understanding of the underlying science including: biostatistics, computational methods and
pharmacokinetic/pharmacodynamic modeling.

Population pharmacokinetics studies the variability in drug exposure for clinically safe and
e-ffective doses by focusing on identi-fication of patient characteristics which signi-ficantly a-ect
or are highly correlated with this variability. Disease progress modeling uses mathematical
models to describe, explain, investigate and predict the changes in disease status as a function
of time. A disease progress model incorporates functions describing natural disease progression
and drug action. Natural disease progression is the change in disease status solely attributed
to the progression of the disease. Drug action re-flects the e-ffect of a drug on disease status.

**Model evaluation**

Diagnostic tools are recognized as an essential method for model assessment in the process of
model building. Indeed, the modeler needs to confront -his- model with the experimental data
before concluding that this model is able to reproduce the data and before using it for any
purpose, such as prediction or simulation for instance.
The objective of a diagnostic tool is twofold: -first we want to check if the assumptions made
on the model are valid or not ; then, if some assumptions are rejected, we want to get some
guidance on how to improve the model.

We propose to develop new approaches for diagnosing mixed e-ffects models in a general context
and derive formal and unbiased statistical tests for testing separately each feature of the model.

**Precision medicine and pharmacogenomics**

Pharmacogenomics involves using an individual’s genome to determine whether or not a particular
therapy, or dose of therapy, will be e-ffective. Indeed, people’s reaction to a given drug
depends on their physiological state and environmental factors, but also to their individual
genetic make-up.
Precision medicine is an emerging approach for disease treatment and prevention that takes
into account individual variability in genes, environment, and lifestyle for each person. While some advances in precision medicine have been made, the practice is not currently in use for
most diseases.

We therefore aim to develop methods and algorithms for the validation and selection of mixed
e-ects models adapted to the problems of genomic medicine.

**Models for intracellular processes** (joint project with the Lifeware Inria team)

Signi-ficant cell-to-cell heterogeneity is ubiquitously-observed in isogenic cell populations. Cells
respond di-fferently to a same stimulation. For example, accounting for such heterogeneity is
essential to quantitatively understand why some bacteria survive antibiotic treatments, some
cancer cells escape drug-induced suicide, stem cell do not di-fferentiate, or some cells are not
infected by pathogens.

The main ambition of this project is to propose a paradigm change in the quantitative modelling
of cellular processes by shifting from mean-cell models to single-cell and population models. The
main contribution of Xpop focuses on methodological developments for mixed-e-ffects model
identification in the context of growing cell populations.

**mlxR, a R package for mixed effects models **

Xpop is developing the mlxR package, a R package for
the simulation and visualization of complex models for longitudinal data.
The models are encoded using the model coding language MLXtran, automatically converted
into C++ codes, compiled on the -fly and linked to R using the Rcpp package. That allows one to
implement very easily complex ODE-based models and complex statistical models, including
mixed e-ffects models, for continuous, count, categorical, and time-to-event data.

Fast simulation of realistic clinical trials is made possible with mlxR. Clinical trial simulation is
the center piece of quantitative model based drug development (MBDD). Indeed, from repeated
simulations of a certain trial with di-fferent treatments and di-fferent numbers of virtual patients,
the probability of achieving a given target value, may be estimated in silico.