Jan Hasenauer: Modelling and statistical inference for cancer signaling using concepts from machine learning
Large-scale studies like The Cancer Genome Atlas revealed that cancers are multi-factorial diseases, which strongly vary between patients. This inter-patient variability poses a challenge for clinicians. A priori it is not clear which drug (combination) will be most beneficial for an individual. In a multi-national collaboration, we approached the problem of drug response prediction. We developed a mechanistic model covering several of cancer associate signaling pathways. This model can be individualized using sequencing data. For statistical inference we develop a tailored minibatch optimization method which facilitating the study of models with thousands of parameters. To evaluate our model-based approach, we studied data response from the Cancer Cell Line Encyclopedia for 7 drugs and more than 200 cell lines. On the validation set we achieved a prediction accuracy of roughly 80%. These results demonstrate the potential of large-scale mechanistic modeling for drug selection in personalized therapy.
Estelle Kuhn: Joint modelling for parameter estimation involving genotypic effects in crop model from platform and open field experiments
Crop models were developed by ecophysiologists to describe plant development. They allow in particular to report difference existing between several genotypes in several environments, due to genotype by environment interaction. It is first necessary to calibrate these models to use them for prediction purpose. We consider the crop model APSIM and present a joint bayesian model with mixed effects. We infer model parameters values from data collected in the field and in phenotyping platform. Prior distributions are chosen in order to integrate expert knowledge. We implement a hybrid Gibbs algorithm to simulate the posterior distribution. Results obtained from simulated and real data highlight clearly the advantage of using phenotyping platform data in addition to field data.
Joint work with Jean-Benoist Leger (UTC, Heudiasyc), Boris Parent, François Tardieu, Claude Welcker (INRAE, LEPSE)
Stanley Durrleman: Modelling and predicting the progression of neurodegenerative diseases
In this talk, we will review disease course mapping, a statistical technique aiming to chart the range of trajectories of a series of imaging biomarkers and clinical endpoints changing during disease progression. The technique relies on differential geometric principles and may be used for any data that can be represented on Riemannian manifolds. It uniquely decompose variations due differences in the dynamics of the progression from differences due to the presentation of the disease.
We will show that this technique can forecast the values of the biomarkers and clinical endpoints with smaller errors than state-of-the-art methods. Such predictions can be used, in turn, to design clinical trials with better statistical power by selecting patients with homogeneous progression profiles.
We will illustrate these methods on three therapeutic areas: Alzheimer, Parkinson and Huntington disease.
Marc Lavielle: Automatic model building in mixed effect models. Applications in population pharmacology
Mixed effects models are a reference tool to describe complex biological phenomena while taking into account the variability between individuals of the same population.
These models are used to describe processes as diverse as the pharmacokinetics (PK) and pharmacodynamics (PD) of drugs, the dynamics of viruses, tumor growth, etc.
Construction of a pharmacometric model is a complex process which requires confirmed expertise, advanced statistical methods, the use of sophisticated software tools, but above all time and patience.
Indeed, the success of correctly identifying all the components of the model is far from straightforward: it is a question of finding the best structural model, determining the type of relationship between covariates and individual parameters, detecting possible correlations between random effects or also modelling residual errors.
I will present SAMBA (Stochastic Approximation for Model Building Algolrithm) and show how this algorithm can be used to speed up and optimize this process of model building by identifying at each step how best to improve some of the model components.
The principle of this algorithm basically consists in “learning something” about the “best model”, even when a “poor model” is used to fit the data.
This algorithm is now implemented in Monolix, one of the most popular platforms for PKPD modeling, and in the R package Rsmlx (R speaks Monolix).
Jeremie Guedj: Modeling viral dynamics of SARS-CoV2 : insights into virus pathogenesis, transmission & antiviral treatment
In this talk, I will show how we used viral dynamic modeling to and to guide strategies to reduce the risk of acquisition and the risk to develop severe forms of the disease. Relying on both human and animal data, we first evaluated the efficacy that could be achieved with repurposed antiviral drugs, depending on the time of their administration. Using data from hospitalized patients, we built the first joint model to assess the impact of viral dynamics on the risk of mortality. Finally I will discuss more recent projects on the effects of viral load on the risk of transmission.
Maisonnasse, Guedj et al. “Hydroxychloroquine against SARS-CoV-2 infection in non-human primates”. Nature 2020
Néant et al. “Modeling SARS-CoV-2 viral kinetics and association with mortality in hospitalized patients: results from the French Covid-19 cohort”. PNAS 2021.
Gonçalves et al. “SARS-CoV-2 viral dynamics in non-human primates”. PLoS Computational Biology 2021.
Czuppon et al. “Success of prophylactic antiviral therapy for SARS-CoV-2: predicted critical efficacies and impact of different drug-specific mechanisms of action”. PLoS Computational Biology 2021.
Annabelle Collin & Mélanie Prague: Using population based Kalman estimator to model COVID-19 epidemics in France: estimating the burden of SARS-Cov-2 and the effects of non-pharmaceutical interventions
Bärbel Finkenstädt: A spatio-temporal model to reveal oscillator phenotypes in molecular clocks
We develop a method for estimating and modelling transcriptional processes in living tissue samples by means of a stochastic distributed delay model which provides a model that is significantly reduced in the number of parameters — and thus is amenable to parameter estimation — but can realistically account for the intrinsic noise and rhythm generation inherent in the single-cell. The model incorporates a form of dependence of the processes between nearby cells by means of a Markov random field prior between parameters. The model thus describes the cyclical behaviour of the production of the population of some molecular species within cells, along with the spatial variation of the process across a network of cells. This approach is suitable for modelling circadian gene expression in the suprachiasmatic nucleus (SCN), the region of the brain which is responsible for the `circadian master clock’ which coordinates the bodies daily rhythms. This model is applied to three sample tissues from mice SCN. Based on the inferred dynamic behaviour of the cells, we are able to divide the organ into two regions: a central core in which the rhythm is intrinsic and resilient and the more entrainable outer region which is much more heavily influenced by external stimuli. The findings highlight a trade-off between resilient cyclic behaviour and ability to adapt to environmental cues.
Joint work with Måns Unosson and Adam M. Johansen (Department of Statistics, University of Warwick), Marco Brancaccio (UK Dementia Research Institute at Imperial College London), Michael Hastings (MRC Laboratory of Molecular Biology, University of Cambridge)
Adeline Samson-Leclerq: Computational statistics for neuronal mathematical models
We will present some neuronal mathematical models and the associated challenges in terms of statistical inference. These models are hypoelliptic stochastic differential equations which are partially observed at discrete times. Exact likelihoods are not available in that case. We will present statistical methods based on pseudo-likelihood with a stochastic EM algorithm coupled to particle filter. We will also discuss the problem of approximating solutions of the diffusion by adapted numerical schemes such as splitting methods.
Sébastien Benzekry: COMPO – COMPutational pharmacology and clinical Oncology: Optimization of therapeutic strategies by mechanistic and statistical modeling
In this talk, I will first introduce a new Inria-Inserm unit entitled COMPO (COMPutational pharmacology and clinical Oncology, Inria-Inserm, Center for Cancer Research of Marseille, France) which uniquely gathers clinical oncologists, pharmacists and mathematicians. The objective of the team is to develop novel mathematical constructs to model data arising from experimental and clinical oncology. Ultimately, the models are translated into numerical software of direct use in the clinic, either for the design of dosing regimen in clinical trials, or personalized medicine.
I will first give an example using mixed-effects modeling to describe and understand experimental tumor growth kinetics. We observed that the experimental and logistic growth models were unable to describe the data, in contrast with the Gompertz model. The population approach was then further leveraged to define a new model, the reduced Gompertz model, with only one individual-specific parameter (instead of two for the Gompertz) but still similarly good descriptive power. Such reduction in the number of parameters substantially improved the performance of the model when trying to predict the initiation time (inoculation) from late measurements. Improvements were particularly drastic when combining the population approach with Bayesian estimation.
Then I will present a second application for predicting metastatic relapse in early-stage breast cancer. A combination of machine learning techniques and mixed-effects statistical modeling methods was used for individualized predictions of the model parameters from data available at diagnosis. In turn, this allowed to infer the biological role of specific biomarkers and provides a tool for patient-specific prediction of the time to metastatic relapse.
If time allows, I will then present a concrete example of routine use of Bayesian estimation in the Marseille university hospital for adaptive and personalized dosing of cisplatin in head and neck cancer patients.
I will then conclude by presenting a few starting projects involving large dimensional multi-modal data for prediction of the response to immunotherapy and the associated methodological challenges from a statistical learning point of view.
“Population modeling of tumor growth curves and the reduced Gompertz model improve prediction of the age of experimental tumors”. C. Vaghi, A. Rodallec, R. Fanciullino, J. Ciccolini, J. Mochel, M. Mastri, C. Poignard, J. ML Ebos, S. Benzekry, PLoS Computational Biology, Volume 16, Issue 2, e1007178, bioRxiv, 2020
“Machine learning and mechanistic modeling for prediction of metastatic relapse in breast cancer”. C. Nicolo, C. Perier, M. Prague, G. MacGrogan, O. Saut, S. Benzekry, JCO: Clinical Cancer Informatics, Volume 4, pp. 259-274, bioRxiv, 2020
“Artificial intelligence and mechanistic modeling for clinical decision making in oncology”. S. Benzekry, Clinical Pharmacology and Therapeutics, Volume 108, Issue 3, pp.471-486, 2020
Julien Martinelli: Model learning to identify systemic regulators of the peripheral circadian clock. Personalized medicine aims at providing patient-tailored therapeutics based on multi-type data towards improved treatment outcomes. Chronotherapy that consists in adapting drug administration to the patient’s circadian rhythms may be improved by such approach. Recent clinical studies demonstrated large variability in patients’ circadian coordination and optimal drug timing. Consequently, new eHealth platforms allow the monitoring of circadian biomarkers in individual patients through wearable technologies (rest- activity, body temperature), blood or salivary samples (melatonin, cortisol), and daily questionnaires (food intake, symptoms). A current clinical challenge involves designing a methodology predicting from circadian biomarkers the patient peripheral circadian clocks and associated optimal drug timing. The mammalian circadian timing system being largely conserved between mouse and humans yet with phase opposition, the study was developed using available mouse datasets. We investigated at the molecular scale the influence of systemic regulators (e.g. temperature, hormones) on peripheral clocks, through a model learning approach involving systems biology models based on ordinary differential equations. Using as prior knowledge our existing circadian clock model, we derived an approximation for the action of systemic regulators on the expression of three core-clock genes: Bmal1, Per2 and Rev-Erbα. These time profiles were then fitted with a population of models, based on linear regression. Best models involved a modulation of either Bmal1 or Per2 transcription most likely by temperature or nutrient exposure cycles. This agreed with biological knowledge on temperature-dependent control of Per2 transcription. The strengths of systemic regulations were found to be significantly different according to mouse sex and genetic background. https://hal.inria.fr/hal-03183579/document
Marielle Péré: Early prediction of cell response upon cancer drug treatment identifies dynamic determinants of efficient cell death initiation, enabling control of therapeutic response heterogeneity. Cell response heterogeneity upon drug treatment is a leading cause of reduced drug efficacy in preclinical cancer research. Although single-cell studies have revealed the depth of cellular heterogeneity observed between in tumor cells, the regulatory impact of cell variability on therapeutic response remains unclear. In this study, we integrated single-cell data and dynamical features of an ODE system modeling the extrinsic apoptosis triggered by death receptor ligands, to determine an early cell response predictor that enabled the discovery of key regulators of the cell death initiation. This model, calibrated on single-cell FRET ratio time-trajectories of clonal HeLa cells treated with TNF-related apoptosis-inducing ligand (TRAIL), produces two distinct response phenotypes (sensitive and resistant) that allows accurate cell fate prediction. Analysing the timeline of the core reactions and the dynamic properties of the model, we identified regulatory steps of the cell decision, locating a first resolution upon TRAIL binding but also the existence of a ruling time frame during which the sensitive cells benefit from additional regulation at the receptor level, before cell death commitment. Finally, our cell fate predictor accuracy was tested on experimental data sets and served determining the dynamic origins of fractional killing. Here, we emphasised the role of key regulatory dynamics, revealing measurable factors such as pro-capase 8, that can be used as inputs of early prediction assessment, allowing single-cell isolation for molecular profiling.
Hugo Martin: Glioblastoma cell variability and circadian rhythms control temozolomide efficacy: from cellular pharmacokinetics-pharmacodynamics to heterogeneous cancer cell population models. Glioblastoma (GBM) is the most common and aggressive primary brain tumor in adults, and is currently associated with a dismal prognosis despite intensive treatments combining surgery, radiotherapy and temozolomide-based chemotherapy. Clinical trials over the last two decades testing various multi-agent pharmacotherapies have failed demonstrating any significant patient survival improvement so far. Chronotherapy, that consists in administering antitumor drug according to the patient’s 24h-rhythms is considered as a promising therapeutic approach to improve treatment tolerability and efficacy. Interestingly, recent clinical and preclinical studies have highlighted the dependency of temozolomide (TMZ) efficacy on administration timing (E Slat et al., 2017; AR Damato et la., 2021). Median overall survival (OS) of GBM patients receiving TMZ in the morning was equal to 1.43 years as compared to 1.13 for patients taking the same drug dose in the evening. In a subgroup of patients whose tumor presented methylated promoter of MGMT DNA repair enzyme (resulting in decreased MGMT protein expression and increased sensitivity to TMZ), the difference in survival was even higher as the median OS was 6 months longer for AM patients as compared to evening patients. In order to obtain quantitative predictions on the mechanisms underlying temozolomide chronoefficacy, we designed a systems pharmacology model at the cell population level as follows. A simplified ODE-based model of TMZ pharmacokinetics-pharmacodynamics (PK-PD) was connected to a model representing the cancer cell population dynamics though a PDE structured in the amount of DNA damage in a cell and sensitivity to damage. The PK part of the ODE model was fully designed and calibrated to data (Ballesta et al., 2014), whereas the remaining elements of this combined model were inferred from cell culture circadian datasets (E Slat et al., 2017, and unpublished data. To properly fit all datasets, we had to include in the model an inter-cell variability accounting for different rates of DNA damage formation for a given drug dose. This addition allowed a successful model calibration, in contrast to the model in which population heterogeneity came solely from the initial damage distribution, prior any drug exposure.