[Utilisation de modèles dynamiques pour l’optimisation des traitements des patients infectés par le VIH : une approche par analyse bayésienne séquentielle]
L’utilisation des modèles mécanistes dynamiques basés sur des équations différentielles ordinaires (ODE) a considérablement amélioré les connaissances de la dynamique HIV-système immunitaire. Leur flexibilité á ajuster des données et leur capacité de prédictions en font un bon outil pour l’optimisation du plan d’expérience et de l’analyse d’efficacité d’interventions nouvelle dans le domaine du VIH. Nous traitons des méthodes d’estimation pour les ODEs dont les paramètres sont représentés par des modèles á effet mixtes. Nous proposons une estimation bayésienne par maximisation de la vraisemblance pénalisée et basée sur l’approximation normale des a posteriori, implémentée dans le logiciel NIMROD. Nous discutons l’impact d’une analyse séquentielle bayésienne (SBA) permettant d’analyser plusieurs jeux de données en utilisant comme nouvel loi a priori la loi a posteriori des analyses précédentes. Nous illustrons que l’approximation normale de la loi a posteriori, qui contraint la forme des nouvelles lois a priori, permet un gain en précision de l’estimation et diminue les temps de calculs. Nous illustrons la méthode avec des données issues de deux essais cliniques testant des combinaisons d’antirétroviraux (cART) : ALBI ANRS 070 et PUZZLE ANRS 104. Cet article reproduit des résultats non publiés de mon manuscrit de thèse. C’est une extension de la conférence sur le même sujet que j’ai eu l’honneur de donner lors de la réception du prix Marie-Jeanne Laurent-Duhamel, dans le cadre des 47èmes Journées de Statistique organisées par la Société Française de Statistique á Lille, France, en mai 2015.
The use of dynamic mechanistic models based on ordinary differential equations (ODE) has greatly improved the knowledge of the dynamics of HIV and of the immune system. Their flexibility for fitting data and prediction abilities make them a good tool for optimization of the design delivery and efficacy of new intervention in the HIV field. We present the problem of inference in ODE models with mixed effects on parameters. We introduce a Bayesian estimation procedure based on the maximization of the penalized likelihood and a normal approximation of posteriors, which is implemented in the NIMROD software. We investigate the impact of pooling different data by using a sequential Bayesian analysis (SBA), which uses posteriors of a previous study as new priors. We show that the normal approximation of the posteriors, which constrains the shape of new priors, leads to gains in accuracy of estimation while reducing computation times. The illustration is from two clinical trials of combination of antiretroviral therapies (cART): ALBI ANRS 070 and PUZZLE ANRS 104. This paper reproduces some unpublished work from my PhD thesis. It is an extension of my oral presentation on the same topic at the 47th Journées de Statistique organized by the French Statistical Society (SFdS) in Lille, France, May 2015, when being awarded the Marie-Jeanne Laurent-Duhamel prize.
Mot clés : antirétroviraux, approximation normale de l’a posteriori, approche bayésienne, choix de modèle, équation différentielles ordinaire (ODE), in vitro, in vivo, médecine personnalisée, mutations, modèles causaux, modèles dynamiques, modèles á effets mixtes, optimisation numérique, pharmacologie, prédiction, SIDA, VIH
@article{JSFS_2016__157_2_19_0,
author = {Prague, M\'elanie},
title = {Use of dynamical models for treatment optimization in {HIV} infected patients: a sequential {Bayesian} analysis approach},
journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique},
pages = {19--38},
publisher = {Soci\'et\'e fran\c{c}aise de statistique},
volume = {157},
number = {2},
year = {2016},
zbl = {1358.62103},
language = {en},
url = {http://www.numdam.org/item/JSFS_2016__157_2_19_0/}
}
TY - JOUR AU - Prague, Mélanie TI - Use of dynamical models for treatment optimization in HIV infected patients: a sequential Bayesian analysis approach JO - Journal de la société française de statistique PY - 2016 SP - 19 EP - 38 VL - 157 IS - 2 PB - Société française de statistique UR - http://www.numdam.org/item/JSFS_2016__157_2_19_0/ LA - en ID - JSFS_2016__157_2_19_0 ER -
%0 Journal Article %A Prague, Mélanie %T Use of dynamical models for treatment optimization in HIV infected patients: a sequential Bayesian analysis approach %J Journal de la société française de statistique %D 2016 %P 19-38 %V 157 %N 2 %I Société française de statistique %U http://www.numdam.org/item/JSFS_2016__157_2_19_0/ %G en %F JSFS_2016__157_2_19_0
Prague, Mélanie. Use of dynamical models for treatment optimization in HIV infected patients: a sequential Bayesian analysis approach. Journal de la société française de statistique, Tome 157 (2016) no. 2, pp. 19-38. http://www.numdam.org/item/JSFS_2016__157_2_19_0/
[1] HIV dynamics: modeling, data analysis, and optimal treatment protocols, Journal of Computational and Applied Mathematics, Volume 184 (2005) no. 1, pp. 10-49 | Zbl
[2] Causality, mediation and time: a dynamic viewpoint, Journal of the Royal Statistical Society: Series A (Statistics in Society), Volume 175 (2012) no. 4, pp. 831-861
[3] An analysis of transformations, Journal of the Royal Statistical Society. Series B (Methodological) (1964), pp. 211-252
[4] Modelling HIV immune response and validation with clinical data, Journal of biological dynamics, Volume 2 (2008) no. 4, pp. 357-385 | Zbl
[5] Risks and benefits of structured antiretroviral drug therapy interruptions in HIV-1 infection, AIDS, Volume 14 (2000) no. 15, pp. 2313-2322
[6] Isolation of a T-lymphotropic retrovirus from a patient at risk for acquired immune deficiency syndrome (AIDS), Science, Volume 220 (1983) no. 4599, pp. 868-871
[7] Longitudinal models for AIDS marker data, Statistical Methods in Medical Research, Volume 7 (1998) no. 1, pp. 13-27
[8] Quantifying thymic export: combining models of naive T cell proliferation and TCR excision circle dynamics gives an explicit measure of thymic output, The Journal of Immunology, Volume 183 (2009) no. 7, pp. 4329-4336
[9] HIV monotherapy with ritonavir-boosted protease inhibitors: a systematic review, AIDS, Volume 23 (2009) no. 3, pp. 279-291
[10] A Stochastic model of latently infected cell reactivation and viral blip generation in treated HIV patients, PLoS computational biology, Volume 7 (2011) no. 4
[11] Latent reservoirs of HIV: obstacles to the eradication of virus, Proceedings of the National Academy of Sciences, Volume 96 (1999) no. 20, pp. 10958-10961
[12] Effect of highly active antiretroviral therapy on time to acquired immunodeficiency syndrome or death using marginal structural models, American Journal of Epidemiology, Volume 158 (2003) no. 7, pp. 687-694
[13] Inference in HIV dynamics models via hierarchical likelihood, Computational Statistics & Data Analysis, Volume 55 (2011) no. 1, pp. 446-456 | Zbl
[14] The use of the SAEM algorithm in MONOLIX software for estimation of population pharmacokinetic-pharmacodynamic-viral dynamics parameters of maraviroc in asymptomatic HIV subjects, Journal of pharmacokinetics and pharmacodynamics, Volume 38 (2011) no. 1, pp. 41-61
[15] Using marginal structural measurement-error models to estimate the long-term effect of antiretroviral therapy on incident AIDS or death, American journal of epidemiology, Volume 171 (2010) no. 1, pp. 113-122
[16] Towards an HIV cure: a global scientific strategy, Nature reviews Immunology (2012)
[17] Score tests for exploring complex models: application to HIV dynamics models, Biometrical journal, Volume 52 (2010) no. 1, pp. 10-21 | Zbl
[18] Maximum a Posteriori Estimation in Dynamical Models of Primary HIV Infection, Statistical Communications in Infectious Diseases, Volume 4 (2012) no. 1
[19] Modeling the dynamics of biomarkers during primary HIV infection taking into account the uncertainty of infection date, The Annals of Applied Statistics, Volume 4 (2010) no. 4, pp. 1847-1870 | Zbl
[20] Modelling progression of CD4-lymphocyte count and its relationship to survival time, Biometrics (1994), pp. 1003-1014 | Zbl
[21] HIV dynamics with multiple infections of target cells, Proceedings of the National Academy of Sciences of the United States of America, Volume 102 (2005) no. 23, pp. 8198-8203
[22] A review on estimation of stochastic differential equations for pharmacokinetic/pharmacodynamic models, Advanced Drug Delivery Reviews, Volume 65 (2013) no. 7, pp. 929-939
[23] Assessing antiviral potency of anti-HIV therapies in vivo by comparing viral decay rates in viral dynamic models, Biostatistics, Volume 2 (2001) no. 1, pp. 13-29 | Zbl
[24] Prognosis of HIV-1-infected patients starting highly active antiretroviral therapy: a collaborative analysis of prospective studies, The Lancet, Volume 360 (2002) no. 9327, pp. 119-129
[25] Normal approximation to the posterior distribution for generalized linear models with many covariates, Mathematical Methods of Statistics, Volume 6 (1997) no. 3, pp. 332-348 | Zbl
[26] A general definition of influence between stochastic processes, Lifetime data analysis, Volume 16 (2010) no. 1, pp. 33-44 | Zbl
[27] Isolation of human T-cell leukemia virus in acquired immune deficiency syndrome (AIDS), Science, Volume 220 (1983) no. 4599, pp. 865-867
[28] Maximum likelihood estimation in dynamical models of HIV, Biometrics, Volume 63 (2007) no. 4, pp. 1198-1206 | Zbl
[29] Practical identifiability of HIV dynamics models, Bulletin of mathematical biology, Volume 69 (2007) no. 8, pp. 2493-2513 | Zbl
[30] Joint modeling of the clinical progression and of the biomarkers’ dynamics using a mechanistic model, Biometrics, Volume 67 (2011) no. 1, pp. 59-66 | Zbl
[31] Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men, Epidemiology, Volume 11 (2000) no. 5, pp. 561-570
[32] Hierarchical Bayesian methods for estimation of parameters in a longitudinal HIV dynamic system, Biometrics, Volume 62 (2006) no. 2, pp. 413-423 | Zbl
[33] Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection, Nature, Volume 373 (1995) no. 6510, pp. 123-126
[34] Analysis of left-censored longitudinal data with application to viral load in HIV infection, Biostatistics, Volume 1 (2000) no. 4, pp. 355-368 | Zbl
[35] Maximum likelihood estimation in nonlinear mixed effects models, Computational Statistics & Data Analysis, Volume 49 (2005) no. 4, pp. 1020-1038 | Zbl
[36] Approximate Bayesian inference in conditionally independent hierarchical models (parametric empirical Bayes models), Journal of the American Statistical Association, Volume 84 (1989) no. 407, pp. 717-726
[37] Newton Raphson and EM algorithms for linear mixed effects models for repeated-measures data, Journal of the American Statistical Association, Volume 83 (1988) no. 404, pp. 1014-1022 | Zbl
[38] Random regression models for human immunodeficiency virus ribonucleic acid data subject to left censoring and informative drop-outs, Journal of the Royal Statistical Society: Series C (Applied Statistics), Volume 49 (2000) no. 4, pp. 485-497 | Zbl
[39] Hierarchical generalized linear models, Journal of the Royal Statistical Society. Series B (Methodological), Volume 58 (1996) no. 4, pp. 619-678 | Zbl
[40] WinBUGS-a Bayesian modelling framework: concepts, structure, and extensibility, Statistics and computing, Volume 10 (2000) no. 4, pp. 325-337
[41] The ALBI trial: a randomized controlled trial comparing stavudine plus didanosine with zidovudine plus lamivudine and a regimen alternating both combinations in previously untreated patients infected with human immunodeficiency virus, Journal of Infectious Diseases, Volume 180 (1999) no. 2, pp. 351-358
[42] The use of plasma HIV RNA as a study endpoint in efficacy trials of antiretroviral drugs, AIDS, Volume 13 (1999) no. 7, pp. 797-804
[43] On identifiability of nonlinear ODE models and applications in viral dynamics, SIAM review, Volume 53 (2011) no. 1, pp. 3-39 | Zbl
[44] Methods and software tools for design evaluation in population pharmacokinetics–pharmacodynamics studies, British journal of clinical pharmacology, Volume 79 (2015) no. 1, pp. 6-17
[45] The evolutionary dynamics of HIV-1 quasispecies and the development of immunodeficiency disease, AIDS, Volume 4 (1990) no. 11, pp. 1095-1104
[46] Approximations to the log-likelihood function in the nonlinear mixed-effects model, Journal of Computational and Graphical Statistics, Volume 4 (1995) no. 1, pp. 12-35
[47] Adherence profiles and therapeutic responses of treatment-naive HIV-infected patients starting boosted atazanavir-based therapy in the ANRS 134-COPHAR 3 trial, Antimicrobial agents and chemotherapy, Volume 57 (2013) no. 5, pp. 2265-2271
[48] Treatment Monitoring of HIV-Infected Patients based on Mechanistic Models, Biometrics, Volume 68 (2012) no. 3, pp. 902-911 | Zbl
[49] NIMROD: A program for inference via a normal approximation of the posterior in models with random effects based on ordinary differential equations, Computer methods and programs in biomedicine, Volume 111 (2013) no. 2, pp. 447-458
[50] Dynamic versus marginal structural models for estimating the effect of HAART on CD4 in observational studies: application to the Aquitaine Cohort study and the Swiss HIV Cohort Study, arXiv preprint arXiv:1503.08658 (2015) | Zbl
[51] Dynamical models of biomarkers and clinical progression for personalized medicine: The HIV context, Advanced drug delivery reviews, Volume 65 (2013) no. 7, pp. 954-965
[52] Practical identifiability of model parameters by combined respirometric-titrimetric measurements, Water Science and Technology, Volume 43 (2001) no. 7, pp. 347-356
[53] Performance Comparison of Various Maximum Likelihood Nonlinear Mixed-Effects Estimation Methods for Dose–Response Models, Journal of the American Association of Pharmaceutical Scientists, Volume 14 (2012) no. 3, pp. 420-432
[54] Mathematical analysis of HIV-1 dynamics in vivo, SIAM review, Volume 41 (1999) no. 1, pp. 3-44 | Zbl
[55] HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time, Science, Volume 271 (1996) no. 5255, pp. 1582-1586
[56] Systems biology approach predicts immunogenicity of the yellow fever vaccine in humans, Nature immunology, Volume 10 (2009) no. 1, pp. 116-125
[57] Salvage therapy with amprenavir, lopinavir and ritonavir 200 mg/d or 400 mg/d in HIV-infected patients in virological failure, Antiviral therapy, Volume 9 (2004), pp. 615-626
[58] Analysis of Hepatitis C Virus Decline during Treatment with the Protease Inhibitor Danoprevir Using a Multiscale Model, PLoS computational biology, Volume 9 (2013) no. 3 | DOI
[59] Comparing numerical methods for ordinary differential equations, NASA report, Volume ID-113855 (1993)
[60] Marginal structural models and causal inference in epidemiology, Epidemiology, Volume 11 (2000) no. 5, pp. 550-560
[61] Antiretroviral dynamics determines HIV evolution and predicts therapy outcome, Nature medicine, Volume 18 (2012) no. 9, pp. 1378-1385
[62] Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood, Bioinformatics, Volume 25 (2009) no. 15, pp. 1923-1929
[63] Marginal structural models versus structural nested models as tools for causal inference, Statistical models in epidemiology, the environment, and clinical trials, Springer, 2000, pp. 95-133 | Zbl
[64] Optimal structural nested models for optimal sequential decisions, Proceedings of the second seattle Symposium in Biostatistics, Springer (2004), pp. 189-326 | Zbl
[65] Immunologic abnormalities in homosexual men: relationship to Kaposi’s sarcoma, The American journal of medicine, Volume 73 (1982) no. 2, pp. 171-178
[66] Mathematical models of viral latency, Current opinion in virology, Volume 3 (2013) no. 4, pp. 402-407
[67] Dose-response curve slope sets class-specific limits on inhibitory potential of anti-HIV drugs, Nature medicine, Volume 14 (2008) no. 7, pp. 762-766
[68] Drug resistance in an immunological model of HIV-1 infection with impulsive drug effects, Bulletin of Mathematical Biology, Volume 67 (2005) no. 4, pp. 783-813 | Zbl
[69] A stochastic model for analysis of longitudinal AIDS data, Journal of the American Statistical Association, Volume 89 (1994) no. 427, pp. 727-736 | Zbl
[70] Quantifying and predicting the effect of exogenous interleukin-7 on CD4+T cells in HIV-1 infection, Plos computational biology (2014) | DOI
[71] Joint modelling of bivariate longitudinal data with informative dropout and left-censoring, with application to the evolution of CD4+ cell count and HIV RNA viral load in response to treatment of HIV infection, Statistics in medicine, Volume 24 (2005) no. 1, pp. 65-82
[72] Bivariate longitudinal model for the analysis of the evolution of HIV RNA and CD4 cell count in HIV infection taking into account left censoring of HIV RNA measures, Journal of biopharmaceutical statistics, Volume 13 (2003) no. 2, pp. 271-282 | Zbl
[73] Stochastic modeling of the dynamics of CD4+ T-cell infection by HIV and some Monte Carlo studies, Mathematical Biosciences, Volume 147 (1998) no. 2, pp. 173-205 | Zbl
[74] Asymptotic statistics, 3, Cambridge university press, 2000 | Zbl
[75] Current practices in laboratory monitoring of HIV infection, The Indian journal of medical research, Volume 134 (2011) no. 6, pp. 801-822 | DOI
[76] Variations and fluctuations of the number of individuals in animal species living together, Journal of Marine Science, Volume 3 (1928) no. 1, pp. 3-51
[77] Estimating mixed-effects differential equation models, Statistics and Computing, Volume 24 (2012) no. 1, pp. 1-11
[78] Viral dynamics in human immunodeficiency virus type 1 infection, Nature, Volume 373 (1995) no. 6510, pp. 117-122
[79] Stochastic modeling of systems mapping in pharmacogenomics, Advanced drug delivery reviews, Volume 65 (2013) no. 7, pp. 912-917
[80] Parameter identifiability and estimation of HIV/AIDS dynamic models, Bulletin of mathematical biology, Volume 70 (2008) no. 3, pp. 785-799 | Zbl
[81] Modeling antiretroviral drug responses for HIV-1 infected patients using differential equation models, Advanced drug delivery reviews, Volume 65 (2013), pp. 940-953
