Generation of a virtual population for a multi-strain model of natural and vaccinal immunization against influenza
Eulalie Courcelles, Eliott Tixier, Severine Urdy, Jean-Baptiste Gourlet, Matthias Hanke, Emmanuel Peyronnet, Nicolas Ratto, Ana Isis Toledo, Lara Bruezière.
Novadiscovery
Objectives: The generation of a Virtual Population (VP) is the one of the last steps of a QSP model calibration attributing values for a set of model parameters [1,2]. For a certain Context of Use, a VP should include all patient profiles in the correct proportions, to reproduce target behaviors and associated variability. Generating realistic VP is a complex problem [3] with constraints on various inputs and outputs at the population level. We present here a method used to calibrate a VP applied to a multi-strain influenza disease model (MSIDM) to reproduce the variability of vaccine effectiveness observed in annual influenza epidemics.
Methods: We present a MSIDM describing viral and in-host dynamics including immunization due to infection and vaccination. The model accounts for cell migration, interactions between cells, antigens, antibodies and cytokines; as well as cross-reactivity of immune cells formed during previous immunizations with antigens of a circulating strain. MSIDM was initially calibrated on reference patients with an evolutionary method [4] using in vitro data and in vivo data of H1N1 and H3N2 strains that circulated in 2010-2011, to ensure that each behavior (e.g., disease severity, seroprotection) can be reproduced with the model.
From this set of reference patients, representative of characteristic behaviors, a VP of 50,000 patients is generated to account for inter-patient and virus-specific variability. The variability in the VP is represented by 58 descriptors (47 related to patient immunity and 11 to viral characteristics). Among the parameters describing viral characteristics, 3 represent inter-patient variation in viral exposure in the current season, 4 represent the antigenic properties of previously encountered viruses (patient history) and 4 represent the antigenic distances between vaccine and main seasonal circulating strains.
With this virtual population, a 4 arm clinical trial is simulated: one control arm versus a vaccine arm simulated for 2 different influenza A subtypes (H1N1 and H3N2).
After simulations, a filter is applied on the 50k patients to exclude the ones out of our Context of Use: no infection in the control arm as well as unresolved infection one month after exposure in any arm.
Target behaviors are then defined on seroprotection at one month, vaccine effectiveness against H1N1 and H3N2, the correlation between age and cumulated lung damage and their distributions. A subsampling task is then carried out to extract a subpopulation (1000 patients) that exhibits the target behaviors. There are approximately 1e2127 ways of choosing a subsample of size 1,000 from a set of size 50,000 so an exhaustive search of the optimal subset is computationally intractable. Therefore, an approximation of the optimal solution is sought using simulated annealing [5]. The target behaviors are converted to scores ranging from 0 to 1 and the energy function to be minimized by simulated annealing is defined as the average of the scores. For a distribution target, the corresponding score is the Kolmogorov-Smirnov distance and for a correlation target, the score is half the absolute difference between Pearson correlation coefficients.
Results: Out of 50 000 patients, 31 135 are kept after filtering. All targets are matched in the calibrated VP. The corresponding scores are all smaller than 1.5e-2 at the end of the minimization iterations. Seroprotection rate at one month after vaccination is decreased from the initial 86% to the targeted 77% [6,7], vaccine effectiveness decreased from 83% in the initial VP to the targeted 45% for H1N1 and from 78% to 52% from H3N2 [8]. Distributions of age (mean 65 years old) are maintained and cumulative lung damage reaches the target distribution (mean 1.25%, max 12%) with an additional positive correlation of 0.5 between those 2 descriptors.
Realistic dynamics of different in-host variables as well as a clinical stratification between asymptomatic, mild and severe disease forms in each arm can also be observed in the calibrated VP.
Conclusions: This sampling algorithm results in a VP which reproduces realistic behaviors for each variable across all trial arms. This model and VP may be applied to new scenarios for model validation or new exploration. New scenarios may test a different vaccine administration or different antigenic distances between prior immunization, vaccine-strain and/or circulating strain for instance.
References:
[1] Cheng Y, Straube R, Alnaif AE, Huang L, Leil TA, Schmidt BJ. Virtual Populations for Quantitative Systems Pharmacology Models. Methods Mol Biol. 2022;2486:129-179. doi: 10.1007/978-1-0716-2265-0_8. PMID: 35437722.
[2] Rieger TR, Allen RJ, Bystricky L, Chen Y, Colopy GW, Cui Y, Gonzalez A, Liu Y, White RD, Everett RA, Banks HT, Musante CJ. Improving the generation and selection of virtual populations in quantitative systems pharmacology models. Prog Biophys Mol Biol. 2018 Nov;139:15-22. doi: 10.1016/j.pbiomolbio.2018.06.002. Epub 2018 Jun 15. PMID: 29902482.
[3] Allen RJ, Rieger TR, Musante CJ. Efficient Generation and Selection of Virtual Populations in Quantitative Systems Pharmacology Models. CPT Pharmacometrics Syst Pharmacol. 2016 Mar;5(3):140-6. doi: 10.1002/psp4.12063. Epub 2016 Mar 17. PMID: 27069777; PMCID: PMC4809626.
[4] Palgen JL, Perrillat-Mercerot A, Ceres N, Peyronnet E, Coudron M, Tixier E, Illigens BMW, Bosley J, L'Hostis A, Monteiro C. Integration of Heterogeneous Biological Data in Multiscale Mechanistic Model Calibration: Application to Lung Adenocarcinoma. Acta Biotheor. 2022 Jul 7;70(3):19. doi: 10.1007/s10441-022-09445-3. PMID: 35796890; PMCID: PMC9261258.
[5] Kirkpatrick S, Gelatt CD Jr, Vecchi MP. Optimization by simulated annealing. Science. 1983 May 13;220(4598):671-80. doi: 10.1126/science.220.4598.671. PMID: 17813860.
[6] Cox MM, Patriarca PA, Treanor J. FluBlok, a recombinant hemagglutinin influenza vaccine. Influenza Other Respir Viruses. 2008 Nov;2(6):211-9. doi: 10.1111/j.1750-2659.2008.00053.x. PMID: 19453397; PMCID: PMC4634115.
[7] Falsey AR, Treanor JJ, Tornieporth N, Capellan J, Gorse GJ. Randomized, double-blind controlled phase 3 trial comparing the immunogenicity of high-dose and standard-dose influenza vaccine in adults 65 years of age and older. J Infect Dis. 2009 Jul 15;200(2):172-80. doi: 10.1086/599790. PMID: 19508159.
[8] Treanor JJ, Talbot HK, Ohmit SE, Coleman LA, Thompson MG, Cheng PY, Petrie JG, Lofthus G, Meece JK, Williams JV, Berman L, Breese Hall C, Monto AS, Griffin MR, Belongia E, Shay DK; US Flu-VE Network. Effectiveness of seasonal influenza vaccines in the United States during a season with circulation of all three vaccine strains. Clin Infect Dis. 2012 Oct;55(7):951-9. doi: 10.1093/cid/cis574. Epub 2012 Jul 25. PMID: 22843783; PMCID: PMC3657521.