Bayesian multi-response nonlinear mixed-effect model: application of two recent HIV infection biomarkers
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Charlotte Castel
,
Cécile Sommen
Abstract
Since the discovery of the human immunodeficiency virus (HIV) 35 years ago, the epidemic is still ongoing in France. To monitor the dynamics of HIV transmission and assess the impact of prevention campaigns, the main indicator is the incidence. One method to estimate the HIV incidence is based on biomarker values at diagnosis and their dynamics over time. Estimating the HIV incidence from biomarkers first requires modeling their dynamics since infection using external longitudinal data. The objective of the work presented here is to estimate the joint dynamics of two biomarkers from the PRIMO cohort. We thus jointly modeled the dynamics of two biomarkers (TM and V3) using a multi-response nonlinear mixed-effect model. The parameters were estimated using Bayesian Hamiltonian Monte Carlo inference. This procedure was first applied to the real data of the PRIMO cohort. In a simulation study, we then evaluated the performance of the Bayesian procedure for estimating the parameters of multi-response nonlinear mixed-effect models.
Funding source: Santé publique France
Acknowledgements
This research was fully supported by the French Institute for Public Health Surveillance. We would like to thank Dr Laurence Meyer, professor of Public Health at Inserm U822, University Paris-Sud, Hospital Bicêtre for providing us with the dataset of the PRIMO ANRS C05 cohort.
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Author contribution: CC had full access to all the data in the study and takes responsibility for the integrity of the data, the writing of the R programs, and the accuracy of the data analysis. CC drafted the manuscript; CS, EC, AA, and YLS critically revised the manuscript by providing important intellectual content; CS, EC, AA, and YLS supervised the study.
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Research funding: The study was supported by the Santé publique France.
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Conflict of interest statement: The authors declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
References
1. Marty, L, Cazein, F, Panjo, H, Pillonel, J, Costagliola, D, Supervie, V, et al.. Revealing geographical and population heterogeneity in HIV incidence, undiagnosed HIV prevalence and time to diagnosis to improve prevention and care: estimates for France. J Int AIDS Soc 2018;21:e25100. https://doi.org/10.1002/jia2.25100.Search in Google Scholar PubMed PubMed Central
2. Sommen, C, Alioum, A, Commenges, D. A multistate approach for estimating the incidence of human immunodeficiency virus by using HIV and AIDS French surveillance data. Stat Med 2009;28:1554–68. https://doi.org/10.1002/sim.3570.Search in Google Scholar PubMed
3. Sommen, C, Commenges, D, Le Vu, S, Meyer, L, Alioum, A. Estimation of the distribution of infection times using longitudinal serological markers of hiv: implications for the estimation of hiv incidence. Biometrics 2011;67:467–75. https://doi.org/10.1111/j.1541-0420.2010.01473.x.Search in Google Scholar PubMed
4. Le Vu, S, Le Strat, Y, Barin, F, Pillonel, J, Cazein, F, Bousquet, V, et al.. Population-based hiv-1 incidence in France, 2003–08:a modelling analysis. Lancet Infect Dis 2010;10:682–87. https://doi.org/10.1016/S1473-3099(10)70167-5.Search in Google Scholar PubMed
5. Tuerlinckx, F, Rijmen, F, Verbeke, G, De Boeck, P. Statistical inference in generalized linear mixed models: a review. Br J Math Stat Psychol 2006;59:225–55. https://doi.org/10.1348/000711005x79857.Search in Google Scholar PubMed
6. Gad, A, El Kholy, R. Generalized linear mixed models for longitudinal data. Int J Probab Stat 2012;1:41–47. https://doi.org/10.5923/j.ijps.20120103.03.Search in Google Scholar
7. Bock, D, Gibbons, R, Muraki, E. Full-information item factor analysis. Appl Psychol Meas 1988;12:261–80. https://doi.org/10.1177/014662168801200305.Search in Google Scholar
8. Kruschke, J. Doing bayesian data analysis. London: Elsevier; 2015.Search in Google Scholar
9. Lachos, V, Castro, LM, Dey, D. Bayesian inference in nonlinear mixed-effects models using normal independent distributions. Comput Stat Data Anal 2013;64:237–52. https://doi.org/10.1016/j.csda.2013.02.011.Search in Google Scholar
10. Bazzoli, C, Retout, S, Mentré, F. Design evaluation and optimisation in multiple response nonlinear mixed effect models: Pfim 3.0. Comput Methods Progr Biomed 2010;98:55–65. https://doi.org/10.1016/j.cmpb.2009.09.012.Search in Google Scholar PubMed
11. Russu, A, De Nicolao, G, Poggesi, I, Neve, M, Gomeni, R. Bayesian population approaches to the analysis of dose escalation studies. Comput Methods Progr Biomed 2012;107:189–201. https://doi.org/10.1016/j.cmpb.2011.05.010.Search in Google Scholar PubMed
12. Lavielle, M, Mentré, F. Estimation of population pharmacokinetic parameters of saquinavir in hiv patients with the monolix software. J Pharmacokinet Pharmacodyn 2007;34:229–49. https://doi.org/10.1007/s10928-006-9043-z.Search in Google Scholar PubMed PubMed Central
13. Desquilbet, L, Deveau, C, Goujard, C, Hubert, J, Derouineau, J, Meyer, L, The PRIMO Cohort Study Group. Increase in at-risk sexual behaviour among hiv-1- infected patients followed in the French primo cohort. AIDS 2002;16:2329–33. https://doi.org/10.1097/00002030-200211220-00014.Search in Google Scholar PubMed
14. Louder, M, Sambora, A, Chertovab, E, Huntea, T, Barretta, S, Ojonga, F, et al.. Hiv-1 envelope pseudotyped viral vectors and infectious molecular clones expressing the same envelope glycoprotein have a similar neutralization phenotype, but culture in peripheral blood mononuclear cells is associated with decreased neutralization sensitivity. Virology 2005;339:226–38. https://doi.org/10.1016/j.virol.2005.06.003.Search in Google Scholar PubMed
15. Gelman, A. Prior distributions for variance parameters in hierarchical models (comment on article by browne and draper). Bayesian Anal 2006;3:515–34.10.1214/06-BA117ASearch in Google Scholar
16. Lewandowski, D, Kurowicka, D, Joe, H. Generating random correlation matrices based on vines and extended onion method. J Multivariate Anal 2009;100:1989–2001. https://doi.org/10.1016/j.jmva.2009.04.008.Search in Google Scholar
17. Burkner, P. brms: an R package for bayesian multilevel models using stan. J Stat Software 2017;80:1–28. https://doi.org/10.18637/jss.v080.i01.Search in Google Scholar
18. Watanabe, S. Algebraic geometry and statistical learning theory. Cambridge: Cambridge University Press; 2009.10.1017/CBO9780511800474Search in Google Scholar
19. Watanabe, S. Asymptotic equivalence of bayes cross validation and widely applicable information criterion in singular learning theory. J Mach Learn Res 2010;11:3571–94.Search in Google Scholar
20. McElreath, R. Statistical rethinking: a bayesian course with examples in R and stan. New York: CRC Press; 2016.Search in Google Scholar
21. Kurz, S. Statistical Rethinking with brms, ggplot2, and the tidyverse; 2019.Search in Google Scholar
22. Gelman, A, Hwang, J, Vehtari, A. Understanding predictive information criteria for bayesian models. Stat Comput 2013;24:997–1016. https://doi.org/10.1007/s11222-013-9416-2.Search in Google Scholar
23. Barin, F, Meyer, L, Lancar, R, Deveau, C, Gharib, M, Laporte, A, et al.. Development and validation of an immunoassay for identification of recent human immunodeficiency virus type 1 infections and its use on dried serum spots. J Clin Microbiol 2005;43:4441–7. https://doi.org/10.1128/jcm.43.9.4441-4447.2005.Search in Google Scholar PubMed PubMed Central
24. Gelman, A, Carlinb, J, Stern, H, Dunson, D, Vehtari, A, Rubin, D. Bayesian Data Analysis, 3rd ed. London: CRC Press; 2013.10.1201/b16018Search in Google Scholar
25. Carpenter, B, Gelman, A, Hoffman, M, Lee, D, Goodrich, B, Betancourt, M, et al.. Stan: a probabilistic programming language. J Stat Software 2017;76:1–32. https://doi.org/10.18637/jss.v076.i01.Search in Google Scholar
26. R Core Team. R: a language and environment for statistical computing. Vienna: R Foundation for Statistical Computing; 2018. Available from: https://www.R-project.org/.Search in Google Scholar
27. Goldstein, H, Browne, W, Rasbash, J. Partitioning variation in multilevel models. In: Understanding statistics: statistical issues in psychology, education, and the social sciences; 2002, vol 1. https://doi.org/10.1207/s15328031us0104_02.Search in Google Scholar
28. Comets, E, Lavenu, A, Lavielle, M. Parameter estimation in nonlinear mixed effect models using saemix, an r implementation of the saem algorithm. J Stat Software 2017;80:1–41. https://doi.org/10.18637/jss.v080.i03.Search in Google Scholar
Supplementary Material
The online version of this article offers supplementary material (https://doi.org/10.1515/ijb-2021-0030).
© 2021 Walter de Gruyter GmbH, Berlin/Boston
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- Frontmatter
- Research Articles
- Doubly robust adaptive LASSO for effect modifier discovery
- Increasing the efficiency of randomized trial estimates via linear adjustment for a prognostic score
- Review
- Review and comparison of treatment effect estimators using propensity and prognostic scores
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- Error rate control for classification rules in multiclass mixture models
- Regression trees and ensembles for cumulative incidence functions
- Causal inference under over-simplified longitudinal causal models
- Causal inference under interference with prognostic scores for dynamic group therapy studies
- Bayesian multi-response nonlinear mixed-effect model: application of two recent HIV infection biomarkers
- A Bayesian semiparametric accelerate failure time mixture cure model
- Quantifying the extent of visit irregularity in longitudinal data
- An improved method for analysis of interrupted time series (ITS) data: accounting for patient heterogeneity using weighted analysis
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- The number of response categories in ordered response models
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