IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v77y2021i3p1061-1074.html
   My bibliography  Save this article

Joint penalized spline modeling of multivariate longitudinal data, with application to HIV‐1 RNA load levels and CD4 cell counts

Author

Listed:
  • Lihui Zhao
  • Tom Chen
  • Vladimir Novitsky
  • Rui Wang

Abstract

Motivated by the need to jointly model the longitudinal trajectories of HIV viral load levels and CD4 counts during the primary infection stage, we propose a joint penalized spline modeling approach that can be used to model the repeated measurements from multiple biomarkers of various types (eg, continuous, binary) simultaneously. This approach allows for flexible trajectories for each marker, accounts for potentially time‐varying correlation between markers, and is robust to misspecification of knots. Despite its advantages, the application of multivariate penalized spline models, especially when biomarkers may be of different data types, has been limited in part due to its seemingly complexity in implementation. To overcome this, we describe a procedure that transforms the multivariate setting to the univariate one, and then makes use of the generalized linear mixed effect model representation of a penalized spline model to facilitate its implementation with standard statistical software. We performed simulation studies to evaluate the validity and efficiency through joint modeling of correlated biomarkers measured longitudinally compared to the univariate modeling approach. We applied this modeling approach to longitudinal HIV‐1 RNA load and CD4 count data from Southern African cohorts to estimate features of the joint distributions such as the correlation and the proportion of subjects with high viral load levels and high CD4 cell counts over time.

Suggested Citation

  • Lihui Zhao & Tom Chen & Vladimir Novitsky & Rui Wang, 2021. "Joint penalized spline modeling of multivariate longitudinal data, with application to HIV‐1 RNA load levels and CD4 cell counts," Biometrics, The International Biometric Society, vol. 77(3), pages 1061-1074, September.
    • Handle: RePEc:bla:biomet:v:77:y:2021:i:3:p:1061-1074
    DOI: 10.1111/biom.13339
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13339
    Download Restriction: no
    File URL: https://libkey.io/10.1111/biom.13339?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Yuedong Wang, 1998. "Mixed effects smoothing spline analysis of variance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 159-174.
    2. John A. Rice & Colin O. Wu, 2001. "Nonparametric Mixed Effects Models for Unequally Sampled Noisy Curves," Biometrics, The International Biometric Society, vol. 57(1), pages 253-259, March.
    3. Hadfield, Jarrod D., 2010. "MCMC Methods for Multi-Response Generalized Linear Mixed Models: The MCMCglmm R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i02).
    4. Kiranmoy Das & Michael J. Daniels, 2014. "A semiparametric approach to simultaneous covariance estimation for bivariate sparse longitudinal data," Biometrics, The International Biometric Society, vol. 70(1), pages 33-43, March.
    5. Lan Zhou & Jianhua Z. Huang & Raymond J. Carroll, 2008. "Joint modelling of paired sparse functional data using principal components," Biometrika, Biometrika Trust, vol. 95(3), pages 601-619.
    6. Wang, Lifeng & Li, Hongzhe & Huang, Jianhua Z., 2008. "Variable Selection in Nonparametric Varying-Coefficient Models for Analysis of Repeated Measurements," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1556-1569.
    7. Arũnas P. Verbyla & Brian R. Cullis & Michael G. Kenward & Sue J. Welham, 1999. "The Analysis of Designed Experiments and Longitudinal Data by Using Smoothing Splines," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 269-311.
    8. Elizabeth R. Brown & Joseph G. Ibrahim & Victor DeGruttola, 2005. "A Flexible B-Spline Model for Multiple Longitudinal Biomarkers and Survival," Biometrics, The International Biometric Society, vol. 61(1), pages 64-73, March.
    9. M. P. Wand, 2003. "Smoothing and mixed models," Computational Statistics, Springer, vol. 18(2), pages 223-249, July.
    10. X. Lin & D. Zhang, 1999. "Inference in generalized additive mixed modelsby using smoothing splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 381-400, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. M. P. Wand, 2003. "Smoothing and mixed models," Computational Statistics, Springer, vol. 18(2), pages 223-249, July.
    2. Faustin Habyarimana & Shaun Ramroop, 2015. "Determinants of Poverty of Households: Semi parametric Analysis of Demographic and Health Survey Data from Rwanda," Journal of Economics and Behavioral Studies, AMH International, vol. 7(3), pages 47-55.
    3. Göran Kauermann & Tatyana Krivobokova & Ludwig Fahrmeir, 2009. "Some asymptotic results on generalized penalized spline smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 487-503, April.
    4. Lee, Dae-Jin & Durbán, María, 2008. "Smooth-car mixed models for spatial count data," DES - Working Papers. Statistics and Econometrics. WS ws085820, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Veerabhadran Baladandayuthapani & Bani K. Mallick & Mee Young Hong & Joanne R. Lupton & Nancy D. Turner & Raymond J. Carroll, 2008. "Bayesian Hierarchical Spatially Correlated Functional Data Analysis with Application to Colon Carcinogenesis," Biometrics, The International Biometric Society, vol. 64(1), pages 64-73, March.
    6. Lee, Dae-Jin & Durbán, María, 2009. "P-spline anova-type interaction models for spatio-temporal smoothing," DES - Working Papers. Statistics and Econometrics. WS ws093312, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Jaroslaw Harezlak & Louise M. Ryan & Jay N. Giedd & Nicholas Lange, 2005. "Individual and Population Penalized Regression Splines for Accelerated Longitudinal Designs," Biometrics, The International Biometric Society, vol. 61(4), pages 1037-1048, December.
    8. Welham, S.J. & Thompson, R., 2009. "A note on bimodality in the log-likelihood function for penalized spline mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 920-931, February.
    9. Woojoo Lee & Hans‐Peter Piepho & Youngjo Lee, 2021. "Resolving the ambiguity of random‐effects models with singular precision matrix," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(4), pages 482-499, November.
    10. Xiao Ni & Daowen Zhang & Hao Helen Zhang, 2010. "Variable Selection for Semiparametric Mixed Models in Longitudinal Studies," Biometrics, The International Biometric Society, vol. 66(1), pages 79-88, March.
    11. Øystein Sørensen & Anders M. Fjell & Kristine B. Walhovd, 2023. "Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 456-486, June.
    12. Sue J. Welham & Brian R. Cullis & Michael G. Kenward & Robin Thompson, 2006. "The Analysis of Longitudinal Data Using Mixed Model L-Splines," Biometrics, The International Biometric Society, vol. 62(2), pages 392-401, June.
    13. Laurini, Fabrizio & Pauli, Francesco, 2009. "Smoothing sample extremes: The mixed model approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3842-3854, September.
    14. Kyunghee Han & Pantelis Z Hadjipantelis & Jane-Ling Wang & Michael S Kramer & Seungmi Yang & Richard M Martin & Hans-Georg Müller, 2018. "Functional principal component analysis for identifying multivariate patterns and archetypes of growth, and their association with long-term cognitive development," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-18, November.
    15. Fu, Eric & Heckman, Nancy, 2019. "Model-based curve registration via stochastic approximation EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 159-175.
    16. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 121-142, April.
    17. Nadja Klein & Michel Denuit & Stefan Lang & Thomas Kneib, 2013. "Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape," Working Papers 2013-24, Faculty of Economics and Statistics, Universität Innsbruck.
    18. Wei, Jiawei & Zhou, Lan, 2010. "Model selection using modified AIC and BIC in joint modeling of paired functional data," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1918-1924, December.
    19. Adhya Sumanta & Banerjee, Tathagata & Chattopadhyay, G., 2007. "Inference on Categorical Survey Response: A Predictive Approach," IIMA Working Papers WP2007-05-07, Indian Institute of Management Ahmedabad, Research and Publication Department.
    20. Hua Liang, 2009. "Generalized partially linear mixed-effects models incorporating mismeasured covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 27-46, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:biomet:v:77:y:2021:i:3:p:1061-1074. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.