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Ridge Regression for Longitudinal Biomarker Data

Author

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  • Eliot Melissa
  • Ferguson Jane
  • Reilly Muredach P.
  • Foulkes Andrea S.

Abstract

Technological advances facilitating the acquisition of large arrays of biomarker data have led to new opportunities to understand and characterize disease progression over time. This creates an analytical challenge, however, due to the large numbers of potentially informative markers, the high degrees of correlation among them, and the time-dependent trajectories of association. We propose a mixed ridge estimator, which integrates ridge regression into the mixed effects modeling framework in order to account for both the correlation induced by repeatedly measuring an outcome on each individual over time, as well as the potentially high degree of correlation among possible predictor variables. An expectation-maximization algorithm is described to account for unknown variance and covariance parameters. Model performance is demonstrated through a simulation study and an application of the mixed ridge approach to data arising from a study of cardiometabolic biomarker responses to evoked inflammation induced by experimental low-dose endotoxemia.

Suggested Citation

  • Eliot Melissa & Ferguson Jane & Reilly Muredach P. & Foulkes Andrea S., 2011. "Ridge Regression for Longitudinal Biomarker Data," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-11, September.
    • Handle: RePEc:bpj:ijbist:v:7:y:2011:i:1:n:37
    DOI: 10.2202/1557-4679.1353
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    References listed on IDEAS

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    1. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    2. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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    Cited by:

    1. Caroline Bazzoli & Sophie Lambert-Lacroix & Marie-José Martinez, 2023. "Partial least square based approaches for high-dimensional linear mixed models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 769-786, September.
    2. Jan Pablo Burgard & Joscha Krause & Ralf Münnich, 2019. "Penalized Small Area Models for the Combination of Unit- and Area-level Data," Research Papers in Economics 2019-05, University of Trier, Department of Economics.
    3. M. Revan Özkale & Funda Can, 2017. "An evaluation of ridge estimator in linear mixed models: an example from kidney failure data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(12), pages 2251-2269, September.
    4. Ramalingam Shanmugam & Arashi M & Salarzadeh Jenatabadi H, 2018. "Longitudinal Data Analysis Using Liu Regression," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 7(5), pages 102-105, July.
    5. Mozhgan Taavoni & Mohammad Arashi & Samuel Manda, 2023. "Multicollinearity and Linear Predictor Link Function Problems in Regression Modelling of Longitudinal Data," Mathematics, MDPI, vol. 11(3), pages 1-9, January.

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