Lasso-type estimators for non-parametric mixed-effects models: application to high-dimensional data from a vaccine clinical trial for HIV

Abstract : The penalization of likelihoods by L1–norms has become a relatively standard technique for highdimensional data when the assumed models are based on n independent and identically distributed observations. These techniques should improve prediction accuracy (since regularization leads to variance reduction) together with interpretability (since sparsity identifies a subset of variables with strong effects). Computationally, these penalties are attractive and their theoretical properties have been intensively studied during the last years. Several authors have recently suggested analyzing high-dimensional clustered or longitudinal data using L1–penalization methods in mixed effects models. These approaches are mostly developed for variable selection purposes in linear and generalized linear mixed effects models and also, but less extensive, in parametric nonlinear mixed effects models. Only a few works have considered the problem of selecting nonlinear functions using L1–penalization methods in nonparametric mixed effects models, with additive or nonadditive predictors. Nonlinear functions are approximated by a linear combination of smooth functions (spline, wavelet or Fourier basis functions) possibly combined with more irregular functions (spiky basis functions). The resulting estimator depends only on a relatively small number of variables and/or a relatively small number of basis functions [1]. In this study we illustrate the interest of such approaches in the analysis of the DALIA-1 longitudinal trial [2]. Eighteen HIV infected patients received vaccine injections at weeks 0, 4, 8 and 12. Antiretroviral treatment was interrupted at week 24. The patients were followed up to week 48, leading to 14 repeated measures per subject. Our aim was to predict the evolution of viral loads (continuous response) from the about 260 gene sets (predictors). The incorporation of the temporal effect is a key point to reach accurate predictions. References [1] Arribas-Gil, A. and Bertin, K. and Meza, C. and Rivoirard, V. (2012). LASSO-type estimators for Semiparametric Nonlinar Mixed-Effects Models Estimation, Statistics and Computing, 24 (3), 443-460. [2] Lévy, Y. and Thiébaut, R. and Montes, M. and Lacabaratz, C. and Sloan, L. and King, B. et al. (2014). Dendritic cell-based therapeutic vaccine elicits polyfunctional HIV-specific T-cell immunity associated with control of viral load. European journal of immunology, 44 (9), 2802-2810.
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Submitted on : Monday, November 14, 2016 - 1:35:54 PM
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  • HAL Id : hal-01396378, version 1



Perrine Soret, Cristian Meza, Marta Avalos, Karine Bertin, Rodolphe Thiébaut. Lasso-type estimators for non-parametric mixed-effects models: application to high-dimensional data from a vaccine clinical trial for HIV. 3rd conference of the International Society for Non-Parametric Statistics (ISNPS), Jun 2016, Avignon, France. ⟨hal-01396378⟩



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