Lasso-SAMBA Algorithm.

lasso-SAMBA

Implementation of lasso in SAMBA relies on sharp package [1], containing lasso enhanced by stability selection algorithm, and Rsmlx package [2], containing SAMBA algorithm [3].For lasso, categorical covariates need to be numerical and no missing values in the covariates table.

Installation

devtools::install_github("aurianegbt/LSAMBA")

Example

For the example dataset contain in the demo projet in inst/data folder, we simulate for 100 individuals the antibody production by considering two Antibodies secreting cells (ASC), denoted by S -\textit{for short-live}- and L -\textit{for long-live}- (at rates $\varphi_S$ and $\varphi_L$ resp.) and characterized by their half-life ($\delta_S$ and $\delta_L$ resp.), [4], [5]. Antibodies are supposed to decay at rate $\delta_{Ab}$. We add significant covariates on $\varphi_S$, $\varphi_L$ and $\delta_{Ab}$ parameters. The mechanistic model is then :

\forall i\leq N,j\leq n_i,   \left\{\begin{array}{rcl}
    \frac{d}{dt} Ab_i(t_{ij}) &=& {\varphi_S}_i e^{-\delta_S t_{ij}} + {\varphi_L}_i e^{-\delta_L t_{ij}} - {\delta_{Ab}}_i Ab_i(t_{ij}) \\
    Ab_i(t_{i0}=0) &=& {Ab_0}
\end{array}\right.

with

 \displaystyle\left\{
\begin{array}{rcl}
         \log({\varphi_S}_i) &=& \log({\varphi_S}_{pop}) + \eta^{\varphi_S}_i \\
         \log({\varphi_L}_i) &=& \log({\varphi_L}_{pop})  + \eta^L_i \\
         \log({\delta_{Ab}}_i) &=& \log({\delta_{Ab}}_{pop})   +\eta^{Ab}_i
    \end{array}\right. 

where

\displaystyle\left\{
\begin{array}{rcl}
\eta^{\varphi_S}_i&\overset{iid}{\sim}&\mathcal N(0,\omega_{\varphi_S}^2) \\
\eta^L_i&\overset{iid}{\sim}&\mathcal N(0,\omega_L^2) \\
\eta^{Ab}_i&\overset{iid}{\sim}&\mathcal N(0,\omega_{Ab}^2)
    \end{array}\right. 

The observation are the defined as $Y_{ij} = log_{10}(Ab_i(t_{ij}))+\varepsilon_{ij}$ where

\varepsilon_i\overset{iid}{\sim}\mathcal N(0,\Sigma=\sigma^2_{Ab}I_{n_i})

We then add to the dataset noisy genes in order to have finally 200 covariates. These covariates are correlated gaussian covariates.

To build the model, we will use Monolix software [4] and the Rsmlx package [2] (containing implemented SAMBA algorithm [3]) from which we had several other function to enable our lasso approach.

library(LSAMBA)
project <- getMLXdir()

res = buildmlx(project = project,
                buildMethod = "lasso",
                model='covariate',
                test=FALSE)
getIndividualParameterModel()

References

[1] Bodinier B (2024). sharp: Stability-enHanced Approaches using Resampling Procedures. R package version 1.4.6, https://CRAN.R-project.org/package=sharp.

[2] Mihaljevic F, Lavielle M (2024). Rsmlx: R Speaks 'Monolix'. R package version 2024.1.0, https://CRAN.R-project.org/package=Rsmlx.

[3] Prague M, Lavielle M. SAMBA: A novel method for fast automatic model building in nonlinear mixed-effects models. CPT Pharmacometrics Syst Pharmacol. 2022; 11: 161-172. doi:10.1002/psp4.12742

[4] Pasin CBalelli IVan Effelterre T, Bockstal V, Solforosi L, Prague MDouoguih M, Thiébaut R2019. Dynamics of the Humoral Immune Response to a Prime-Boost Ebola Vaccine: Quantification and Sources of Variation. J Virol93:10.1128/jvi.00579-19.https://doi.org/10.1128/jvi.00579-19

[5] Alexandre M, Prague M, McLean C, Bockstal V, Douoguih M, Thiébaut R; EBOVAC 1 and EBOVAC 2 Consortia. Prediction of long-term humoral response induced by the two-dose heterologous Ad26.ZEBOV, MVA-BN-Filo vaccine against Ebola. NPJ Vaccines. 2023 Nov 8;8(1):174. doi: 10.1038/s41541-023-00767-y. PMID: 37940656; PMCID: PMC10632397.

[6] Monolix, Lixoft SAS, a Simulations Plus company, Version 2024R1, https://lixoft.com/products/monolix/