# Adoption of Machine Learning in Pharmacometrics: An Overview of Recent Implementations and Their Considerations

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## Abstract

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## 1. Introduction

#### 1.1. Background

#### 1.2. Structure of This Review

#### 1.3. Literature Search

## 2. Data Preparation

#### 2.1. Data Imputation

#### 2.1.1. Standard Methods for Data Imputation

#### 2.1.2. Machine Learning Methods for Data Imputation

#### 2.1.3. Considerations

#### 2.2. Dimensionality Reduction

#### Considerations

## 3. Hypothesis Generation

#### 3.1. Discovery of Patient Sub-Populations

#### Considerations

#### 3.2. Covariate Selection

#### 3.2.1. Limitations of Stepwise Covariate Selection Methods

#### 3.2.2. Linear Machine Learning Methods

#### 3.2.3. Tree-Based Methods

#### 3.2.4. Genetic Algorithms

#### 3.3. Considerations

## 4. Predictive Models

#### 4.1. Machine Learning for Pharmacokinetic Modelling

#### 4.1.1. Evaluation of Different Approaches

#### 4.1.2. Considerations

#### 4.2. Machine Learning for Predicting Treatment Effects

#### 4.2.1. Exposure-Response Modelling

#### 4.2.2. Survival Analysis

#### 4.2.3. Considerations

## 5. Model Validation

#### 5.1. Choosing a Validation Strategy

#### 5.1.1. Options for Estimating Model Generalizability

#### 5.1.2. Considerations

#### 5.2. Model Interpretation

#### Considerations

## 6. Main Points

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AUC | Area under the concentration time curve |

DeepLIFT | Deep learning important features |

EM | Expectation maximization |

GAN | Generative adverserial network |

GP | Gaussian Process |

IIV | inter-individual variation |

k-NN | k-nearest neighbour |

LASSO | Least absolute shrinkage and selection operator |

LIME | local interpretable model agnostic explanations |

LOOCV | Leave-one-out cross validation |

MAR | Missing at random |

MARS | Multivariate adaptive regression splines |

MCAR | Missing completely at random |

MICE | Multiple imputation by chained equations |

ML | Machine learning |

MNAR | Missing not at random |

NLME | Non-linear mixed effect |

ODE | Ordinary differential equation |

PCA | Principal component analysis |

PD | Pharmacodynamic |

PK | Pharmacokinetic |

SCM | Stepwise covariate modelling |

SHAP | Shapley additive explanations |

t-SNE | t-distributed stochastic neighbour embedding |

UMAP | Uniform manifold approximation and projection |

VAE | Variational autoencoder |

## Appendix A. Machine Learning for Covariate Selection

#### Appendix A.1. Data

#### Appendix A.2. Models

## Appendix B. Neural Network for Drug Concentration Prediction

#### Appendix B.3. Data

#### Appendix B.4. Prediction of Warfarin Concentrations

#### Appendix B.5. SHAP Analysis

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**Figure 1.**Examples of machine learning-based covariate importance scores. LASSO coefficients (

**A**), random forest importance scores (

**B**), MARS covariate importance (

**C**), explainable gradient boosting scores (

**D**), MARS (

**E**) and explainable gradient boosting (

**F**) approximation of the effect of covariate 1 are shown. Coloured bars indicate true covariates, whereas white bars represent noise covariates. Bar height represents the importance of each covariate. Importance should be larger for true covariates than for noise covariates. The resulting scores can for example be used to select covariates eligible for inclusion in a NLME model. Error bars indicate standard deviation of each score following a ten-fold cross validation. In (

**E**), the point indicates the piecewise split location (i.e., a knot). In (

**F**), shaded area represents the standard deviation of model predictions in the explainable gradient boosting model. Figure inset represents the function used for covariate 1 in the simulations.

**Figure 2.**Examples of predicting drug concentrations using neural networks. Concentration-time curves for a single test set patient are shown as predicted using naive (

**A**) and ODE-based (

**B**) neural networks. Model prediction when artificially setting the dose to zero is depicted by the colored lines. Stars represent the measured warfarin concentrations for the patient.

**Figure 3.**Examples of methods for estimation of model generalization accuracy. Schematic overview of three common validation strategies: k-fold cross validation, random subsampling, and bootstrapping (with replacement). The white shapes denote the training data, whereas grey shapes denote testing data. Here, e represents the total number of experiments to run.

**Figure 4.**Examples of using SHAP for model interpretation. Change in warfarin absorption rate ($\Delta $mg/h) prediction by the neural network as estimated by SHAP values. Here, circles represent the SHAP values calculated for men, whereas triangles represent SHAP values calculated for female patients. Lines represent the neural network predicting when fixing patient sex (solid for male, and dashed for female) and predicting absorption rate based on different values for age.

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**MDPI and ACS Style**

Janssen, A.; Bennis, F.C.; Mathôt, R.A.A.
Adoption of Machine Learning in Pharmacometrics: An Overview of Recent Implementations and Their Considerations. *Pharmaceutics* **2022**, *14*, 1814.
https://doi.org/10.3390/pharmaceutics14091814

**AMA Style**

Janssen A, Bennis FC, Mathôt RAA.
Adoption of Machine Learning in Pharmacometrics: An Overview of Recent Implementations and Their Considerations. *Pharmaceutics*. 2022; 14(9):1814.
https://doi.org/10.3390/pharmaceutics14091814

**Chicago/Turabian Style**

Janssen, Alexander, Frank C. Bennis, and Ron A. A. Mathôt.
2022. "Adoption of Machine Learning in Pharmacometrics: An Overview of Recent Implementations and Their Considerations" *Pharmaceutics* 14, no. 9: 1814.
https://doi.org/10.3390/pharmaceutics14091814