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

Applying Neural ODEs to Derive a Mechanism-Based Model for Characterizing Maturation-Related Serum Creatinine Dynamics in Preterm Newborns

Serum creatinine in neonates follows complex dynamics due to maturation processes, most pronounced in the first few weeks of life. The development of a mechanism-based model describing complex dynamics requires high expertise in pharmacometric (PMX) modeling and substantial model development time. A recently published machine learning (ML) approach of low-dimensional neural ordinary differential equations (NODEs) is capable of modeling such data from newborns automatically. However, this efficient data-driven approach in itself does not result in a clinically interpretable model. In this work, an approach to deriving an interpretable model with reasonable PMX-type functions is presented. This "translation" was applied to derive a PMX model for serum creatinine in neonates considering maturation processes and covariates. The developed model was compared to a previously published mechanism-based PMX model whereas both models had similar mechanistic structures. The developed model was then utilized to simulate serum creatinine concentrations in the first few weeks of life considering different covariate values for gestational age and birth weight. The reference serum creatinine values derived from these simulations are consistent with observed serum creatinine values and previously published reference values. Thus, the presented NODE-based ML approach to model complex serum creatinine dynamics in newborns and derive interpretable, mathematical-statistical components similar to those in a conventional PMX model demonstrates a novel, viable approach to facilitate the modeling of complex dynamics in clinical settings and pediatric drug development.

Model-informed precision dosing: State of the art and future perspectives

Model-informed precision dosing (MIPD) stands as a significant development in personalized medicine to tailor drug dosing to individual patient characteristics. MIPD moves beyond traditional therapeutic drug monitoring (TDM) by integrating mathematical predictions of dosing, and considering patient-specific factors (patient characteristics, drug measurements) as well as different sources of variability. For this purpose, rigorous model qualification is required for the application of MIPD in patients. This review delves into new methods in model selection and validation, also highlighting the role of machine learning in improving MIPD, the utilization of biosensors for real-time monitoring, as well as the potential of models integrating biomarkers for efficacy or toxicity for precision dosing. The clinical evidence of TDM and MIPD is discussed for various medical fields including infection medicine, oncology, transplant medicine, and inflammatory bowel diseases, thereby underscoring the role of pharmacokinetics/pharmacodynamics and specific biomarkers. Further research, particularly randomized clinical trials, is warranted to corroborate the value of MIPD in enhancing patient outcomes and advancing personalized medicine.

On inductive biases for the robust and interpretable prediction of drug concentrations using deep compartment models

Conventional pharmacokinetic (PK) models contain several useful inductive biases guiding model convergence to more realistic predictions of drug concentrations. Implementing similar biases in standard neural networks can be challenging, but might be fundamental for model robustness and predictive performance. In this study, we build on the deep compartment model (DCM) architecture by introducing constraints that guide the model to explore more physiologically realistic solutions. Using a simulation study, we show that constraints improve robustness in sparse data settings. Additionally, predicted concentration-time curves took on more realistic shapes compared to unconstrained models. Next, we propose the use of multi-branch networks, where each covariate can be connected to specific PK parameters, to reduce the propensity of models to learn spurious effects. Another benefit of this architecture is that covariate effects are isolated, enabling model interpretability through the visualization of learned functions. We show that all models were sensitive to learning false effects when trained in the presence of unimportant covariates, indicating the importance of selecting an appropriate set of covariates to link to the PK parameters. Finally, we compared the predictive performance of the constrained models to previous relevant population PK models on a real-world data set of 69 haemophilia A patients. Here, constrained models obtained higher accuracy compared to the standard DCM, with the multi-branch network outperforming previous PK models. We conclude that physiological-based constraints can improve model robustness. We describe an interpretable architecture which aids model trust, which will be key for the adoption of machine learning-based models in clinical practice.

Mixed effect estimation in deep compartment models: Variational methods outperform first-order approximations

This work focusses on extending the deep compartment model (DCM) framework to the estimation of mixed-effects. By introducing random effects, model predictions can be personalized based on drug measurements, enabling the testing of different treatment schedules on an individual basis. The performance of classical first-order (FO and FOCE) and machine learning based variational inference (VI) algorithms were compared in a simulation study. In VI, posterior distributions of the random variables are approximated using variational distributions whose parameters can be directly optimized. We found that variational approximations estimated using the path derivative gradient estimator version of VI were highly accurate. Models fit on the simulated data set using the FO and VI objective functions gave similar results, with accurate predictions of both the population parameters and covariate effects. Contrastingly, models fit using FOCE depicted erratic behaviour during optimization, and resulting parameter estimates were inaccurate. Finally, we compared the performance of the methods on two real-world data sets of haemophilia A patients who received standard half-life factor VIII concentrates during prophylactic and perioperative settings. Again, models fit using FO and VI depicted similar results, although some models fit using FO presented divergent results. Again, models fit using FOCE were unstable. In conclusion, we show that mixed-effects estimation using the DCM is feasible. VI performs conditional estimation, which might lead to more accurate results in more complex models compared to the FO method.

Simulating realistic patient profiles from pharmacokinetic models by a machine learning postprocessing correction of residual variability

We address the problem of model misspecification in population pharmacokinetics (PopPK), by modeling residual unexplained variability (RUV) by machine learning (ML) methods in a postprocessing step after conventional model building. The practical purpose of the method is the generation of realistic virtual patient profiles and the quantification of the extent of model misspecification, by introducing an appropriate metric, to be used as an additional diagnostic of model quality. The proposed methodology consists of the following steps: After developing a PopPK model, the individual residual errors IRES = DV-IPRED, are computed, where DV are the observations and IPRED the individual predictions and are modeled by ML to obtain IRESML. Correction of the IPREDs can then be carried out as DVML = IPRED + IRESML. The methodology was tested in a PK study of ropinirole, for which a PopPK model was developed while a second deliberately misspecified model was also considered. Various supervised ML algorithms were tested, among which Random Forest gave the best results. The ML model was able to correct individual predictions as inspected in diagnostic plots and most importantly it simulated realistic profiles that resembled the real data and canceled out the artifacts introduced by the elevated RUV, even in the case of the heavily misspecified model. Furthermore, a metric to quantify the extent of model misspecification was introduced based on the R2 between IRES and IRESML, following the rationale that the greater the extent of variability explained by the ML model, the higher the degree of model misspecification present in the original model.

Warfarin-A natural anticoagulant: A review of research trends for precision medication

BACKGROUND

Warfarin is a widely prescribed anticoagulant in the clinic. It has a more considerable individual variability, and many factors affect its variability. Mathematical models can quantify the quantitative impact of these factors on individual variability.

PURPOSE

The aim is to comprehensively analyze the advanced warfarin dosing algorithm based on pharmacometrics and machine learning models of personalized warfarin dosage.

METHODS

A bibliometric analysis of the literature retrieved from PubMed and Scopus was performed using VOSviewer. The relevant literature that reported the precise dosage of warfarin calculation was retrieved from the database. The multiple linear regression (MLR) algorithm was excluded because a recent systematic review that mainly reviewed this algorithm has been reported. The following terms of quantitative systems pharmacology, mechanistic model, physiologically based pharmacokinetic model, artificial intelligence, machine learning, pharmacokinetic, pharmacodynamic, pharmacokinetics, pharmacodynamics, and warfarin were added as MeSH Terms or appearing in Title/Abstract into query box of PubMed, then humans and English as filter were added to retrieve the literature.

RESULTS

Bibliometric analysis revealed important co-occuring MeShH and index keywords. Further, the United States, China, and the United Kingdom were among the top countries contributing in this domain. Some studies have established personalized warfarin dosage models using pharmacometrics and machine learning-based algorithms. There were 54 related studies, including 14 pharmacometric models, 31 artificial intelligence models, and 9 model evaluations. Each model has its advantages and disadvantages. The pharmacometric model contains biological or pharmacological mechanisms in structure. The process of pharmacometric model development is very time- and labor-intensive. Machine learning is a purely data-driven approach; its parameters are more mathematical and have less biological interpretation. However, it is faster, more efficient, and less time-consuming. Most published models of machine learning algorithms were established based on cross-sectional data sourced from the database.

CONCLUSION

Future research on personalized warfarin medication should focus on combining the advantages of machine learning and pharmacometrics algorithms to establish a more robust warfarin dosage algorithm. Randomized controlled trials should be performed to evaluate the established algorithm of warfarin dosage. Moreover, a more user-friendly and accessible warfarin precision medicine platform should be developed.

Covariate modeling in pharmacometrics: General points for consideration

Modeling the relationships between covariates and pharmacometric model parameters is a central feature of pharmacometric analyses. The information obtained from covariate modeling may be used for dose selection, dose individualization, or the planning of clinical studies in different population subgroups. The pharmacometric literature has amassed a diverse, complex, and evolving collection of methodologies and interpretive guidance related to covariate modeling. With the number and complexity of technologies increasing, a need for an overview of the state of the art has emerged. In this article the International Society of Pharmacometrics (ISoP) Standards and Best Practices Committee presents perspectives on best practices for planning, executing, reporting, and interpreting covariate analyses to guide pharmacometrics decision making in academic, industry, and regulatory settings.

Reinforcement Learning and PK-PD Models Integration to Personalize the Adaptive Dosing Protocol of Erdafitinib in Patients with Metastatic Urothelial Carcinoma

The integration of pharmacokinetic-pharmacodynamic (PK-PD) modeling and simulations with artificial intelligence/machine learning algorithms is one of the most attractive areas of the pharmacometric research. These hybrid techniques are currently under investigation to perform several tasks, among which precision dosing. In this scenario, this paper presents and evaluates a new framework embedding PK-PD models into a reinforcement learning (RL) algorithm, Q-learning (QL), to personalize pharmacological treatment. Each patient is represented with a set of PK-PD parameters and has a personal QL agent which optimizes the individual treatment. In the training phase, leveraging PK-PD simulations, the QL agent assesses different actions, defined consistently with the clinical knowledge to consider only plausible dose-adjustments, in order to find the optimal rules. The proposed framework was evaluated to optimize the erdafitinib treatment in patients with metastatic urothelial carcinoma. This drug was approved by the US Food and Drug Administration (FDA) with a dose-adaptive protocol based on monitoring the levels of serum phosphate, which represent a biomarker of both treatment efficacy and toxicity. To evaluate the flexibility of the methodology, a heterogeneous virtual population of 141 patients was generated using an erdafitinib population PK (PopPK)-PD literature model. For each patient, treatment response was simulated by using both QL-optimized protocol and the clinical one. QL agents outperform the approved dose-adaptive rules, increasing more than 10% the efficacy and the safety of treatment at each end point. Results confirm the great potentialities of the integration of PopPK-PD models and RL algorithms to optimize precision dosing tasks.

Low-dimensional neural ODEs and their application in pharmacokinetics

Machine Learning (ML) is a fast-evolving field, integrated in many of today's scientific disciplines. With the recent development of neural ordinary differential equations (NODEs), ML provides a new tool to model dynamical systems in the field of pharmacology and pharmacometrics, such as pharmacokinetics (PK) or pharmacodynamics. The novel and conceptionally different approach of NODEs compared to classical PK modeling creates challenges but also provides opportunities for its application. In this manuscript, we introduce the functionality of NODEs and develop specific low-dimensional NODE structures based on PK principles. We discuss two challenges of NODEs, overfitting and extrapolation to unseen data, and provide practical solutions to these problems. We illustrate concept and application of our proposed low-dimensional NODE approach with several PK modeling examples, including multi-compartmental, target-mediated drug disposition, and delayed absorption behavior. In all investigated scenarios, the NODEs were able to describe the data well and simulate data for new subjects within the observed dosing range. Finally, we briefly demonstrate how NODEs can be combined with mechanistic models. This research work enhances understanding of how NODEs can be applied in PK analyses and illustrates the potential for NODEs in the field of pharmacology and pharmacometrics.

Integrating machine learning with pharmacokinetic models: Benefits of scientific machine learning in adding neural networks components to existing PK models

Recently, the use of machine-learning (ML) models for pharmacokinetic (PK) modeling has grown significantly. Although most of the current approaches use ML techniques as black boxes, there are only a few that have proposed interpretable architectures which integrate mechanistic knowledge. In this work, we use as the test case a one-compartment PK model using a scientific machine learning (SciML) framework and consider learning an unknown absorption using neural networks, while simultaneously estimating other parameters of drug distribution and elimination. We generate simulated data with different sampling strategies to show that our model can accurately predict concentrations in extrapolation tasks, including new dosing regimens with different sparsity levels, and produce reliable forecasts even for new patients. By using a scenario of fitting PK data with complex absorption, we demonstrate that including known physiological structure into an SciML model allows us to obtain highly accurate predictions while preserving the interpretability of classical compartmental models.

Using population pharmacokinetics to optimize initial vancomycin dosing guidelines for neonates to treat sepsis caused by coagulase-negative staphylococcus

INTRODUCTION

Vancomycin dosing tailored for newborns is challenging due to the significant influence of maturation and organ function on pharmacokinetics. Population pharmacokinetic (popPK) models can be used to improve target attainment in neonates.

OBJECTIVES

The primary objective was to derive and evaluate a popPK model of intravenous vancomycin for neonates. Second, the predictive performance of this popPK model was compared with published popPK models.

METHODS

This is a retrospective cohort study of neonates admitted to the neonatal intensive care unit receiving intravenous vancomycin. A popPK model was derived with 70% of the dataset using a nonlinear mixed effects modeling method. The predictive performance of the current popPK model was validated and compared with 22 published popPK models using the remaining 30% of the dataset. Monte Carlo simulations (MCS) were performed to derive optimal dosing regimens to treat neonatal sepsis caused by coagulase-negative staphylococci (CoNS).

RESULTS

Among 655 vancomycin courses from 448 neonates, 78% of vancomycin trough concentrations were outside target range (10-15 mg/L) for central nervous system infections and 43% were outside target range (5-12 mg/L) for other infections using the institution's vancomycin dosing. A one-compartment model best described the observed data with a mean clearance of 0.11 ± 0.03 L/kg/h and volume of distribution (V) of 1.02 ± 0.08 L/kg. Body weight (WT), postmenstrual age (PMA), and serum creatinine (SCr) were significant covariates associated with clearance (p < 0.001) and body WT was a significant covariate associated with V (p = 0.009). Our study's popPK model has similar or better accuracy and precision than other published models. MCS-derived vancomycin doses from the validated model achieved >90% target attainment for a steady state through target range of 10-15 mg/L in the majority of PMA and SCr categories (78%) to treat CoNS sepsis.

CONCLUSION

A vancomycin dosing guideline derived from a validated popPK model in neonates with CoNS sepsis is recommended to improve target attainment.

Clinical decision support for chemotherapy-induced neutropenia using a hybrid pharmacodynamic/machine learning model

Consensus guidelines recommend use of granulocyte colony stimulating factor in patients deemed at risk of chemotherapy-induced neutropenia, however, these risk models are limited in the factors they consider and miss some cases of neutropenia. Clinical decision making could be supported using models that better tailor their predictions to the individual patient using the wealth of data available in electronic health records (EHRs). Here, we present a hybrid pharmacokinetic/pharmacodynamic (PKPD)/machine learning (ML) approach that uses predictions and individual Bayesian parameter estimates from a PKPD model to enrich an ML model built on her data. We demonstrate this approach using models developed on a large real-world data set of 9121 patients treated for lymphoma, breast, or thoracic cancer. We also investigate the benefits of augmenting the training data using synthetic data simulated with the PKPD model. We find that PKPD-enrichment of ML models improves prediction of grade 3-4 neutropenia, as measured by higher precision (61%) and recall (39%) compared to PKPD model predictions (47%, 33%) or base ML model predictions (51%, 31%). PKPD augmentation of ML models showed minor improvements in recall (44%) but not precision (56%), and data augmentation required careful tuning to control overfitting its predictions to the PKPD model. PKPD enrichment of ML shows promise for leveraging both the physiology-informed predictions of PKPD and the ability of ML to learn predictor-outcome relationships from large data sets to predict patient response to drugs in a clinical precision dosing context.

Joint use of population pharmacokinetics and machine learning for optimizing antiepileptic treatment in pediatric population

Purpose

Unpredictable drug efficacy and safety of combined antiepileptic therapy is a major challenge during pharmacotherapy decisions in everyday clinical practice. The aim of this study was to describe the pharmacokinetics of valproic acid (VA), lamotrigine (LTG), and levetiracetam (LEV) in a pediatric population using nonlinear mixed-effect modeling, while machine learning (ML) algorithms were applied to identify any relationships among the plasma levels of the three medications and patients' characteristics, as well as to develop a predictive model for epileptic seizures.

Methods

The study included 71 pediatric patients of both genders, aged 2-18 years, on combined antiepileptic therapy. Population pharmacokinetic (PopPK) models were developed separately for VA, LTG, and LEV. Based on the estimated pharmacokinetic parameters and the patients' characteristics, three ML approaches were applied (principal component analysis, factor analysis of mixed data, and random forest). PopPK models and ML models were developed, allowing for greater insight into the treatment of children on antiepileptic treatment.

Results

Results from the PopPK model showed that the kinetics of LEV, LTG, and VA were best described by a one compartment model with first-order absorption and elimination kinetics. Reliance on random forest model is a compelling vision that shows high prediction ability for all cases. The main factor that can affect antiepileptic activity is antiepileptic drug levels, followed by body weight, while gender is irrelevant. According to our study, children's age is positively associated with LTG levels, negatively with LEV and without the influence of VA.

Conclusion

The application of PopPK and ML models may be useful to improve epilepsy management in vulnerable pediatric population during the period of growth and development.

Machine Learning for Exposure-Response Analysis: Methodological Considerations and Confirmation of Their Importance via Computational Experimentations

Exposure-response (E-R) is a key aspect of pharmacometrics analysis that supports drug dose selection. Currently, there is a lack of understanding of the technical considerations necessary for drawing unbiased estimates from data. Due to recent advances in machine learning (ML) explainability methods, ML has garnered significant interest for causal inference. To this end, we used simulated datasets with known E-R "ground truth" to generate a set of good practices for the development of ML models required to avoid introducing biases when performing causal inference. These practices include the use of causal diagrams to enable the careful consideration of model variables by which to obtain desired E-R relationship insights, keeping a strict separation of data for model-training and for inference generation to avoid biases, hyperparameter tuning to improve the reliability of models, and estimating proper confidence intervals around inferences using a bootstrap sampling with replacement strategy. We computationally confirm the benefits of the proposed ML workflow by using a simulated dataset with nonlinear and non-monotonic exposure-response relationships.

Deep Learning Methods Applied to Drug Concentration Prediction of Olanzapine

Pharmacometrics and the utilization of population pharmacokinetics play an integral role in model-informed drug discovery and development (MIDD). Recently, there has been a growth in the application of deep learning approaches to aid in areas within MIDD. In this study, a deep learning model, LSTM-ANN, was developed to predict olanzapine drug concentrations from the CATIE study. A total of 1527 olanzapine drug concentrations from 523 individuals along with 11 patient-specific covariates were used in model development. The hyperparameters of the LSTM-ANN model were optimized through a Bayesian optimization algorithm. A population pharmacokinetic model using the NONMEM model was constructed as a reference to compare to the performance of the LSTM-ANN model. The RMSE of the LSTM-ANN model was 29.566 in the validation set, while the RMSE of the NONMEM model was 31.129. Permutation importance revealed that age, sex, and smoking were highly influential covariates in the LSTM-ANN model. The LSTM-ANN model showed potential in the application of drug concentration predictions as it was able to capture the relationships within a sparsely sampled pharmacokinetic dataset and perform comparably to the NONMEM model.

Predicting the Temperature Evolution during Nanomilling of Drug Suspensions via a Semi-Theoretical Lumped-Parameter Model

Although temperature can significantly affect the stability and degradation of drug nanosuspensions, temperature evolution during the production of drug nanoparticles via wet stirred media milling, also known as nanomilling, has not been studied extensively. This study aims to establish both descriptive and predictive capabilities of a semi-theoretical lumped parameter model (LPM) for temperature evolution. In the experiments, the mill was operated at various stirrer speeds, bead loadings, and bead sizes, while the temperature evolution at the mill outlet was recorded. The LPM was formulated and fitted to the experimental temperature profiles in the training runs, and its parameters, i.e., the apparent heat generation rate Q_gen and the apparent overall heat transfer coefficient times surface area UA, were estimated. For the test runs, these parameters were predicted as a function of the process parameters via a power law (PL) model and machine learning (ML) model. The LPM augmented with the PL and ML models was used to predict the temperature evolution in the test runs. The LPM predictions were also compared with those of an enthalpy balance model (EBM) developed recently. The LPM had a fitting capability with a root-mean-squared error (RMSE) lower than 0.9 °C, and a prediction capability, when augmented with the PL and ML models, with an RMSE lower than 4.1 and 2.1 °C, respectively. Overall, the LPM augmented with the PL model had both good descriptive and predictive capability, whereas the one with the ML model had a comparable predictive capability. Despite being simple, with two parameters and obviating the need for sophisticated numerical techniques for its solution, the semi-theoretical LPM generally predicts the temperature evolution similarly or slightly better than the EBM. Hence, this study has provided a validated, simple model for pharmaceutical engineers to simulate the temperature evolution during the nanomilling process, which will help to set proper process controls for thermally labile drugs.