Machine Learning for PK/PD Modeling in Drug Development

Traditionally, pharmacometricians build PK/PD models step-wise. First, they start by building a simple baseline model. They then add new features (an extra compartment, delayed absorption factor, etc.) individually. Finally, they determine whether each change improves the model’s ability to fit the data. Using this step-by-step approach helps the modeler understand the impact of each modification while ensuring the model remains interpretable. However, this approach can be tedious, time-consuming, and error-prone for complex models with numerous parameters.

Machine learning (ML) is a branch of artificial intelligence (AI) that enables computers to learn from data and make data-based decisions.

Addressing Patient Variability and Complexity: Population PK models seek to capture the variability of responses from individual drug concentration-time profiles within a study cohort. Since the model needs many parameters, it creates a complex, multi-dimensional ‘landscape’ full of small dips (Figure 1). Conventional modeling methods might get stuck in one of these dips instead of finding the best overall solution.

Non-Sequential Approach: ML algorithms can explore the entire model space at once instead of building models sequentially. For example, when developing a PK/PD model, an algorithm can simultaneously test configurations like delayed absorption, multiple distribution compartments, and non-linear elimination. This non-sequential approach captures critical interactions between model features that might be missed when features are added one at a time.

Automated Model Evaluation: ML tools can assess goodness of fit, model robustness, and parsimony (low number of parameters) simultaneously by applying specific penalties that form a fitness score. ML automatically evaluates models and picks the ones with the best fitness scores (Figure 2). This process doesn’t require manual interference from a scientist.

Using ML for PK/PD modeling can help pharmacometricians and pharmacokineticists work faster and create higher-quality models. ML can automatically sift through hundreds of potential models to rapidly identify the one that best fits the data. This capability ultimately leads to a model that more accurately captures the drug’s behavior.

A Phase 1 case study demonstrated the power of machine learning in PK modeling. The study involved 12 subjects receiving several doses of a drug subcutaneously. The goal of building the model was to characterize the drug’s pharmacokinetics as well as the effect of patient characteristics (sex and weight) on PK.

Data Analysis: An exploratory data analysis revealed complex drug absorption patterns and indications of capacity-limited elimination. This is important because, with saturated elimination pathways, small dose increases can lead to disproportionately high drug concentrations. The ML algorithm favored a one-compartment model with first-order elimination due to robustness, but it didn’t exclude capacity-limited elimination. The high inter-individual PK variability underscored the need to consider individual patient characteristics.

Model Space: A model space was defined by combining variations of structural models for absorption (first-order with lag-time or distributed delay function) and elimination (one-compartment model with first-order or saturable elimination). Several statistical models were considered to capture the variability of the data. They included combinations of inter-individual parameters with covariate relationships (sex and weight).

Machine Learning: A genetic algorithm was used to search the model space. The algorithm selected random starting points and evaluated 950 models based on a fitness score (Figure 3). It also considered goodness of fit and model robustness with penalties for additional parameters. This automated approach enables pharmacometricians to explore a far larger set of models than would be feasible manually. Therefore, using ML for PK/PD modeling allows scientists to discover optimal solutions that might otherwise be overlooked.

Results: ML proposed a one-compartment model with a distributed delay absorption function. The model included inter-individual variability for clearance, volume, absorption rate, and lag time. It did not identify any significant covariate relationships. The distributed delay function selected by ML for absorption was superior to simple first-order absorption with lag time. The ML model was superior to a traditionally built initial model.

Superior Models: ML can build superior models by identifying model features with critical interactions that might be overlooked in a sequential build. These models will make more accurate predictions for untested clinical study scenarios.

Time-Saving: ML can significantly speed up the modeling process by reducing the time required for manual evaluation of models.

Model Robustness: ML helps select models that fit the data well and are robust, parsimonious, and avoid convergence issues. That means that they avoid problems where the optimization process fails to settle on stable parameter estimates.

Using ML does not replace the analyst! The analyst defines the model space, formulates hypotheses, and evaluates the final model for biological plausibility (Figure 4).

Machine learning may help address the challenges of complex PK/PD modeling. ML tools such as Pirana software can speed up the modeling process, improve model robustness, and select superior models. However, analysts are critical in defining the model space and assessing the final model. As artificial intelligence research and development progress, ML will become an integral part of the PK/PD modeling toolbox. Would you like to deepen your understanding of modeling and other PK/PD concepts and applications? Get free access to the 5th edition of Prof. Johan Gabrielsson’s standard reference book, “Pharmacokinetic and Pharmacodynamic Data Analysis!”