A five-part series exploring the foundational quantitative analysis methodologies that shape clinical pharmacology strategy and pharmacometrics approaches.

At A2-Ai, we believe robust drug development decisions start with asking the right question and a shared understanding of what approaches to take and how the models are built and applied. Modeling Monday is a five-part blog series that highlights the core considerations and modeling methodologies used across drug discovery and development, with a focus of “demystifying” them.

The series is authored by Rosa Luo, MS, SVP of Clinical Pharmacology, and Sean McCann, PhD, Associate Pharmacometrician, who bring complementary perspectives from clinical pharmacology and pharmacometrics. Together, they will walk through commonly used quantitative analysis and modeling techniques, when they are most impactful, and how they inform real-world decision making.

This week, we are discussing two common approaches for characterizing drug exposure and informing key development decisions: fixed effects modeling and mixed effects modeling. Fixed effects models estimate pharmacokinetic (PK) parameters as single-valued (one value per subject or group) without explicitly modeling the underlying population distribution of those parameters. Whereas mixed effects models, commonly used in population pharmacokinetic (PopPK) analysis, simultaneously estimate typical parameter values and quantify between-subject and between-study variability (e.g., changes in formulations or dosing regimens, fed versus fasted administration, as well as differences in study populations). While fixed effects approaches are widely used in preclinical analysis and early clinical studies, mixed effects modeling becomes especially valuable when the goal is to understand variability across various intrinsic and extrinsic factors.

Fixed Effects Modeling (Naïve Pooling of Preclinical Data):

Why Preclinical Data is Often Pooled:

Preclinical PK studies are typically conducted in animals that are bred and maintained in controlled conditions, reducing genetic and environmental differences. Because intrinsic variability is minimized, PK profiles are generally expected to be broadly similar across animals within a study and dose level. Though it is worth noting that even within inbred strains, biological variability is not truly zero; it is simply small enough relative to the analytical question that pooling is a reasonable simplification.

In contrast, extrinsic factors, such as differences in drug formulations (e.g., vehicle and its solubilization properties) and/or routes of administration, can introduce meaningful differences in exposure and should be considered carefully before pooling data across studies.

What “Naïve Pooling” Means:

Fixed effects modeling often uses naïve pooling, where data from multiple animals are combined as if they came from a single individual. In practice, this means constructing a “composite” concentration-time profile from animals that were each sampled at different individual timepoints. When sampling times are appropriately staggered between animals in each cohort, this composite profile can improve the ability to characterize the central tendency of drug exposure. This is often necessary due to blood volume limits for individual animals and is aligned with the 3Rs principles (Replacement, Reduction, and Refinement) of animal use in scientific research.

Model Outputs and Key Parameters:

Once pooled, fixed effects models can support selection of an appropriate compartmental structure and estimation of parameters such as clearance and volume of distribution. When multiple routes are available (e.g., intravenous and oral), they may also support estimation of bioavailability, which can be especially helpful for interpreting exposure differences across formulations.

Importantly, these models provide more than a summary of exposure metrics. They generate continuous concentration-time predictions that can capture multiphasic elimination behavior, which enable the time-matched pharmacokinetic/pharmacodynamic (PK/PD) analyses that otherwise may not be feasible, given PK and PD data are often collected in separate studies with limited and non-overlapping timepoints. Additionally, fixed effects models may also enable exploratory assessment of scaling relationships (e.g., body size across species) or other covariate effects when appropriate.

Why Sampling Design Matters:

The usefulness of fixed effects modeling depends heavily on the timing and richness of the underlying data. Sparse sampling, missing terminal phase information, or poorly aligned PK and PD timepoints can limit the utility of the model application. This is especially important when the objective is to evaluate direct versus indirect PD responses, time-varying PD effects, and/or mechanistic hypotheses of the PK/PD relationship.

When supported by informative data and intentional study design, fixed effects preclinical modeling provide a quantitative foundation for allometric scaling, first-in-human dose prediction, and early PK/PD hypothesis generation.

Mixed Effects Modeling (Population Pharmacokinetics)

Why Variability Must Be Modeled in Humans:

In clinical studies, inter-individual variability is a fundamental part of human PK. Differences in physiology, disease state, organ function, genetic polymorphisms in drug-metabolizing enzymes, and concomitant therapies mean that exposure cannot be fully described by a single “typical” profile.

Mixed effects modeling addresses this by estimating both the typical population parameters (fixed effects) and the individual deviations from those parameters (random effects). This framework allows dose-exposure relationships to be characterized across a population rather than for a central tendency alone.

Model Structure and Variability Components:

Mixed effects models typically quantify two to three key classifications of variability:

1. Between-subject variability describes how individuals differ from the population mean for each estimated parameter (e.g., clearance, volume of distribution). It captures the spread of individual parameter values around the typical population estimate.
2. Residual variability describes the difference between observed concentrations and model-predicted individual parameters, which encompasses all remaining unmodeled sources variability, such as assay precision, sampling timing errors, and model misspecification.
3. Inter-occasion variability may be incorporated for estimated parameters to describe how individual PK profiles change between sampling occasions. For example, differences in absorption between visits due to variations in food intake or adherence.

Model evaluation replies on a combination of statistical criteria (such as changes in the objective function value) and diagnostic tools (e.g., goodness-of-fit plots and visual predictive checks) to assess how well the model and its variability components explains the observed PK data.

##Covariates, Simulation, and Extrapolation:

PopPK models provide a structured way to evaluate covariate effects and determine which patient-level factors meaningfully influence exposure. The model-building process is iterative and uses objective criteria to guide which covariates and random effects are retained in the final model, ensuring that variability components are only estimated when the available data are sufficient to support them reliably.

The objective of developing mixed effects models is to simulate concentration-time profiles for virtual patients. When combined with PD modeling, quantifying inter-individual variability in exposure enables prediction of the expected range of exposure-response across a population, moving beyond reliance on fixed covariates such as dose or body weight alone. Together, PopPK and PK/PD simulations inform clinical trial design by evaluating dosing regimens, identifying sampling schemes, and adequately powering studies for determination of individual drug exposures and response.

Planning for Modeling Success in Drug Development:

The value of any PK model, fixed effects or mixed effects, is ultimately determined by the data behind it. A model can almost always be built, but the questions it can reliably answer depend on whether the underlying studies were designed with the modeling objectives in mind.

PK modeling is an imperative tool that is uniquely suited to inform decision-making throughout drug development, from translational analyses, to dose optimization, to generating and refining quantitative evidence, and to ultimately supporting dose/dose regimen recommendations for the product labeling. The most impactful modeling programs are those where quantitative goals are integrated with clinical pharmacology, regulatory, and the broader development strategy.