Example PK Model Selection Benchmark

A synthetic two-compartment model with covariates

Authors
Affiliations

Jane Researcher

Example University

John Modeler

Pharma Institute

Published

October 16, 2025

Abstract

This benchmark dataset provides a synthetic pharmacokinetic dataset generated from a two-compartment model with covariate effects. The primary task is model selection: identifying the correct structural model and covariate relationships from the data. The dataset includes irregular sampling, informative dropout, and realistic inter-individual variability.

Keywords: pharmacokinetics, model selection, two-compartment, synthetic data

Background

Model selection is a fundamental challenge in pharmacometrics. This benchmark represents a controlled scenario where the true data-generating mechanism is known, allowing for rigorous evaluation of model selection methodologies.

Motivation

  • Evaluate different model selection strategies (stepwise, LASSO, Bayesian methods)
  • Compare information criteria (AIC, BIC, cross-validation)
  • Assess performance under realistic data conditions

Data Generation

True Model Structure

The data were generated using a two-compartment model with first-order absorption and elimination:

\[ \frac{dA_{gut}}{dt} = -k_a \cdot A_{gut} \]

\[ \frac{dA_{central}}{dt} = k_a \cdot A_{gut} - \left(\frac{CL}{V_c} + \frac{Q}{V_c}\right) \cdot A_{central} + \frac{Q}{V_p} \cdot A_{peripheral} \]

\[ \frac{dA_{peripheral}}{dt} = \frac{Q}{V_c} \cdot A_{central} - \frac{Q}{V_p} \cdot A_{peripheral} \]

Parameter Values

Population typical values:

  • \(CL = 10\) L/h
  • \(V_c = 50\) L
  • \(Q = 5\) L/h
  • \(V_p = 30\) L
  • \(k_a = 0.5\) h\(^{-1}\)

Covariate Effects

Clearance: \[ CL_i = 10 \cdot \left(\frac{WT_i}{70}\right)^{0.75} \cdot e^{\eta_{CL,i}} \]

Central Volume: \[ V_{c,i} = 50 \cdot \left(\frac{WT_i}{70}\right) \cdot e^{\eta_{V_c,i}} \]

Where \(WT\) is body weight in kg.

Variability

Inter-individual variability (IIV):

  • \(\omega_{CL}^2 = 0.09\) (30% CV)
  • \(\omega_{V_c}^2 = 0.04\) (20% CV)
  • \(\omega_{Q}^2 = 0.16\) (40% CV)
  • \(\omega_{V_p}^2 = 0.04\) (20% CV)

Residual error:

Combined proportional and additive error: \[ Y_{ij} = C_{pred,ij} \cdot (1 + \epsilon_{prop,ij}) + \epsilon_{add,ij} \]

Where \(\epsilon_{prop} \sim N(0, 0.01)\) and \(\epsilon_{add} \sim N(0, 0.25)\).

Study Design

  • Sample size: 200 subjects
  • Dosing: 100 mg oral dose once daily for 7 days
  • Sampling: Sparse sampling (3-5 samples per subject) at irregular times
  • Dropout: 15% dropout rate, higher for subjects with extreme exposure

Dataset Description

Variables

See data/data-dictionary.csv for complete descriptions. Key variables:

  • ID: Subject identifier (1-200)
  • TIME: Time since first dose (hours)
  • AMT: Dose amount (mg)
  • DV: Dependent variable (concentration, mg/L)
  • EVID: Event ID (0=observation, 1=dose)
  • CMT: Compartment (1=gut, 2=central)
  • WT: Body weight (kg)
  • AGE: Age (years)
  • SEX: Sex (0=Female, 1=Male)

Sample Size

  • Training set: 140 subjects (70%), 673 observations
  • Test set: 60 subjects (30%), 287 observations

Tasks

Task 1: Structural Model Selection

Objective: Identify the correct structural model from candidates.

Candidates:

  1. One-compartment model
  2. Two-compartment model (true)
  3. Three-compartment model

Evaluation Metric: Model selection accuracy, AIC/BIC values on test set

Task 2: Covariate Model Selection

Objective: Identify the correct covariate relationships.

Covariates to test:

  • Weight on CL (true effect)
  • Weight on Vc (true effect)
  • Age on CL (no effect)
  • Sex on CL (no effect)

Evaluation Metric: True positive and false positive rates for covariate selection

Task 3: Prediction Accuracy

Objective: Predict concentrations in the test set.

Evaluation Metrics:

  • Root Mean Squared Error (RMSE)
  • Mean Absolute Error (MAE)
  • Normalized Root Mean Squared Error (NRMSE)

Train/Test Split

The dataset was split 70/30 maintaining:

  • Representative distribution of covariates
  • Similar dropout rates between sets
  • Balanced sparse sampling patterns

Rationale: This split allows for robust model development while reserving sufficient data for meaningful external validation.

Usage Example

import pandas as pd

# Load data
train = pd.read_csv('data/train.csv')
test = pd.read_csv('data/test.csv')

# Load data dictionary
data_dict = pd.read_csv('data/data-dictionary.csv')
print(data_dict)

References

  1. Jonsson EN, Karlsson MO. Xpose–an S-PLUS based population pharmacokinetic/pharmacodynamic model building aid for NONMEM. Comput Methods Programs Biomed. 1999;58(1):51-64.

  2. Holford N. A size standard for pharmacokinetics. Clin Pharmacokinet. 1996;30(5):329-332.

License

This dataset is provided under the CC-BY-4.0 license. You are free to use, share, and adapt this benchmark with attribution.

Citation

If you use this benchmark, please cite:

Researcher J, Modeler J. (2025). Example PK Model Selection Benchmark. Pharmacometrics Benchmarks Initiative. DOI: TBD