Goodness-of-fit for continuous data

Q: What is pharmacometrics?

Pharmacometrics is the science of quantitative pharmacology that uses mathematical models to describe and predict drug behavior in patients. It combines pharmacokinetics (what the body does to the drug) and pharmacodynamics (what the drug does to the body) to optimize drug development and dosing.

Q: What is NONMEM used for?

NONMEM (NONlinear Mixed Effects Modeling) is specialized software for population pharmacokinetic/pharmacodynamic modeling. It's used to analyze drug concentration-time data from clinical trials to understand variability between patients and optimize dosing regimens.

Q: How is pharmacometrics used in drug development?

Pharmacometrics supports drug development by predicting optimal doses, identifying patient populations likely to benefit, designing efficient clinical trials, and supporting regulatory submissions with quantitative evidence of drug efficacy and safety.

Published

August 24, 2025

Under construction

The graphs are broadly separated into two categories: prediction-based (basic) and simulation-based tools.

Plot	Model assumption tested	What to evaluate	Model impact
Exploratory plots
Time course of HR stratified by dose	No drug effect on HR	Consistency of change from baseline HR ΔHR with time, dose and treatment	If dose- or concentration-dependent effects on HR are observed, the relationship between QT and RR may differ between on- and off-treatment, impacting the QT correction differently between the two conditions This could potentially violate the assumption that the applied QTc correction is an adequate heart rate correction method
QTc versus RR intervals	QTc is independent of HR for drug-free and/or placebo treatments	Linear regression line should show the lack of relationship between QTc and RR intervals Range of HR are similar off- and on-drug	Individual correction factor is potentially poorly estimated due to narrow range of RR intervals within each subject which could bias the C-QTc model
Time course of mean concentrations and mean ΔQTc, ΔΔQTc intervals	Explore direct effect assumption Evaluate PK/PD hysteresis	Shape of PK- and QTc-time profiles, e.g., time course of effect, time of peak, return to baseline Magnitude of variability in PK and QTc	High inter-subject variability in ΔQTc can mask signal in mean curves-this is important in small-sized studies
C-ΔQTc	Evaluate linearity and heterogeneity assumptions between exposure and QTc across doses and studies	Shape of C-QTc relationship Magnitude of ΔQTc over observed concentration range Concentration range covers worse case clinical exposure scenario	Model-independent observations are not corrected for covariates and might therefore not appear to match model prediction Confounding factors not accounted for Heterogeneity between doses/trials

Prediction-based evaluation

Population-based graphs

Table 1: Various evaluation graphs in nonlinear mixed effect model aand proposal for a core set of evaluation graphs

Plot	What is evaluated?	What to evaluate
DV vs. PRED	Structural model, RUV model or IIV model	Trends
CWRES vs (TIME, PRED)		Trends may suggest a modification of structural model, RUV model, or IIV model. Trends by conditioning on covariates suggest including covariates.
CWRES vs COV		Trends suggest including covariates or changing the covariate model.

Individual-based graphs

Table 2: Various evaluation graphs in nonlinear mixed effect model aand proposal for a core set of evaluation graphs

Graphs	What does it assess?
Individual fits: (DV, PRED, IPRED) vs TIME	Expect evenly distributed observation around the individual predicted curve, not spot-on predictions (indication of overfit). This diagnostic is not useful for sparse data.
DV vs IPRED	Only evaluates strutural model and RUV, not IIV.
IWRES vs (TIME, IPRED)	Evaluates RUV. A cone-shaped graph of IWRES vs IPRED suggests a change in the error model.
ETAx vs ETAy	Prefer random sampling of ETAs from posterior distribution. Correlation between EBE suggests including correlation between random effects unless data are sparse.
ETA vs COV	Trends between EBE and covariates suggest including covariates or changing the covariate model.

Simulation-based evaluation

(pc)VPC: Trends may suggest a modification of the structural model, the residual error model, or the parameter variability model. Trends when conditioning on covariates suggest including covariates or changing the covariate model.

Explanation of pcVPC

A Prediction-Corrected Visual Predictive Check (pcVPC) addresses limitations of conventional VPCs by correcting for predictable sources of variability, allowing clearer detection of model misspecification.

More specifically, a pcVPC divides (normalizes) the dependent variable by the population prediction for each bin. This correction removes the influence of variability due to independent variables.

This is especially important when data includes large variations in covariates (e.g., dose), or when adaptive dosing strategies are applied.