Concentration-QT (C-QT) modeling

Published

May 5, 2025

Under construction

Data

The default dependent variable (DV) is ΔQTcF.

Modeling

The pre-specified linear mixed effect (LME) C-QTc model () is used as the primary analysis.

(1)ΔQTcijk=(θ1+η1,i)+θ2TRTj+(θ3+η3,i)Cijk+θ4TIMEj+θ5(QTci,j=0QTc0)

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  • θ1: Population mean intercept wihtout drug effect
  • θ2: Treatment effect (1=drug, 0=placebo)
  • θ3: Slope (Continuous covariate. Parent or metabolite concentrations)
  • θ4: Mean QTc change from baseline at TIME = k for placebo
  • θ5: Baseline QTc effect
  • Cijk: Concentration for subject i in treatment j and time k;
  • QTci,j=0: Baseline QTc
  • QTc0: Mean of all the baselines

Evaluation

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
Goodness of fit plots
Model predicted versus observed ΔQTc Model specification is adequate. Model and observed values should fall around the line of unity without evidence of systematic bias. Loess smooth line with 95% CI should include the unity line over range of values Systematic bias indicates model misspecification. For example, model predictions will be negatively biased at high values when PK/PD hysteresis is ignored and model predictions will be positively biased at high values when a linear model is applied to nonlinear data
Quantile-Quantile plot of residuals Residuals follow normal distribution with mean of zero Residuals should fall on the line of unity Heavy tails indicate model misspecification. The plot does not indicate source of misspecification
Concentrations versus residuals
Baseline QTc versus residuals
Model covariates are adequate Residuals should be randomly scattered around zero
The 95% CI of the loess line should include zero
Bias in residuals indicates model misspecification. A residual plot should be made for each model parameter
Time versus residuals
Active treatment versus residuals
Quantiles of concentrations and ΔQTc overlaid with slope of final model Drug effect model is adequate The concentration-QTc relationship obtained from final model should describe the observed data Any systematic differences between the modeled versus observed data indicates model misspecification

References

[1]
Garnett C, Bonate PL, Dang Q, Ferber G, Huang D, Liu J, et al. Scientific white paper on concentration-QTc modeling. J Pharmacokinet Pharmacodyn 2018;45:383–97. https://doi.org/10.1007/s10928-017-9558-5.