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## Impact of delayed effects in the exposure-response analysis of clinical QT studies

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Published: | September 10, 2008 |
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#### Introduction

The ICH E14 guideline [Ref. 1] recommends investigating the risk of QT(c) prolongation of new drugs in a dedicated clinical study, the so called “Thorough QT study” (TQT). The primary analysis of such a study is the quantitative comparison of the QTc change from baseline between drug and placebo at each sampling time point. A recommended statistical methodology is the repeated measurements analysis as proposed by Patterson et al [Ref. 2].

In addition to this analysis, some sponsors had also explored the relationship between the actual drug concentration in the blood (exposure) and the change from baseline of the (heart rate corrected) QT interval effect (response) [Ref. 3], [Ref. 4], [Ref. 5]. This type of analysis had been gained increased visibility since also regulators provided stronger support for it [Ref. 6]. One advantage of this PK-QT analysis is the use of the full data set for the effect estimation which is statistically more efficient than slicing the data by time points as recommended by the E14 analysis [Ref. 7].

On the other hand, the PK-QT analysis depends on the underlying modelling assumptions. While first analyses were based on a linear regression, the methodology rapidly developed towards linear and nonlinear mixed effects models.

The current investigation examines the detection and the impact of a potential delay between concentration and QT(c)-effect in the PK-QT analysis.

#### Methods

The pharmacokinetic-pharmacodynamic model for the exposure response analysis of the QT interval is shown in Figure 1 [Fig. 1].

The pharmacokinetic model consists of an absorption system and an elimination system which are based on monoexponential transit times. The parameters of this model are *F* the fraction of the dose which reaches systemic circulation, *1/ka* the mean absorption time and *1/ke* the mean elimination time.

The concentration of the drug in the body is determining the effect size of the QT interval prolongation, based on the effect function E. The simplest effect model is a linear model

*dQT = c * Conc*

where c is a proportionality factor, and dQT is the change from baseline of the QT(c) interval. Other pharmacodynamic models are possible [Ref. 8] including the non-linear Emax-model

*dQT = E0 + (Emax * Conc)/(EC50 + Conc)*.

The current investigations introduced another change in the pharmacodynamic model: a lag time was added, which leads to delayed onset and offset of the QT(c)-prolongation. The aim was to simulate data with the delayed effects and to study the following questions:

a) Which impact do delayed effects have on the estimation of the model parameters, if the estimation model does not account for the delay?

b) How can delayed effects been identified?

c) If the estimation model accounts for the delay – can the model parameters and the QT(c) effects be estimated efficiently?

Question a) and c) can be addressed by examination of the relationship between the delay parameter and the estimated parameters. Question b) is often investigated by plotting the concentration time profiles of the concentration and the QT(c) change from baseline. In addition, scatter plots of both parameters are examined which shall reveal typical hysteresis loops with counter clockwise direction.

However, there is currently no statistical metric available which indicates whether a delay is of a magnitude that it could potentially bias the effect estimates of the pharmacodynamic model.

The investigations are based on designs and sample sizes of typical TQT studies. Most model parameters are simulated with interindividual variability. The estimations will be based on mixed models. Monte-Carlo-simulations were carried out with 1000 replications of TQT studies for each parameter combination.

#### Results and Discussion

While hysteresis plays an important role in the pre-clinical studies of QT(c)- prolongation, delays of QT(c)-effects have not been addressed statistically in clinical trials yet. Preliminary studies indicated that the magnitude of a delayed QT(c) effect could potentially be underestimated if the estimation model does not account for the delay. Details of the results are still to be derived; they will be presented in the poster.

### References

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