Simulation Study on a Method for PK-QT Analyses When Several Active Compounds or Metabolites Are Present
Jochen Zisowsky, Noelia Nebot, Giulia Lestini, Günter Heimann
Pharmacometrics, Oncology Franchise, Novartis Pharma AG
Objectives: To develop a statistically sound approach for PK-QT analysis when jointly modeling the impact of two active compounds, and to understand its operating characteristics via simulations. The approach should control the type I error for an appropriately defined hypothesis test.
Methods: We consider exposure(PK)-response(QT) analyses when there are several compounds or active metabolites. We used a joint model including all active compounds, which was linear in all compounds (without/with interaction), included a fixed effect parameter for the diurnal effect, and a random patient effect. This model can be viewed as an extension of the model proposed by Hosmane et al.[1] for a single agent to the situation with two active drugs. On the basis of this model we developed a criterion to understand whether the expected effect in the critical exposure region would be ≥10 msec. We used bootstrap to test the corresponding null hypothesis. The null hypothesis was rejected if the proportion of bootstrap copies with an estimated effect >10 msec was <0.05. The bootstrap procedure consisted in randomly drawing entire patient data from the observed pool of patients. We then conducted a simulation study based on real data to understand the operating characteristics of the procedure, and we applied the method to real examples. The simulations were done using R version 3.0.2.
Results: The simulation study demonstrated that the type I error is adequately controlled, and that the procedure is slightly conservative in some situations. When applying the approach to our main example, the PK-QT analysis revealed competing effects of two compounds on QT. The estimated effect in the critical region was <10 msec and the above mentioned null hypothesis could be rejected. None of the observed concentration pairs were above the 10 msec line and none of the 95% ellipsoids representing the joint two-dimensional distribution of the pairs of maximum concentrations crossed the 10 msec line.
Conclusions: The developed approach to analyze PK-QT data when several active compounds are present worked well. Type I error is adequately controlled, which is important for regulatory purposes. In our data example, the reduction of QT interval by the parent compound and the increase of QT interval by the second compound were nicely reflected in our parameter estimates. This contradicting effect would have shown as hysteresis in a separate PK-QT analysis for each compound, leading to biased and not interpretable results. Our two-dimensional approach nicely overcomes this issue.
References:
[1] Hosmane B, Locke C, Chiu YL. Exposure-Response Modeling Approach for Assessing QT Effect in Thorough QT/QTc Studies. J Biopharm Stat (2010) 20(3): 624-640.
