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Test Hysteresis in Pharmacokinetic/Pharmacodynamic Relationship with Mixed-Effect Models: An Instrumental Model Approach

Hysteresis often occurs between drug exposure and response. To model the hysteresis, one approach is to combine an effect compartment with an instantaneous exposure-response model. The combined model may not be easy to fit when the exposure-response model contains random effects. Therefore, it is sometimes useful to test existence of the hysteresis without fitting the model with an effect compartment. Although the likelihood ratio test and Wald test can be implemented based on a fitted model, they do not solve problems in fitting the combined model such as nonconvergence. Fitting a model without the effect compartment is often much easier, as the model contains fewer parameters with random effects. We propose a novel yet simple test based on an instrumental model that only requires fitting an instantaneous exposure-response model. For a wide range of pharmacokinetic/pharmacodynamic (PK/PD) models, this test can be implemented using commonly used software. The test can be used based on a parametric PK model or based on a nonparametric approach such as linear interpolation. The performance of the proposed test was compared with a test based on lagged covariate models and examined by a simulation study and illustrated by implementing it to an analysis of the relationship between drug concentration and QT interval in a cardiac safety trial.