Mixed-effects models and the drug titration paradox.

We read with interest the article of Kristensen et al.1 about overcoming the titration paradox. Their study highlighted how the pooled titration data from all individuals when graphed may indicate the wrong direction of the slope for the dose–response curve and, as we also illustrated,2 would show a flat dose–response when based on end-of-trial data. They demonstrate by means of simulation that the titration paradox may be overcome if longitudinal data from dose titration trials is analyzed using a population approach that accounts for interindividual variability and there is a clear causal relationship between the response and the dose at every timepoint. We appreciate the authors’ interest in this topic. We agree that in some situations a mixed effects model will be helpful in the analysis of data from titration studies. However, we recently showed that a linear mixed-effects model did not identify the correct underlying dose–response relationship in titration data during clinical anesthesia, because of the presence of the titration paradox in the individual data.3 Clearly, when the individual data show a titration paradox, a mixed-effects model, which only accounts for interindividual variability, will still not reveal the correct underlying pharmacology. As highlighted by Kristensen et al., the causal relationship must be clear. If the causal relationship between the measured effect and the titrated dose is confounded by other explanatory variables that were not available to be included in the analysis, a mixed effects model will not overcome the titration paradox. In our data, we believe that these explanatory variables were most likely the changing levels of surgical stimulus, blood loss, and other unmeasured confounders. We all agree that with classical dosing the measured effect is a function of the dose administered (i.e., the dose is the independent variable and the response the dependent variable). However, when the dose is titrated according to the measured effect, we believe that the response becomes the independent variable, and the titrated dose becomes the dependent variable. We would encourage authors to consider switching x–y axes of the dose–response curves to reflect this causal relationship when titration data are graphically displayed. No funding was received for this work. The authors declared no competing interests for this work.