The Drug Titration Paradox: Correlation of More Drug With Less Effect in Clinical Data

Abstract

While analyzing clinical data where an anesthetic was titrated based on an objective measure of drug effect, we observed paradoxically that greater effect was associated with lesser dose. With this study we sought to find a mathematical explanation for this negative correlation between dose and effect, to confirm its existence with additional clinical data, and to explore it further with Monte Carlo simulations. Automatically recorded dosing and effect data from more than 9,000 patients was available for the analysis. The anesthetics propofol and sevoflurane and the catecholamine norepinephrine were titrated to defined effect targets, i.e., the processed electroencephalogram (Bispectral Index, BIS) and the blood pressure. A proportional control titration algorithm was developed for the simulations. We prove by deduction that the average dose–effect relationship during titration to the targeted effect will associate lower doses with greater effects. The finding of negative correlations between propofol and BIS, sevoflurane and BIS, and norepinephrine and mean arterial pressure confirmed the titration paradox. Monte Carlo simulations revealed two additional factors that contribute to the paradox. During stepwise titration toward a target effect, the slope of the dose–effect data for the population will be “reversed,” i.e., the correlation between dose and effect will not be positive, but will be negative, and will be “horizontal” when the titration is “perfect.” The titration paradox must be considered whenever data from clinical titration (flexible dose) studies are interpreted. Such data should not be used naively for the development of dosing guidelines.