The Drug Titration Paradox in the Presence of Intra-Individual Variation: Can we Estimate the True Concentration-Effect Relationship?

The drug titration paradox arises when higher drug concentrations are paradoxically associated with poorer efficacy outcomes, due to the titration of an individual's drug dose to achieve a desired effect. In cases with substantial intraindividual variability of the disease state, the drug titration paradox can also occur on the individual level (resulting in a higher dose when the individual has a worse disease state) and it has been suggested that it may not be possible to estimate the true exposure-response (ER) relationship in such situations. We simulated a titration study with strong intra-individual variability of disease state (causing the drug titration paradox at the individual level) and investigated the performance of four PKPD modelling methods in obtaining an unbiased estimate of the ER relationship. Strong bias in the estimated ER relationship was observed with two commonly used modelling methods: the model which only estimated inter-individual variability (IIV) and the model that included IIV and inter-occasion variability (IOV) on disease severity. In contrast, inclusion of stochastic differential equations (SDE) or accounting for the autocorrelation of the residual error between observations did yield successful estimation of the ER relationship without bias. The success of these methods can be understood from the principles of causal inference: confounding is avoided by controlling for the previous observations which drive the drug titration. Our results underline the importance of adequately characterizing intra-individual variability to avoid bias in PKPD modelling, especially for clinical areas where titration designs are common, such as analgesia.