Objectives: Dose titration based on response seeks to optimize individual responses while minimizing the risk of side effects. However, this technique is not widely adopted in drug development due to the selection bias it creates, where responders tend to receive lower doses and non-responders tend to receive higher doses. This bias can sometimes obscure or even reverse the expected dose-response exposure-response (E-R) relationship, a phenomenon known as the "titration paradox” [1]. The objective of this work was to illustrate the effects of dose titration on E-R analysis for a binary endpoint and to examine factors that could help resolve the paradox.
Methods: A simple dose titration study was simulated: 200 patients treated for 24 weeks for a liver disease resulting in elevated alkaline phosphatase (ALP) levels at baseline, with no dropouts. Participants were randomly assigned to either the 50 mg or the 100 mg dose arm in a 1:1 ratio, and a 2-fold increase in dose was permitted at 12 weeks if a participant had an ALP > 1.67×upper limit of normal (ULN). At 24 weeks, the relationship between drug exposure and a binary efficacy endpoint of ALP (BALP) was evaluated: whether a patient achieved ALP ≤ 1.67×ULN or not. Baseline ALP, steady-state drug exposure, and the intrinsic half-maximal effective exposure (EC50) for percent change in ALP were simulated to follow a lognormal distribution across subjects, while maximal percent decrease in ALP (Emax) was assumed to follow a normal distribution. Responses in terms of absolute ALP, change from baseline ALP, and the BALP endpoint were derived from the simulated percent change in ALP values, modeled as: E0 + Emax * exposure / (EC50 + exposure) + random error
Results: The simulations demonstrated the titration paradox, where the E-R relationship for BALP in a logistic model unexpectedly reversed at week 24. Adding a titration flag as an interaction term to drug exposure in the logistic model allowed for dynamic E-R relationships in subgroups of patients with and without up-titration. Results showed that the titration flag helped resolve the paradox in patients without up-titration, as higher drug exposure increased the probability of achieving BALP. The positive E-R relationship became less significant with increasing random dropouts. The titration paradox was also observed in the E-R relationship of continuous absolute ALP but not continuous change from baseline ALP.
Conclusions: The simulations suggest that continuous response measured as change from baseline is a better endpoint than the absolute response or the binary form because it is less susceptible to the titration paradox, and that a titration flag could help unveil the true E-R relationship in the subgroup of patients without dose titration.
Citations: [1] Schnider T W et al. (2021). The drug titration paradox: correlation of more drug with less effect in clinical data. Clinical Pharmacol. Ther. 110(2), 401-408.
