Impact of study design for characterising PKPD covariance and nonlinearity in exposure-dichotomous response relationships
Rocío Lledó-García, Stefanie Hennig, Mats O. Karlsson
Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
Objectives: Characterisation of exposure-response for therapies where the clinical endpoint is a bivariate outcome generally involves two assumptions: (i) the random effect determining the dose-exposure relation is not related to any parameter of the exposure-response relation, and (ii) the drug effect is linear on the logit scale[1-3]. This study aims at assessing the assumptions for randomised dose controlled trials (DCT) and concentration controlled trials (CCT) with a particular focus on drugs with narrow therapeutic index.
Methods: A simulation-based study was performed using NONMEM VI, considering a hypothetical immunosuppressant agent with rejection as main efficacy endpoint. The PK-model was described by a one-compartment model at steady state and the pharmacodynamic relationship with a logistic model. Different scenarios were simulated and analysed: three designs were compared, a DCT and two CCTs (a target equivalent (TCCT) and a variability equivalent (VCCT)). For each design two target levels (low and high dose (DCT) or exposure (CCT)) were considered. In the different scenarios, the exposure-response relationship was described by: a) linear logistic regression model with (-/+) covariance between clearance (CL) and the baseline or slope parameter (“PKPD covariance”); b) nonlinear exposure-response relationship described by a power function, with different grades of nonlinearity expressed by the power parameter value (2, 3, 4). In the latter case, the CCTs were targeting for 3 levels of exposure instead of two, due to the lack of information to estimate the power parameter in the relationship, otherwise.
Results: In regards to precision and bias in parameter estimates: DCT and VCCT were superior for a (+) and (-) PKPD covariance between CL and baseline, respectively. When the PKPD covariance existed between CL and slope, the VCCT design was the more precise regardless of the sign of the correlation. The VCCT and TCCT showed highest power to detect the correlation in all cases. To characterise a nonlinearity in exposure-response, DCT was more precise and less biased in the parameter estimates as well as showing higher power. However, the VCCT was almost as precise. To achieve a >90% power to detect either a PKPD covariance or nonlinearity, studies involving >500 patients would be required.
Conclusions: For drugs with narrow therapeutic index a VCCT or DCT design would be the most informative to describe the exposure-response relationship when there is a PKPD covariance in the parameters, whereas a DCT seems to be more informative when describing nonlinear relationships between exposure and response. However, it appears that typical studies of this type would not have enough power to reliably detect such relationships regardless of design.
 Hale, M.D., et al., The pharmacokinetic-pharmacodynamic relationship for mycophenolate mofetil in renal transplantation. Clin Pharmacol Ther, 1998. 64(6): p. 672-83.
 Yassen, A., et al., Pharmacokinetic-pharmacodynamic modeling of the effectiveness and safety of buprenorphine and fentanyl in rats. Pharm Res, 2008. 25(1): p. 183-93.
 Green, B. and S.B. Duffull, Development of a dosing strategy for enoxaparin in obese patients. Br J Clin Pharmacol, 2003. 56(1): p. 96-103.