Daniel Wojtyniak1,2, Jinju Guk2, Sebastian Wicha1
1Dept. of Clinical Pharmacy, Institute of Pharmacy, University Hamburg, 2TMCP Clinical Pharmacy, Boehringer Ingelheim Pharma GmbH & Co.KG
Introduction: Exposure-response (ER) modelling is a crucial step in clinical drug development. Model misspecifications can inflate type I error (T1) for ER models. Individual model averaging (IMA) was proposed to control T1 in treatment-response scenarios [1]. Yet, IMA has a technical limitation to be applied to ER analysis as here the drug effect is directly linked to the exposure. IMA utilizes mixture models to assign placebo and treatment patients to either a zero-drug effect- or a drug effect- sub model. As placebo patients lack exposure completely, the two sub models would be identical for them, therefore IMA is not applicable to ER models. Objectives: The aim of this study was therefore to adapt the concept of the IMA method to leverage mixture models and assess significance through arm allocation, and develop a method applicable to ER data. The here developed method was compared regarding the T1 rate, power, predictive performance as well as precision and accuracy for the estimated ER parameter against the standard approach (STA). Methods: Parameter significance test using mixture models (PaSTUM) is presented and elaborated in this study. This method assesses the significance of a parameter of interest by imputing it randomly in a reference group (if missing). Therefore, to test the ER relationship, the exposure is randomly sampled for the placebo patients. Afterwards, a base model (BM) and a full model (FM), similar as in the original IMA method, was built using the mixture modeling technique [1]. A simulation study of a hypothetical drug in development effecting fasting plasma glucose (FPG) given every 8 hours via infusion was performed. The treatment arm consisted of either two or three different dose groups. The placebo arm was of equal size. Simulations with either 3, 10, 30, or 100 patients per dose group were performed (16 in total). To evaluate different structural models, direct relationships (linear, loglinear, emax), and an indirect relationship (turnover with emax effect on Kout) were examined, giving 64 scenarios in total. A stochastic simulation and re-estimation analysis was performed by simulating 1000 datasets per scenario utilizing NONMEM version 7.5.0. Individual area under the concentration-time curve (AUC) values were used as exposure metric in turn for the ER analysis. Effect on FPG was the response. To investigate the T1 rate, the arm allocation was randomly permutated, while the treatment arm AUC values were sampled with replacement. For the power investigation, no permutation was performed and only the placebo arm was imputed with AUC values, while the treatment arm remained unchanged. The corresponding FM and BM for the STA as well as for PaSTUM were compared via the likelihood ratio test with degrees of freedom equal to the number of drug effect parameter for STA and one for PaSTUM, as the only difference between BM and FM is one parameter [1]. To validate the predictive performance, the relative root mean squared error (rRMSE) as well as relative bias (rBias) for predicted vs. observed FPG was calculated (power setting). Precision and accuracy of drug effect parameter (power setting) were assessed by comparing the mean as well as the 95% confidence interval to the STA FM predictions in the setting with the most patients. Results: Overall PaSTUM showed substantially lower T1 rates than STA. In scenarios with low number of patients or worse predictive performance, PaSTUM T1 rates inflated as well but not nearly as much as STA (T1 > 6.54%: 16vs.64, for PaSTUM vs. STA). The statistical power was marginally better for STA but PaSTUM power was above 80% in all scenarios. Overall, the predicted vs. observed FPG values were often more precisely described (rRMSE PaSTUM < STA 59/64) and less biased (|rBias| PaSTUM < STA 63/64) predicted with PaSTUM – than with STA models. The precision and accuracy of the ER model parameter estimates were inconsistent for different scenarios. EMAX model parameter were often imprecise for small study sizes, while for the linear and loglinear structural models BM and FM PaSTUM as well as FM STA performed well even for small study sizes. Conclusion: PaSTUM was able to handle model misspecification in ER analysis and provided substantially lower and well controlled T1 rates compared to STA. PaSTUM produces similarly precise and accurate parameter estimates and guarantees reasonable statistical power and better predictive performance compared to STA. Application of PaSTUM in clinical datasets is warranted.
1. Chasseloup E, Tessier A, Karlsson MO. Assessing Treatment Effects with Pharmacometric Models: A New Method that Addresses Problems with Standard Assessments. AAPS J. 2021;23:63.
Reference: PAGE 33 (2025) Abstr 11752 [www.page-meeting.org/?abstract=11752]
Poster: Methodology - New Modelling Approaches