Zhe Huang 1, Guibi Yu 1, Skanda Narayanaswamy 1, Mats . O. Karlsson 1
1 Uppsala University (Uppsala, Sweden)
Objectives
Causality and homogeneity in exposure–response (E-R) analyses can be assessed by the partitioned effects (PE) model, based on an instrumental variable (IV) framework [1]. Homogeneity being a single E-R relation regardless of reason for variation in exposure. In the PE model, randomized dose serves as the IV for exposure, enabling causal interpretation under the key exclusion restriction assumption that dose affects response only through exposure.
In this moxonidine case study, we applied the PE model to decompose the E–R relationship into dose, covariate (COV), and random effects (RE) components, quantifying their contributions to response variability. To assess the validity of the exclusion restriction assumption and add mechanistic understanding, we conducted mediation analyses.
Methods
The moxonidine dataset originated from a Phase II study in patients with NYHA class II–III congestive heart failure who received placebo (n = 23) or twice-daily moxonidine at three randomized dose levels (0.1, 0.2, or 0.3 mg; n = 74). Repeated PK samples and PD measurements, including plasma noradrenaline (NA) and blood pressure (BP), were obtained over 8 hours after the first dose and steady-state doses. The published PKPD model [2,3] served as the reference for PE model comparison, with NA and BP reductions described by inhibitory Emax functions.
A PE model with three components—dose effect, covariate effect (COV), and random effects (RE)—was developed for the PK–BP relationship. To quantify contributions to BP, the pure typical concentration (PTC) represented the effect attributable to dose, the typical concentration (TC) minus PTC represented the effect attributable to COV, and the individual concentration (C) minus TC represented the effect attributable to RE.
To investigate the D–E–R relationship, a mediation framework was developed incorporating (i) a KPD model to characterize the direct dose effect on BP and (ii) a PK–BP model to describe the exposure-mediated indirect effect. An additional structure assuming NA as a mediator in the PK–BP pathway (PK-NA-BP) was also evaluated for mechanistic understanding and indirect support for the exclusion restriction assumption.
To quantify the proportion of the total effect mediated by exposure or NA, counterfactual decomposition [4] was employed to estimate the mediation proportion (MP). Model comparisons used likelihood ratio tests (LRTs) and Bayesian Information Criterion (BIC).
Results
The fit of the PE model was not significantly better than that of the PKPD model (p>0.05). Hence there is no evidence of deviation from homogeneity in the PKPD model. PD parameters were similar between the PE models causal (i.e., IV) relation (Slope 0.10±0.05; Emax 0.34±0.11) and the PKPD model (0.11±0.04; 0.33±0.10). The PD parameters of the COV and RE components of the PE model were similar, but estimated with higher imprecision as only 5.8% and 10.9% of the PK variability are attributed to these components.
In the D–E–R mediation analysis, the mediation model achieved the lowest BIC, outperforming the indirect-only (ΔBIC = +14) and direct-only models (ΔBIC = +30). The median MP was 98.9% (IQR: 98.5–99.3%), indicating near-complete mediation through exposure, although three individuals showed low MP values and were better described by the KPD model.
In the PK-NA-BP analysis, the median MP was 7% (IQR:3.2-20.5%) and 63 of 74 subjects had MP < 50%, indicating that most of the effect was driven directly by exposure. The direct-only model provided the lowest BIC, the indirect-only model was similar (ΔBIC = +0.47), the mediation model showed the highest BIC (ΔBIC = +7.5).
Conclusion
The performed analysis addressed standard assumptions made, but typically not assessed, in the course of an ER analysis. The results supported the original PKPD model as a valid representation also of the causal relation.
Acknowledgement
The work was performed with resources from the project INVENTS, which has received funding from the European Union’s Horizon Europe Research and Innovation programme under grant agreement 101136365.
References:
1. Karlsson MO, Brundavanam D. Addressing Causality and Homogeneity Assumptions in Exposure-Response Analyses. Clin Pharmacol Ther. 2026;119:703–12. https://doi.org/10.1002/cpt.70132
2. Karlsson MO, Jonsson EN, Wiltse CG, Wade JR. Assumption testing in population pharmacokinetic models: illustrated with an analysis of moxonidine data from congestive heart failure patients. J Pharmacokinet Biopharm. 1998;26:207–46. https://doi.org/10.1023/a:1020561807903
3. Brynne L, McNay JL, Schaefer HG, Swedberg K, Wiltse CG, Karlsson MO. Pharmacodynamic models for the cardiovascular effects of moxonidine in patients with congestive heart failure. Br J Clin Pharmacol. 2001;51:35–43. https://doi.org/10.1046/j.1365-2125.2001.01320.x
4. Goulooze SC, Marostica E, Snelder N. Tutorial on Causal Mediation Analysis for Pharmacometricians. CPT Pharmacomet Syst Pharmacol. 2026;15:e70193. https://doi.org/10.1002/psp4.70193
Reference: PAGE 34 (2026) Abstr 11906 [www.page-meeting.org/?abstract=11906]
Poster: Methodology - Model Evaluation