Sebastiaan Goulooze1, Nelleke Snelder1
1LAP&P Consultants BV
Objectives Mediation analyses can provide strong support for biomarker development by demonstrating that a biomarker mediates a (large) part of the treatment effect on a clinical outcome [1]. Mediation analysis decomposes a total treatment effect into two parts: an indirect effect that is mediated by the mediator (i.e. biomarker) of interest, and a direct effect that is not mediated. We previously demonstrated the potential value for PK-PD modelling of using the traditional approach to mediation analysis, which estimates the indirect effect as the part of the treatment effect that is ‘explained away’ by implementing the mediator as a time-varying covariate in the PK-PD model [2]. Given the potential complexity of PK-PD models (which may violate assumptions in the traditional approach), the more advanced causal mediation analysis approach can be more appropriate in certain applications. Here, we will illustrate the concepts used in causal mediation analysis in a pharmacometrics context. Methods Causal mediation analysis uses counterfactual definitions from causal inference to formally define the direct and indirect effects [3]. These counterfactual definitions (defined below) can be seen as ‘what if’ questions and may be estimated through simulations [4]. M(a) is the value of mediator M with treatment a. Y(a, M(a)) is the expected value of the outcome Y and depends on the treatment a and the value of the mediator M. The causal effect definitions for the total effect (TE) of a 4 mg treatment is the difference between the counterfactual outcomes of ‘4 mg treatment’ versus ‘no treatment’: TE = Y(4 mg, M(4mg)) – Y(0 mg, M(0 mg)). The pure indirect effect (PIE) reflects the effect that the treatment would have if (potentially contrary to fact) its only effect would be to change the mediator and therefore: PIE = Y(0 mg, M(4 mg)) – Y(0 mg, M(0 mg)). While Y(0, M(4 mg)) can, by definition, not be observed in any particular subject, under certain assumption of non-confounding, it can be simulated to calculate PIE [4]. The level of mediation is defined as PIE/TE. The concepts were numerically illustrated with a PK-PD model for the mediator and the outcome. AUC = DOSE/CL, with typical CL of 10 L/h. M = 100 * exp(-0.001 * AUC). Y = EMAX * AUC/(AUC+EC50) – 0.01 * M, with Emax = 0.15 and EC50 = 300 ng*h/ml. In this specific example, Y is the log of the relative change from baseline of a continuous endpoint. From these equations, we can see drug treatment (driven by AUC) has a direct increasing effect on Y (via the Emax equation), as well as an indirect increasing effect (driven by the reduction in the mediator M). Using PK-PD models for the mediator and outcome, the counterfactual definitions were estimated through simulation for a typical subject (for a 4 mg and 8 mg dose). Results Using the model for the mediator, M(0 mg), M(4 mg) and M(8 mg) were calculated as 100, 67 and 45, respectively. For the 4 mg treatment, using these as input for the model for Y(a, M(a)), the TE and PIE on log(outcome) were calculated as 0.415 and 0.330, respectively, which translates to a proportion mediated of 79.4% for the 4 mg dose. For the 8 mg dose (due to saturation of direct effect characterized by Emax relationship, while the indirect effect increases proportionally with dose), the proportion mediated increases to 83.5%. Conclusions Here, we illustrated the concepts of causal mediation analysis with a simple example. However, a key strength of the causal mediation analysis approach is that its general definitions for direct and indirect effects and the simulation approach for their estimation are independent of the parametric structure of the PKPD model and thus widely applicable for the diverse models used in the PK-PD modelling community. The simulations used here to calculate the level of mediation for a typical subject, can be extended to population simulations to calculate the average level of mediation for a population and study design of interest (and confidence intervals when including model parameter uncertainty), or to investigate inter-individual differences in the level of mediation.
[1] Fleming et al. Ther Innov Regul Sci (2023) 57:109–120. [2] Goulooze et al. CPT Pharmacometrics Syst Pharmacol (2024) 13:1285-1288. [3] VanDerWeele et al. Annu Rev Public Health (2016) 37:17-32. [4] Imai et al. Psychol Method (2010) 15:309-334.
Reference: PAGE 33 (2025) Abstr 11450 [www.page-meeting.org/?abstract=11450]
Poster: Methodology - Estimation Methods