Manuela Zimmermann 1, Thomas Dumortier 1
1 Novartis Pharma AG (Basel, Switzerland)
Introduction:
In pharmacometrics, it is often (implicitly) assumed that the exposure-response relationship in a dose randomized study is unconfounded, at least after adjusting for measured covariates. However, a growing body of examples in the literature illustrates that this unconfoundedness assumption might not be plausible in some practically relevant settings. [1,2] This is because exposure is a post-randomization variable that may be influenced alongside the response by potentially unmeasured factors.
In population modelling, between-patient variability in exposure and response is explained via individual PK and PD parameters. [3] A confounder of the exposure-response relationship may therefore exert its effects via at least one individual PK and at least one individual PD parameter. This induces a correlation between these parameters. However, in many popPKPD models, the variance-covariance matrix of the random effects (Ω) is chosen to be (block-)diagonal, either explicitly or implicitly, e.g. through certain sequential modelling approaches. [4] Karlsson et al. [5] have recently illustrated this shortcoming, but a systematic investigation of the potential cost of this very common popPKPD modelling choice is currently lacking.
Objectives:
To investigate whether incorporating a full (unstructured) Ω in a popPKPD modelling approach can i) help diagnose and ii) partially mitigate bias in the model-based estimation of the average causal dose–response relationship when the exposure–response relationship is confounded by an unmeasured time-invariant covariate.
Methods:
A simulation re-estimation experiment was conducted under a one-compartmental IV bolus PK model coupled to an Emax PD model. The assignment to one of two dose levels was randomized. A latent, time-invariant confounder was implemented via a correlation between the PK parameter clearance and PD parameter Emax. In the estimation step, the simulated dense PK and PD data following single dose administration were fitted with the following modelling approaches, each based on the IV bolus and Emax models used to generate the data: i) A joint popPKPD model with a full Ω, ii) a joint but decoupled popPKPD model with block-diagonal Ω, iii) a PPP&D approach in which the PK population parameters were fixed to their estimated values based on a proceeding PK fit, with fitting either a full Ω or iv) a block-diagonal Ω, and v) an IPP approach based on a sequential popPKPD model in which the estimated individual PK parameters were used as regressors in the PD fit. [4] The estimands of interest were the mean causal effects of selected doses on response at a pre-defined time point in the same population. Model-based estimates were obtained via Monte Carlo simulations (Monolix Suite).
Results:
In the described setting of a time-invariant confounder, enforcing that Ω has separate blocks for the PK and PD model parameters misrepresents the data-generating process. Therefore, [6] modelling approaches implementing a block-diagonal Ω are expected to yield biased estimates of the causal dose-response relationship in these settings. We illustrated this concept in a simple simulation re-estimation experiment in which the modelling approaches with a full Ω where practically unbiased in the tested dose range, as measured by the bias contribution to the mean squared error. In contrast, the modelling approaches enforcing a block-diagonal Ω yielded increasingly biased results with increasing extents of confounding.
In our simulations, the inferred off-diagonal elements of Ω contained information about the possible presence and approximate strength of the investigated type of confounding. However, with increasing confounding strengths, the extend of confounding was increasingly underestimated, despite the models still being correctly specified. This was attributed to the fact that the true Ω was approaching a boundary (near-singular Ω), which can render the estimation ill-conditioned in these settings.
Conclusions:
Exposure–response associations can be confounded even in dose-randomized studies. We illustrated that allowing the Ω of a popPKPD model to be unstructured (full) can serve two purposes: i) as a diagnostic, by revealing potential non-negligible PK–PD random effects dependences suggestive of unmeasured confounding, and ii) as a partial mitigation strategy at least for certain types of confounding of the dose-response relationship. Therefore, we recommend to routinely incorporate a full Ω in popPKPD modelling approaches where feasible, at least as a sensitivity analysis. Furthermore, benchmarking model-based causal estimates against complementary causal methods (e.g., instrumental-variable and nonparametric g-formula approaches [6]) can provide valuable insights on the potential presence of confounders of the exposure-response relationship.
References:
References:
[1] Proctor, J. R. and Wong, H. (2023). Time‐dependent clearance can confound exposure–response analysis of therapeutic antibodies: A comprehensive review of the current literature. Clinical and Translational Science 17. doi:10.1111/cts.13676.
[2] Turner, D. C., Kondic, A. G., Anderson, K. M., Robinson, A. G., Garon, E. B., Riess, J. W., Jain, L., Mayawala, K., Kang, J., Ebbinghaus, S. W., et al. (2018). Pembrolizumab Exposure–Response Assessments Challenged by Association of Cancer Cachexia and Catabolic Clearance. Clinical Cancer Research 24, 5841–5849.
[3] Mould, D. and Upton, R. (2012). Basic Concepts in Population Modeling, Simulation, and Model‐Based Drug Development. CPT: Pharmacometrics & Systems Pharmacology 1, 1–14.
[4] Zhang, L., Beal, S. L. and Sheiner, L. B. (2003). Simultaneous vs. Sequential Analysis for Population PK/PD Data I: Best-Case Performance. Journal of Pharmacokinetics and Pharmacodynamics 30, 387–404.
[5] Karlsson, M. O. and Brundavanam, D. (2025). Addressing Causality and Homogeneity Assumptions in Exposure‐Response Analyses. Clinical Pharmacology & Therapeutics 119, 703–712.
[6] Hernán MA, Robins JM (2020). Causal Inference: What If. Boca Raton: Chapman & Hall/CRC
Reference: PAGE 34 (2026) Abstr 12033 [www.page-meeting.org/?abstract=12033]
Poster: Methodology - Other topics