Neva Coello1, Manuela Zimmermann1, Guenter Heimann1, Siyan Xu2, Christian Bartels1
1Novartis Pharma AG, 2Novartis Pharmaceuticals
Objective We aim at enhancing the strength of claims that can be made based on pharmacometric analyses by relating them to the estimand framework and causal Inference. The ICH E9 (R1) guidance [1] and the related estimand framework [2] propose to clearly define and separate the clinical question of interest formulated as estimand from the estimation method. With that it becomes important to assess the validity of the estimation method and the assumptions that must be made. When going beyond intention to treat analyses that can rely on randomization, causal inference [3] is usually used to discuss the validity of estimation methods for the estimand of interest. The handling of inter-current events is of particular importance, since these events that occur post-randomization may affect the estimand of interest and consequently the estimation approach. In pharmacometrics, mixed effects models are routinely used to analyze longitudinal clinical trial data. Pharmacometrics modelling is lacking a formal framework to discuss assumptions, and it is rarely discussed as method for causal inference. Methods Here, we position non-linear mixed effects modeling and simulation (NLME M&S) in the context of causal inference as standardization method for longitudinal data in presence of confounders [4-7]. Standardization is a well-known method in causal inference to correct for confounding by analyzing and combining results from groups of similar patients. Having established this, we are evaluating the potential and limitations of NLME M&S to correct for confounding based on analyses of simulated clinical trial data. The focus is on studies in which intercurrent events related to either efficacy or tolerability may lead to deviations from the assigned treatment schedule, and on hypothetical estimands of the efficacy at the end of the trial assuming adherence to a given treatment regimen. Results We derive that NLME modeling is a particular implementation of standardization that conditions on individual parameters described by the random effects of the mixed effects model. To show this, we use a trial with within-subject dose titration. Being interested in the outcome for the hypothetical situation that patients adhere to the planned treatment schedule, we put assumptions in a causal diagram. From the causal diagram, conditional independence assumptions are derived either adjusting on the individual parameters or on earlier outcomes. With either of the conditional independency assumptions fulfilled, unbiased estimates can be obtained. Based on the analyses of simulated clinical trials data, we found that if the PK and PD of a drug are well understood and the clinical studies provide rich PK and PD data, NLME M&S is reliable, even with unobserved confounders affecting both the outcome and the dosing. For the more common situation that PK is well understood and supported by data, but only limited data or knowledge is available for the PD, we show that NLME M&S may provide reliable estimates in some situations but fails in others. Conclusions The estimand framework may be used to express the objective of pharmacometric analyses to clearly define and separate the clinical question of interest formulated as estimand from the estimation method. Causal inference is then used to discuss the validity of pharmacometric NLME estimation methods for the estimand of interest. Having positioned pharmacometric analyses as an implementation of standardization for causal inference will enable pharmacometricians and statisticians to compare and select the appropriate analysis method based on the clinical question of interest and on the available data rather than on perceived differences. Evaluating the potential and limitations of NLME M&S to correct for confounding based on analyses of simulated clinical trial data confirmed that NLME M&S provides reliable estimates in many situations but may fail sometimes.
[1] ICH E9 (R1): addendum on estimands and sensitivity analysis in clinical trials to the guideline on statistical principles for clinical trials. EMA/CHMP/ICH/436221/2017. https://www.ich.org; (2020). [2] Akacha M, et al. Estimands—What they are and why they are important for pharmacometricians. CPT: pharmacometrics & systems pharmacology 10 279. (2021) [3] Hernan MA, Robins J. Causal inference: What if. boca raton: Chapman & hill/crc. (2020) [4] Sheiner LB, Beal SL, Sambol NC. Study designs for dose-ranging. Clinical Pharmacology & Therapeutics 46 63-77. (1989) [5] Rogers JA, Maas H, Pitarch AP. An introduction to causal inference for pharmacometricians. CPT: Pharmacometrics & Systems Pharmacology 12 27-40. (2023) [6] Bartels C, Scauda M, Coello N, Dumortier T, Bornkamp B, Moffa G. Non-linear mixed effects modeling as method for causal inference to predict exposures under desired within-subject dose titration schemes. CPT: Pharmacometrics & Systems Pharmacology 14 68-81. (2025) https://ascpt.onlinelibrary.wiley.com/doi/full/10.1002/psp4.13239 [7] Zimmermann M, Dumortier T, Coello N, and Bartels C. NLME modelling from a causal inference perspective when the dose-exposure-response relationship is confounded by the treatment regimen. PAGE 32 Abstr 10906 [www.page-meeting.org/?abstract=10906] (2024)
Reference: PAGE 33 (2025) Abstr 11379 [www.page-meeting.org/?abstract=11379]
Poster: Methodology - New Modelling Approaches