Manuela Zimmermann, Thomas Dumortier, Neva Coello, and Christian Bartels
Novartis Pharma AG, Basel, Switzerland
Introduction: When a clinical trial is designed to investigate the effects of a treatment regimen rather than of specific dose levels, dose up-titrations for response optimization can be allowed per protocol. However, such a treatment regimen in which the decision for dose up-titration is based on earlier response might introduce a confounding bias when linking dose to exposure and/or exposure to response. This is a form of survivorship bias because only those subjects who did not respond (sufficiently) at the lower dose level get exposed to higher doses. In this case, the inferred estimate of the dose-exposure-response (D-E-R) relationship can be biased without additional assumptions and appropriate estimation methods. While there are a few publications investigating whether such confounding resulting from the treatment regimen leads to biased estimates of the D-E(-R) relationship using linear mixed effects models, we are not aware of any existing literature which investigates non-linear mixed effects (NLME) models in this scenario. However, NLME modelling is the most common technique to integrate longitudinal dose, exposure, and response data acquired in a clinical trial in a single analysis. Since such models are often used to simulate and compare potential outcomes of a population of interest under different treatment regimens, it is important to ensure that the estimated D-E(-R) relationship is indeed causal and not just associational.
Objectives:
- To illustrate why trials designed to investigate the effects of a treatment regimen with dose up-titrations for response optimization can confound the D-E-R relationship analyzed with NLME models and might lead to biased estimates of this relationship.
- To determine whether the D-E-R relationship is theoretically identifiable based on a simple but realistic causal diagram that describes a data-generating process for such a trial, i.e., to infer whether unbiased estimates of the D-E-R relationship can be obtained theoretically using NLME modelling.
- To explore via simulations, given the theoretically identifiable D-E-R relationship, whether unbiased NLME model estimates are also practically identifiable based on a limited sample size.
Methods: In collaboration with clinical, pharmacological, and statistical experts, we developed a simple but realistic causal diagram (directed acyclic graph) to describe the interrelation between dose, exposure, and response in a clinical trial investigating a treatment regimen with dose up-titrations for response optimization. Our estimand [1] is the probability of response at selected time points under a different treatment regimen than the one administered to the subjects during the trial. Using concepts from the Causal Inference literature [2], we then determined whether this estimand of interest is theoretically identifiable [3]. Finally, we performed simulations to assess the practical identifiability of the estimand of interest from a realistic sample size (ca. 100 patients).
Results: We have shown that an unbiased estimate of the estimand of interest can be obtained, under certain assumptions, using NLME modeling even when the data are confounded by a response-treatment feedforward. The key is to condition on individual random effects and the relevant patient characteristics to close the confounding path between late and early exposure/response. As such, NLME modeling can be interpreted as an implementation of a common approach in the Causal Inference literature (standardization).
Conclusion: As an implementation standardization, NLME modelling can be used, under certain assumptions, to correct for confounding in longitudinal experiments with dose up-titrations for clinical response optimization.
[1] European Medicines Agency, ICH E9 (R1) addendum on estimands and sensitivity analysis in clinical trials to the guideline on statistical principles for clinical trials, 2020. https://www.ema.europa.eu/en/documents/scientific-guideline/ich-e9-r1-addendum-estimands-sensitivity-analysis-clinical-trials-guideline-statistical-principles_en.pdf. [2] Hernán MA, Robins JM (2020). Causal Inference: What If. Boca Raton: Chapman & Hall/CRC. [3] Bartels C et al., Correcting for confounding in longitudinal experiments: positioning non-linear mixed effects modeling as implementation of standardization using latent conditional exchangeability, manuscript in preparation, 2024.
Reference: PAGE 32 (2024) Abstr 10906 [www.page-meeting.org/?abstract=10906]
Poster: Methodology - New Modelling Approaches