Performing causal inferences with pharmacometrics models – How to bridge the gap?
Manuela Zimmermann1, Andrew C. Hooker2, Christian Bartels1, Neva Coello1, Siyan Xu3, Francois Mercier4, Mats Karlsson2, Thomas Dumortier1
1Novartis Pharma AG, 2Uppsala University, 3Novartis Pharmaceuticals Corporation, 4F. Hoffmann-La Roche AG
Introduction: The value proposition of pharmacometrics entails integrating longitudinal data, alongside prior knowledge, in a mathematical model to answer causal questions about the dose-response relationship. However, it is not guaranteed that such a model can indeed be interpreted causally, even when the data that it was built on stem from a randomized control trial. This is because even in a randomized study, confounding pathways might be open post randomization, e.g. when the dose is adjusted in response to a safety event. [1] In such situations, the presence of confounding paths can induce spurious associations in the data, in addition to the causal relationship of interest. As a result, the apparent dose-response relationship in the data might appear stronger, weaker, or even reversed compared to the causal dose-response relationship of interest. This poses the question of when a pharmacometrics model, which is precisely built to describe and predict the pharmacokinetics and pharmacodynamics over the entire time course of a study, can indeed be used to answer causal questions. Objectives: •Illustrate the importance of precisely defining the causal question of interest, by contrasting estimators for closely related but distinct causal estimands. [1] •Exemplify that confounders of the dose-response relationship are ubiquitous in datasets used for pharmacometrics modeling, making it non-trivial to infer causal estimands from such data. •Outline the key principles of a selection of causal inference techniques that a pharmacometrician can use to obtain unbiased estimates of the dose-(exposure-)response relationship even when there are confounders in the modeling data. •Prompt and foster discussions on causality within the pharmacometrics community. Methods: We utilize the estimands and potential outcomes framework to precisely define causal questions of interest about the dose-response relationship, i.e. causal estimands. [1,2] To derive valid estimators for these estimands, we employ causal graphs to visualize and discuss assumptions about the processes that generated the data available for fitting a pharmacometrics model. Depending on the estimand and assumptions about the data-generating process, we apply different causal inference techniques to identify the causal estimands. [2,3] Additionally, we conduct simulations to practically demonstrate our theoretical discussion and conclusions. Results: We illustrate, through simplistic examples, that the causal validity of an estimator of a dose-response relationship depends on the assumptions about the data-generating process as well as the chosen estimand. For more realistic scenarios, which we see recurring in clinical development, we showcase how confounders can pose a challenge for pharmacometrics analyses. We sketch several methods that pharmacometricians can use to obtain unbiased estimates of the dose-response relationship even when there are confounders in the modeling data. However, there remain many scenarios of interest for which there are currently no valid estimators available. Conclusions: Pharmacometricians routinely use models to address causal questions about the dose-response relationship but seldom conduct formal causal inferences. Establishing the causal validity of predictions from pharmacometrics models can increase the value and impact of these analyses. Additionally, recognizing when associations and causation cannot be distinguished helps in preventing misinterpretation of potentially biased results. We present initial efforts to integrate pharmacometrics approaches with causal inference methods. However, many questions remain on how and when causal inferences regarding the dose-response relationship can be inferred from clinical data. These questions are the focus of work within the EU-funded INVENTS project. [4]