Some Common Dose–Exposure–Response Estimands and Conditions for Their Causal Identifiability

Exposure-response analyses are central to dose selection in drug development. The estimand framework, formalized in ICH E9(R1) regulatory guidance, provides a structured approach to define scientific objectives with precision. We apply the estimand framework to dose-exposure-response analyses. For simulated example studies inspired by real-world scenarios, we define dose-response estimands of clinical interest. The estimands are formalized using the potential outcome notation. Assumptions on the setup of the studies and the relation between treatment, exposure and response are expressed as a directed acyclic graph (DAG). The estimand is transformed using the assumption into expressions to identify the estimand based on the observed data. Three types of expressions are obtained. First, a pooled dose-exposure-response (DER) analysis that corresponds to a standard DER analysis as executed for many projects. Second, a pooled, covariate adjusted dose-response (DR) analysis, and third summaries of the outcomes in each randomized cohort. In our example, DER provides more precise estimates than DR as judged by the mean square error (MSE) of repeated simulation estimation. This work advances methodological rigor in DER analyses by integrating with causal inference methodologies and the estimand framework, enabling clearer interpretation of modeling assumptions and results. This has important concrete advantages. We obtain different estimation methods for the same estimand that may be compared to validate them. The potential for bias in the different estimation methods can be formally assessed. The proposed approach provides a generalizable strategy to improve exposure-response analyses for dose selection, particularly when the relevant evidence includes data from multiple studies.