Causal Exposure-Response Analysis: Estimands, Time-Varying Confounding, and the Parametric g-Formula

Exposure-response (ER) analysis often informs dose selection in clinical drug development, but the underlying causal assumptions are rarely made explicit. Exposure metrics commonly used in practice can have limitations: time-to-event metrics are outcome-dependent and can be causally incoherent; steady-state metrics can introduce immortal-time bias; and early metrics, while defensible, require unstated assumptions about later exposure or must be interpreted narrowly. Beyond metric selection, challenges persist even with ideal early or time-varying exposure metrics, as dose randomization protects against confounding only for the component of exposure variability driven by the assigned dose. On-treatment clinical variables can affect both exposure and response, inducing time-varying confounding that neither randomization, baseline adjustment, nor naive time-varying covariate adjustment can address. In this work, a directed acyclic graph (DAG) is used to formalize the causal structure and define the average causal exposure-response curve (ACERC) as the target estimand for ER analysis under time-varying confounding. The parametric g-formula is adapted to target this causal estimand and required assumptions are stated explicitly, including key consistency and no-multiple-versions-of-treatment (NMVT) assumptions, with implications for defining exposure metrics. Population pharmacokinetic (popPK) modeling serves an important role beyond computing exposure metrics, partially addressing the no-measurement-error assumption and enabling g-formula implementation via existing software. Two oncology-motivated simulation scenarios of dose-mediated and PK-mediated confounding illustrate the approach. A simulation study shows the g-formula recovers causal ER estimates where standard methods are inaccurate under the specified time-varying confounding. The two-step workflow combining popPK modeling with existing g-formula software is presented as a practical template for further development.