{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T12:52:00Z","timestamp":1792068720352,"version":"4.4.0"},"reference-count":60,"publisher":"Wiley","issue":"10","license":[{"start":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T00:00:00Z","timestamp":1791504000000},"content-version":"vor","delay-in-days":8,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["ascpt.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["CPT Pharmacom &amp;amp; Syst Pharma"],"published-print":{"date-parts":[[2026,10]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Exposure\u2010response (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\u2010to\u2010event metrics are outcome\u2010dependent and can be causally incoherent; steady\u2010state metrics can introduce immortal\u2010time 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\u2010varying exposure metrics, as dose randomization protects against confounding only for the component of exposure variability driven by the assigned dose. On\u2010treatment clinical variables can affect both exposure and response, inducing time\u2010varying confounding that neither randomization, baseline adjustment, nor naive time\u2010varying 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\u2010response curve (ACERC) as the target estimand for ER analysis under time\u2010varying confounding. The parametric g\u2010formula is adapted to target this causal estimand and required assumptions are stated explicitly, including key consistency and no\u2010multiple\u2010versions\u2010of\u2010treatment (NMVT) assumptions, with implications for defining exposure metrics. Population pharmacokinetic (popPK) modeling serves an important role beyond computing exposure metrics, partially addressing the no\u2010measurement\u2010error assumption and enabling g\u2010formula implementation via existing software. Two oncology\u2010motivated simulation scenarios of dose\u2010mediated and PK\u2010mediated confounding illustrate the approach. A simulation study shows the g\u2010formula recovers causal ER estimates where standard methods are inaccurate under the specified time\u2010varying confounding. The two\u2010step workflow combining popPK modeling with existing g\u2010formula software is presented as a practical template for further development.<\/jats:p>","DOI":"10.1002\/psp4.70346","type":"journal-article","created":{"date-parts":[[2026,10,10]],"date-time":"2026-10-10T04:20:43Z","timestamp":1791606043000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Causal Exposure\u2010Response Analysis: Estimands, Time\u2010Varying Confounding, and the Parametric g\u2010Formula"],"prefix":"10.1002","volume":"15","author":[{"given":"Nathan","family":"Braniff","sequence":"first","affiliation":[{"name":"Pharmacometrics and Systems Pharmacology Pfizer Inc  San Diego California USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,10,9]]},"reference":[{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/psp4.12015"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10928-023-09850-2"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/psp4.70149"},{"key":"e_1_2_9_6_1","unstructured":"United States Food and Drug Administration \u201cGuidance for Industry: Exposure\u2010Response Relationships\u2014Study Design Data Analysis and Regulatory Applications \u201d 2003 https:\/\/www.fda.gov\/media\/71277\/download."},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.5686"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/cpt.70144"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/psp4.70119"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1111\/cts.13676"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/psp4.13280"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/psp4.13074"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.3389\/fphar.2024.1487062"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1002\/cpt.2564"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1002\/psp4.70253"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/0270-0255(86)90088-6"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1201\/9781420011579.ch23"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.5316"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1093\/ije\/dyp192"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12561-011-9040-7"},{"key":"e_1_2_9_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/0009-9236(95)90260-0"},{"key":"e_1_2_9_22_1","doi-asserted-by":"publisher","DOI":"10.1046\/j.1365-2125.2002.01628.x"},{"key":"e_1_2_9_23_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2542"},{"key":"e_1_2_9_24_1","doi-asserted-by":"publisher","DOI":"10.1201\/b18717-11"},{"key":"e_1_2_9_25_1","unstructured":"European Medicines Agency \u201cICH E9 (R1) Addendum on Estimands and Sensitivity Analysis in Clinical Trials to the Guideline on Statistical Principles for Clinical Trials \u201d(2020) https:\/\/www.ema.europa.eu\/en\/documents\/scientific\u2010guideline\/ich\u2010e9\u2010r1\u2010addendum\u2010estimands\u2010and\u2010sensitivity\u2010analysis\u2010clinical\u2010trials\u2010guideline\u2010statistical\u2010principles\u2010clinical\u2010trials\u2010step\u20105_en.pdf."},{"key":"e_1_2_9_26_1","doi-asserted-by":"publisher","DOI":"10.1002\/psp4.12617"},{"key":"e_1_2_9_27_1","unstructured":"Food and Drug Administration \u201cFramework for FDA's Real\u2010World Evidence Program \u201d2018 https:\/\/www.fda.gov\/media\/120060\/download."},{"key":"e_1_2_9_28_1","doi-asserted-by":"publisher","DOI":"10.1002\/psp4.12395"},{"key":"e_1_2_9_29_1","doi-asserted-by":"publisher","DOI":"10.1002\/psp4.12894"},{"key":"e_1_2_9_30_1","doi-asserted-by":"publisher","DOI":"10.1002\/psp4.13239"},{"key":"e_1_2_9_31_1","doi-asserted-by":"publisher","DOI":"10.1177\/09622802231212274"},{"key":"e_1_2_9_32_1","doi-asserted-by":"publisher","DOI":"10.1002\/cpt.70132"},{"key":"e_1_2_9_33_1","doi-asserted-by":"publisher","DOI":"10.1002\/psp4.70202"},{"key":"e_1_2_9_34_1","doi-asserted-by":"publisher","DOI":"10.1002\/psp4.70227"},{"key":"e_1_2_9_35_1","doi-asserted-by":"publisher","DOI":"10.1002\/psp4.13200"},{"key":"e_1_2_9_36_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12561-024-09426-9"},{"key":"e_1_2_9_37_1","doi-asserted-by":"publisher","DOI":"10.1002\/cpt.70436"},{"key":"e_1_2_9_38_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.10246"},{"key":"e_1_2_9_39_1","unstructured":"P. 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