Abstract
In randomized trials, the primary analysis often estimates the average treatment effect on a clinical endpoint. Some treatments also lead to early changes in a biomarker that is prognostic for the clinical endpoint, prompting investigators to explore how these acute biomarker changes might inform the treatment's effect on long-term clinical outcomes. A naive analysis that directly examines treatment-by-biomarker-change interactions may lead to biased estimates because it fails to account for the fact that biomarker changes are influenced by the treatment and post-randomization factors. A key statistical challenge is that we do not know whether the observed biomarker change in an individual patient truly reflects a treatment-induced effect or whether the change would have occurred under placebo as well. This uncertainty makes it difficult to disentangle the causal effect of the treatment from natural biomarker variability. We apply principal stratification with a normal copula governed by the correlation [Formula: see text] between the potential acute biomarker changes under treatment and placebo. A flexible model for the conditional distribution of the clinical endpoint given the biomarker change enables estimation of the conditional average treatment effect on the clinical endpoint, given the acute biomarker change under treatment, as a function of [Formula: see text]. We illustrate the method by determining how knowledge of acute change in estimated glomerular filtration rate modifies the expected effect of sodium-glucose cotransporter-2 inhibitors (SGLT-2i) on clinical endpoints in patients with chronic kidney disease.