In clinical trials randomizing participants to active vs. control conditions and following study units until the occurrence of a primary clinical endpoint, evaluating the efficacy of a quantitative exposure or mediator (e.g., drug dosage, drug- or vaccine-induced biomarker activity) is challenging. This is due, in part, to the fact that statistical innovations in causal inference have historically focused on defining interpretable estimands compatible only with categorical (or binary) treatments. We will introduce stochastic-interventional causal effects, which provide a measure of the effect attributable to perturbing a treatment’s natural (i.e., observed or induced) value, focusing primarily on how these effect definitions provide a scientifically informative solution when working with quantitative (continuous-valued) intervention variables. Unfortunately, the estimation of these, and other, estimands in treatment or vaccine efficacy clinical trials often requires significant additional care, for such trials measure immunologic biomarkers – critical to understanding the mechanisms by which vaccines confer protection or as surrogate endpoints in future clinical trials – via outcome-dependent two-phase sampling (e.g., case-cohort) designs. These biased sampling designs have earned their popularity: they circumvent the administrative burden of collecting potentially expensive biomarker measurements on all study units without limiting opportunities to detect biomarkers mechanistically informative of the disease or infection process. To address this, we outline a semiparametric correction procedure that recovers population-level estimates (in spite of two-phase sampling of the intervention variable), with guarantees of asymptotically efficient inference (i.e., minimal variance within a suitable regularity class), of a causally informed vaccine efficacy measure defined by contrasting assignments of study units to active vs. control conditions while simultaneously hypothetically shifting biomarker expression in the active condition. This results in a descriptive causal dose-response analysis informative of next-generation vaccine efficacy and useful for bridging vaccine efficacy from a source pathogen strain (e.g., SARS-CoV-2 at outbreak, i.e., D614G) to reasonably similar variants of concern (e.g., Delta). We present the results of applying this approach in an analysis of the joint U.S. Government and COVID-19 Prevention Network’s COVE COVID-19 vaccine efficacy clinical trial of Moderna’s two-dose mRNA-1273 vaccine.