Inference on Controlled Effects for Assessing Immune Correlates of Protection Based on a Cox Model

In vaccine research, it is important to identify biomarkers that can reliably predict vaccine efficacy against a clinical endpoint. Such biomarkers are known as immune correlates of protection (CoP) and can serve as surrogate endpoints in vaccine efficacy trials to accelerate the approval process. CoPs must be rigorously validated, and one method of doing so is through the controlled risk (CR) curve, a function that represents the causal effect of the biomarker on population-level risk of experiencing the endpoint of interest by a certain time post-vaccination. The CR curve can be estimated by leveraging a Cox proportional hazards model, but researchers currently rely on the bootstrap for inference, which can be computationally demanding. In this article, we analytically derive the asymptotic variance of this estimator, providing an analytic approach for constructing both pointwise and uniform confidence bands. We evaluate the finite sample performance of these methods in a simulation study and illustrate their use on data from the Coronavirus Efficacy (COVE) placebo-controlled phase 3 trial (NCT04470427) of the mRNA-1273 COVID-19 vaccine.