Covariate Adjusted Logit Model (CALM) for Generating Dose-Response Curves from Observational Data with Applications to Vaccine Effectiveness Trials

Establishing dose-response relationships from observational data is challenging due to confounding and sample selection bias. Standard causal methods adjust for confounding but typically require knowledge of covariate distributions in the target population--often via a well-defined probability sampling scheme. We propose the Covariate Adjusted Logit Model (CALM), which generalizes log-linear structural mean models for binary exposures to continuous exposures by modeling a relative dose-response curve anchored to a baseline level. By separating this curve from the null disease risk (NDR) at baseline, CALM enables valid inference under biased sampling while adjusting for confounding effects. A Gibbs sampler--the All-or-Nothing algorithm--is introduced to support Bayesian modeling, drawing on a vaccine-effect-inspired interpretation of the relative dose-response curve. Simulation studies demonstrate that CALM recovers dose-response relationships more accurately in the presence of bias and confounding. In vaccine trials, where confounding covariates affect immune responses differently across study arms, CALM provides a more accurate and robust antibody-disease curve to serve as a surrogate for evaluating vaccine effectiveness.