Establishing dose-response relationships with observational data is challenging due to confounding covariates and selection bias, particularly when the bias causes marginal distributions of confounding covariates to differ between the sample and the target population. In this scenario, standard causal analysis approaches like g-formula are not applicable without further modeling of the dose-response relationship. To address this limitation, we extend the log-linear structure mean model for binary treatments into a Covariate Adjusted Logit Model (CALM) for continuous treatments, introducing a new causal estimand that measures relative dose-response relationship. Based on one interpretation of vaccine effectiveness, the relative dose response curve can be described as a function that reduces susceptibility to disease, making the adjustment for confounding covariates equivalent to revealing latent susceptibility status. Accordingly, we leverage a Gibbs sampler called the All-or-Nothing (AoN) algorithm for Bayesian and non-parametric estimation of the relative response curve, providing new options beyond regular causal techniques, such as those based on generalized propensity scores. In the context of vaccine effectiveness (VE) clinical trials, CALM addresses the issue of confounding covariates that affect dose-response relationships differently in placebo and vaccine arms. While deriving a common absolute dose-response curve for both arms to evaluate VE is generally infeasible, our model provides a common relative dose-response curve for this purpose. Simulation studies confirm that CALM outperforms alternative methods in scenarios with confounding factors, making it a valuable tool for future immunological response-based vaccine trials.

The authors have declared no competing interest.

This study did not receive any funding

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Ethics committee/IRB of Centers for Disease Control and Prevention gave ethical/approval for this work

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The code to simulate data is available upon request