Semiparametric logistic regression for inference on relative vaccine efficacy in case-only studies with informative missingness

Abstract: We develop semiparametric methods for estimating subgroup-specific relative vaccine efficacy against multiple viral strains in a partially vaccinated population. Focusing on observational case-only studies, we address informative missingness in strain type due to vaccination status, pre-vaccination characteristics, and post-infection factors such as viral load. We establish general conditions for the nonparametric identification of relative conditional vaccine efficacy between strains using covariate-adjusted conditional odds ratio parameters. Assuming a log-linear parametric form for strain-specific conditional vaccine efficacy, we propose targeted maximum likelihood estimators based on partially linear logistic regression, leveraging machine learning for flexible confounding adjustment. Finally, we apply our methods to estimate relative strain-specific conditional vaccine efficacy in the ENSEMBLE COVID-19 vaccine trial.