Causal Inference
Identifying vaccine effectiveness in the test-negative design under an equi-confounding assumption Christopher Boyer* Christopher Boyer Kendrick Li
The test-negative design (TND) is often used to monitor the effectiveness of vaccines under real-world conditions. In a TND study, individuals who develop the same symptoms and seek care are tested for the infectious disease of interest and effectiveness is estimated by comparing the vaccination history of test-positive and test-negative controls. Traditional approaches have justified the TND under the assumption that either a) receipt of a test is a perfect proxy for unmeasured (binary) health-seeking behavior or b) vaccination is unconfounded conditional on measured covariates, both of which are likely to be violated in practice. Here, we return to original motivation for the TND and show that the design may alternatively be justified under a scale-invariant assumption that unmeasured confounder(s) act equivalently for test positive and test negative illnesses, i.e. odds ratio equi-confounding. We discuss the implications of this assumption for the design of TNDs. In addition to providing alternative justification for the conventional logistic regression estimator, we derive estimators for the marginal risk ratio based on outcome modeling and inverse probability weighting using the generalized propensity score. We also derive a doubly-robust estimator allowing for the use of more flexible machine learning models. We provide proofs of our results as well as simulations to examine the finite sample performance of our estimators and illustrate the consequences when our assumptions are violated.