Vaccine randomized trials are typically designed to be blinded, ensuring that the estimated vaccine efficacy (VE) reflects the immunological effect of the vaccine. When blinding is broken, however, the estimated VE reflects not only the immunological effect but also behavioral effects stemming from participants' awareness of their treatment status. Recent work has proposed alternative causal estimands to the standard VE to address this issue, but their point identification results require a strong assumption: the absence of unmeasured common causes of infection risk and participants' belief about whether they received the vaccine. Personality traits, for example, may plausibly violate this assumption. We relax this assumption and derive nonparametric causal bounds for different types of VE. We construct these bounds using two approaches: linear programming-based and monotonicity-based methods. We further consider several possible causal structures for vaccine trials and show how the nonparametric bounds differ across these scenarios. Finally, we illustrate the performance of the proposed bounds using fully synthetic data and a semi-synthetic data example based on a COVID-19 vaccine trial.

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