Nonparametric bounds for vaccine effects in randomized trials

TL;DR

This work derives nonparametric causal bounds for different types of VE using linear programming-based and monotonicity-based methods and considers several possible causal structures for vaccine trials and shows how the nonparametric bounds differ across these scenarios.

Abstract

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.

Figures (13)

• Figure 1: DAGs describing six-arm trial $\mathcal{T}_{VI}$. In these trials, the VEs are identifiable.
• Figure 2: A DAG describing a six-arm trial $\mathcal{T}_{VI}$. In this trial the VEs are not identifiable because Assumption \ref{['assump:y.dismissible']} is violated due to the dashed arrow.
• Figure 3: DAGs describing six-arm trials $\mathcal{T}_{VI}$. In these trials the VEs are not identifiable because Assumptions \ref{['assump:y.dismissible']} or \ref{['assump:y.s.dis']} are violated.
• Figure 4: The relationship between magnitude of broken blinding ($\beta_S$) and the width of the bounds for $VE(0)$, $VE(1)$ and $VE_T$ under the setting of Figure \ref{['fig:DAG_with_s_violation']}. Assumptions \ref{['assump:non.negative.m.general']}\ref{['assump:non.negative.m']} and \ref{['assump:U.mon.S.general.SU']} are satisfied. A value of $\beta_S=0$ corresponds to the case where the belief was not influenced by AEs, $\beta_S=\log(1.5)$ represented moderate, and $\beta_S=\log(2)$ strong, broken blinding due to AEs. Circles represent the true values. LP: bounds constructed via Proposition \ref{['prop:bounds.4ab.LP']} and the results in Appendix \ref{['app:sharp.LP.bounds']}; Monotonicity: bounds constructed via Proposition \ref{['prop:bounds.4ab.mon']}. Triangles at the lower boundary indicate bounds that extended below 0% but were truncated for display.
• Figure 5: Monotonicity-based bounds for $\mathrm{VE}(0)$, $\mathrm{VE}(1)$, and $\mathrm{VE}_T$ for $\gamma_U \in \{-\log(2),\log(2)\}$ and across values of $\beta_U$ when Assumption \ref{['assump:U.mon.S.general']} is violated and Assumption \ref{['assump:non.negative.m.general']} is maintained. The parameters $\beta_U$ and $\gamma_U$ controlled the monotone relationships between $U$ and $B$ or $Y$, respectively: setting either to zero enforced monotonicity by removing the corresponding non-linear effect of $U$, while increasing their magnitude strengthened violations of the assumption. Circles indicate the true values. The monotonicity-based bounds were calculated using Proposition \ref{['prop:bounds.4ab.mon']}. Triangles at the lower boundary indicate bounds that extended below 0% but were truncated for display.

Theorems & Definitions (22)

• Proposition 1
• Proposition 2
• Proposition 3
• Proposition 4
• Proposition 5
• Proposition 6
• Proposition 7
• Proposition 8
• Proposition 9
• Proposition 10