# Efficient nonparametric inference on the effects of stochastic interventions under two-phase sampling, with applications to vaccine efficacy trials

arXiv: https://arxiv.org/abs/2003.13771 · HTML: https://mlsanity.com/paper/2003.13771/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2020.

## Built on by (most cited first, 3 of 3)

- [Application of targeted maximum likelihood estimation in public health and epidemiological studies: a systematic review](https://mlsanity.com/paper/2303.07329/) (2023)
- [Generalized Prediction-Powered Inference, with Application to Binary Classifier Evaluation](https://mlsanity.com/paper/2602.10332/) (2026)
- [Identifying and Estimating Causal Direct Effects Under Unmeasured Confounding](https://mlsanity.com/paper/2604.01501/) (2026)

## Abstract (arXiv)

The advent and subsequent widespread availability of preventive vaccines has altered the course of public health over the past century. Despite this success, effective vaccines to prevent many high-burden diseases, including HIV, have been slow to develop. Vaccine development can be aided by the identification of immune response markers that serve as effective surrogates for clinically significant infection or disease endpoints. However, measuring immune response marker activity is often costly, which has motivated the usage of two-phase sampling for immune response evaluation in clinical trials of preventive vaccines. In such trials, the measurement of immunological markers is performed on a subset of trial participants, where enrollment in this second phase is potentially contingent on the observed study outcome and other participant-level information. We propose nonparametric methodology for efficiently estimating a counterfactual parameter that quantifies the impact of a given immune response marker on the subsequent probability of infection. Along the way, we fill in theoretical gaps pertaining to the asymptotic behavior of nonparametric efficient estimators in the context of two-phase sampling, including a multiple robustness property enjoyed by our estimators. Techniques for constructing confidence intervals and hypothesis tests are presented, and an open source software implementation of the methodology, the txshift R package, is introduced. We illustrate the proposed techniques using data from a recent preventive HIV vaccine efficacy trial.