Efficient nonparametric estimation of the covariate-adjusted threshold-response function, a support-restricted stochastic intervention

TL;DR

This paper introduces a nonparametric, efficient estimator for the covariate-adjusted threshold-response function, crucial for identifying risk thresholds in clinical trials, using machine learning and TMLE, with applications to dengue vaccine data.

Contribution

It extends existing methods by proposing a more general estimator that handles outcome missingness and biased sampling, with proven efficiency and asymptotic properties.

Findings

Estimator is statistically efficient and asymptotically normal.

Constructs simultaneous confidence bands for the threshold-response function.

Applied to dengue vaccine trials to identify protective antibody thresholds.

Abstract

Identifying a biomarker or treatment-dose threshold that marks a specified level of risk is an important problem, especially in clinical trials. This risk, viewed as a function of thresholds and possibly adjusted for covariates, we call the threshold-response function. Extending the work of Donovan, Hudgens and Gilbert (2019), we propose a nonparametric efficient estimator for the covariate-adjusted threshold-response function, which utilizes machine learning and Targeted Minimum-Loss Estimation (TMLE). We additionally propose a more general estimator, based on sequential regression, that also applies when there is outcome missingness. We show that the threshold-response for a given threshold may be viewed as the expected outcome under a stochastic intervention where all participants are given a treatment dose above the threshold. We prove the estimator is efficient and characterize its asymptotic distribution. A method to construct simultaneous 95% confidence bands for the threshold-response function and its inverse is given. Furthermore, we discuss how to adjust our estimator when the treatment or biomarker is missing-at-random, as is the case in clinical trials with biased sampling designs, using inverse-probability-weighting. The methods are assessed in a diverse set of simulation settings with rare outcomes and cumulative case-control sampling. The methods are employed to estimate neutralizing antibody thresholds for virologically confirmed dengue risk in the CYD14 and CYD15 dengue vaccine trials.