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

arXiv: https://arxiv.org/abs/2107.11459 · HTML: https://mlsanity.com/paper/2107.11459/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jul 2021.

## Built on by (most cited first, 1 of 1)

- [Application of targeted maximum likelihood estimation in public health and epidemiological studies: a systematic review](https://mlsanity.com/paper/2303.07329/) (2023)

## Abstract (arXiv)

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.