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.

翻译：识别标志物或治疗剂量阈值以标记特定风险水平是一个重要问题，尤其在临床试验中。我们将此风险视为阈值的函数（可能经协变量调整），称为阈值响应函数。扩展Donovan、Hudgens和Gilbert（2019）的工作，我们提出了一种协变量调整阈值响应函数的非参数有效估计量，该估计量利用机器学习和目标最小损失估计（TMLE）。我们还基于序贯回归提出了一种更通用的估计量，该估计量同样适用于存在结果缺失的情况。我们证明，给定阈值下的阈值响应可视为所有参与者接受高于阈值治疗剂量的随机干预下的期望结果。我们证明了该估计量的有效性，并刻画了其渐近分布。我们提供了一种构建阈值响应函数及其反函数的同时95%置信带的方法。此外，我们讨论了当治疗或标志物随机缺失时（如存在偏倚抽样设计的临床试验中的情况），如何使用逆概率加权调整我们的估计量。这些方法在一系列模拟设置中进行了评估，涵盖罕见结果和累积病例对照抽样。我们将这些方法应用于CYD14和CYD15登革热疫苗试验中，以估计病毒学确诊登革热风险的中和抗体阈值。