Nonparametric estimation of the causal effect of a stochastic threshold-based intervention

Identifying a biomarker or treatment-dose threshold that marks a specified level of risk is an important problem, especially in clinical trials. In view of this goal, we consider a covariate-adjusted threshold-based interventional estimand, which happens to equal the binary treatment-specific mean estimand from the causal inference literature obtained by dichotomizing the continuous biomarker or treatment as above or below a threshold. The unadjusted version of this estimand was considered in Donovan et al.. Expanding upon Stitelman et al., we show that this estimand, under conditions, identifies the expected outcome of a stochastic intervention that sets the treatment dose of all participants above the threshold. We propose a novel nonparametric efficient estimator for the covariate-adjusted threshold-response function for the case of informative outcome missingness, which utilizes machine learning and targeted minimum-loss estimation (TMLE). We prove the estimator is efficient and characterize its asymptotic distribution and robustness properties. Construction of simultaneous 95% confidence bands for the threshold-specific estimand across a set of thresholds is discussed. In the Supporting Information, we discuss how to adjust our estimator when the biomarker is missing at random, as occurs in clinical trials with biased sampling designs, using inverse probability weighting. Efficiency and bias reduction of the proposed estimator are assessed in simulations. The methods are employed to estimate neutralizing antibody thresholds for virologically confirmed dengue risk in the CYD14 and CYD15 dengue vaccine trials.