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

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  • Lars van der Laan
  • Wenbo Zhang
  • Peter B. Gilbert

Abstract

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.

Suggested Citation

  • Lars van der Laan & Wenbo Zhang & Peter B. Gilbert, 2023. "Nonparametric estimation of the causal effect of a stochastic threshold‐based intervention," Biometrics, The International Biometric Society, vol. 79(2), pages 1014-1028, June.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:2:p:1014-1028
    DOI: 10.1111/biom.13690
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    References listed on IDEAS

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    1. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    2. Porter Kristin E. & Gruber Susan & van der Laan Mark J. & Sekhon Jasjeet S., 2011. "The Relative Performance of Targeted Maximum Likelihood Estimators," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-34, August.
    3. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
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