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Causal Inference on Quantiles with an Obstetric Application


  • Zhiwei Zhang,

    Corresponding author
    1. Division of Biostatistics, Office of Surveillance and Biometrics, Center for Devices and Radiological Health, Food and Drug Administration, Silver Spring, Maryland 20993, U.S.A.
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  • Zhen Chen,

    1. Biostatistics and Bioinformatics Branch, Division of Epidemiology, Statistics and Prevention Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, U.S.A.
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  • James F. Troendle,

    1. Office of Biostatistics Research, Division of Cardiovascular Sciences, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, U.S.A.
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  • Jun Zhang

    1. MOE and Shanghai Key Laboratory of Children’s Environmental Health, Xinhua Hospital, Shanghai Jiaotong University School of Medicine, Shanghai 200092, P. R. China
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Summary The current statistical literature on causal inference is primarily concerned with population means of potential outcomes, while the current statistical practice also involves other meaningful quantities such as quantiles. Motivated by the Consortium on Safe Labor (CSL), a large observational study of obstetric labor progression, we propose and compare methods for estimating marginal quantiles of potential outcomes as well as quantiles among the treated. By adapting existing methods and techniques, we derive estimators based on outcome regression (OR), inverse probability weighting, and stratification, as well as a doubly robust (DR) estimator. By incorporating stratification into the DR estimator, we further develop a hybrid estimator with enhanced numerical stability at the expense of a slight bias under misspecification of the OR model. The proposed methods are illustrated with the CSL data and evaluated in simulation experiments mimicking the CSL.

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