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Semiparametric estimation and inference for distributional and general treatment effects
Author(s) -
Cheng Jing,
Qin Jing,
Zhang Biao
Publication year - 2009
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2009.00715.x
Subject(s) - estimator , parametric statistics , outcome (game theory) , econometrics , average treatment effect , inference , randomized controlled trial , instrumental variable , statistic , semiparametric model , empirical likelihood , statistical inference , asymptotic distribution , causal inference , statistics , computer science , mathematics , medicine , artificial intelligence , surgery , mathematical economics
Summary. There is a large literature on methods of analysis for randomized trials with noncompliance which focuses on the effect of treatment on the average outcome. The paper considers evaluating the effect of treatment on the entire distribution and general functions of this effect. For distributional treatment effects, fully non‐parametric and fully parametric approaches have been proposed. The fully non‐parametric approach could be inefficient but the fully parametric approach is not robust to the violation of distribution assumptions. We develop a semiparametric instrumental variable method based on the empirical likelihood approach. Our method can be applied to general outcomes and general functions of outcome distributions and allows us to predict a subject's latent compliance class on the basis of an observed outcome value in observed assignment and treatment received groups. Asymptotic results for the estimators and likelihood ratio statistic are derived. A simulation study shows that our estimators of various treatment effects are substantially more efficient than the currently used fully non‐parametric estimators. The method is illustrated by an analysis of data from a randomized trial of an encouragement intervention to improve adherence to prescribed depression treatments among depressed elderly patients in primary care practices.