Semiparametric estimation and inference for distributional and general treatment effects

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 71; no. 4; pp. 881 - 904
• Main Authors: Cheng, Jing, Qin, Jing, Zhang, Biao
• Format: Journal Article
• Language: English
• Published: Oxford, UK Oxford, UK : Blackwell Publishing Ltd 01.09.2009; Blackwell Publishing Ltd; Blackwell Publishing; Blackwell; Royal Statistical Society; Oxford University Press
• Series: Journal of the Royal Statistical Society Series B
• Subjects: Averages; Causal effect; Causal inference; Causality; Clinical trials; Compliance; Cumulative distribution functions; Data analysis; Density estimation; Distribution theory; elderly; Empirical likelihood; Empirical tests; Estimation; Estimation methods; Estimators; Exact sciences and technology; Experimentation; Exponential tilt model; Functions of a complex variable; General topics; Inference; Instrumental variable; Intervention; Mathematical analysis; Mathematics; Medical practices; Medical research; Medical treatment; Mental depression; Mixture model; Non-compliance; Noncompliance; Older people; Parametric inference; Parametric models; Patients; Primary care; Primary health care; Probability; Probability and statistics; probability distribution; Probability theory and stochastic processes; Random allocation; Random sampling; Randomized trials; Sciences and techniques of general use; Semiparametric estimation and inference; Simulation; Statistical methods; Statistics; Studies; Treatment compliance; Treatment effects; Mixture model; Non parametric estimation; Statistical simulation; Parametric method; Randomized trials; Distribution function; Latent class model; Likelihood function; Mixed distribution; Instrumental variable; Data analysis; Non-compliance; Treatment efficiency; Asymptotic behavior; Empirical method; Average; Likelihood ratio; Empirical likelihood; Statistical estimation; Semiparametric method; Mean estimation; Statistical method; Causal effect; Randomized design; Treatment effect; Exponential tilt model; Entire function
• ISSN: 1369-7412; 1467-9868; 1467-9868
• DOI: 10.1111/j.1467-9868.2009.00715.x

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.