Display options
Cite
Wang L, Rotnitzky A, Lin X. Nonparametric Regression With Missing Outcomes Using Weighted Kernel Estimating Equations. J Am Stat Assoc. 2012;105(491):1135-1146doi: 10.1198/jasa.2010.tm08463.
Wang, L., Rotnitzky, A., & Lin, X. (2010). Nonparametric Regression With Missing Outcomes Using Weighted Kernel Estimating Equations. Journal of the American Statistical Association, 105(491), 1135-1146. https://doi.org/10.1198/jasa.2010.tm08463
Wang, Lu, et al. "Nonparametric Regression With Missing Outcomes Using Weighted Kernel Estimating Equations." Journal of the American Statistical Association vol. 105,491 (2010): 1135-1146. doi: https://doi.org/10.1198/jasa.2010.tm08463
Wang L, Rotnitzky A, Lin X. Nonparametric Regression With Missing Outcomes Using Weighted Kernel Estimating Equations. J Am Stat Assoc. 2010 Sep;105(491):1135-1146. doi: 10.1198/jasa.2010.tm08463. Epub 2012 Jan 01. PMID: 23144520; PMCID: PMC3491912.
Copy Download .nbib Format: NLM
Share it on

J Am Stat Assoc. 2010 Sep;105(491):1135-1146. doi: 10.1198/jasa.2010.tm08463. Epub 2012 Jan 01.

Nonparametric Regression With Missing Outcomes Using Weighted Kernel Estimating Equations.

Journal of the American Statistical Association

Lu Wang, Andrea Rotnitzky, Xihong Lin

Affiliations

  1. Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109.

PMID: 23144520 PMCID: PMC3491912 DOI: 10.1198/jasa.2010.tm08463

Abstract

We consider nonparametric regression of a scalar outcome on a covariate when the outcome is missing at random (MAR) given the covariate and other observed auxiliary variables. We propose a class of augmented inverse probability weighted (AIPW) kernel estimating equations for nonparametric regression under MAR. We show that AIPW kernel estimators are consistent when the probability that the outcome is observed, that is, the selection probability, is either known by design or estimated under a correctly specified model. In addition, we show that a specific AIPW kernel estimator in our class that employs the fitted values from a model for the conditional mean of the outcome given covariates and auxiliaries is double-robust, that is, it remains consistent if this model is correctly specified even if the selection probabilities are modeled or specified incorrectly. Furthermore, when both models happen to be right, this double-robust estimator attains the smallest possible asymptotic variance of all AIPW kernel estimators and maximally extracts the information in the auxiliary variables. We also describe a simple correction to the AIPW kernel estimating equations that while preserving double-robustness it ensures efficiency improvement over nonaugmented IPW estimation when the selection model is correctly specified regardless of the validity of the second model used in the augmentation term. We perform simulations to evaluate the finite sample performance of the proposed estimators, and apply the methods to the analysis of the AIDS Costs and Services Utilization Survey data. Technical proofs are available online.

References

  1. Biometrics. 2000 Mar;56(1):31-9 - PubMed
  2. Bioinformatics. 2007 Sep 15;23(18):2441-8 - PubMed

Publication Types

Grant support