Adjustment for Measurement Error

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Title: Adjustment for Measurement Error
Author: Elliott, Laine E
Advisors: Dr. Anastasios Tsiatis, Committee Member
Dr. Daowen Zhang, Committee Member
Dr. Marie Davidian, Committee Co-Chair
Dr. Len Stefanski, Committee Co-Chair
Abstract: A variety of complications arise when imperfect measurements, W, are observed in place of a true variable of interest, X. In the context of linear and non-linear regression models where X is a covariate, regression parameter estimators obtained when W is substituted for X may be substantially biased. Many strategies for correcting for measurement error depend on the specific modeling or regression context and can be intractable in highly non-linear models. In addition, previous methods often assume that the measurement error is normally distributed. In our work, we focus on re-creating the distribution of X from the observed W, either as the primary quantity of interest or as a means to improving parameter estimation. We obtain estimators of X for which the first M sample moments are unbiased for the corresponding moments of X. We investigate the benefit of substituting these estimates in density estimation, logistic regression and survival models. We compare this moment adjusted imputation (MAI) approach to existing alternatives in applications with normally distributed measurement error. We identify an important case of chi-square measurement error and propose a variety of methods to adjust for it, including a version of MAI. We find that MAI is often superior and has the advantage that once the estimates of X are obtained, they can be substituted in any model, including complicated non-linear models.
Date: 2009-11-02
Degree: PhD
Discipline: Statistics

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