Multicovariate-adjusted regression models

D. V. Nguyen, D. Şentürk

Research output: Contribution to journalArticle

27 Scopus citations

Abstract

We introduce multicovariate-adjusted regression (MCAR), an adjustment method for regression analysis, where both the response (Y) and predictors (X1, , Xp) are not directly observed. The available data have been contaminated by unknown functions of a set of observable distorting covariates, Z1, , Zs, in a multiplicative fashion. The proposed method substantially extends the current contaminated regression modelling capability, by allowing for multiple distorting covariate effects. MCAR is a flexible generalisation of the recently proposed covariate-adjusted regression method, an effective adjustment method in the presence of a single covariate, Z. For MCAR estimation, we establish a connection between the MCAR models and adaptive varying coefficient models. This connection leads to an adaptation of a hybrid backfitting estimation algorithm. Extensive simulations are used to study the performance and limitations of the proposed iterative estimation algorithm. In particular, the bias and mean square error of the proposed MCAR estimators are examined, relative to a baseline and a consistent benchmark estimator. The method is also illustrated with a Pima Indian diabetes data set, where the response and predictors are potentially contaminated by body mass index and triceps skin fold thickness. Both distorting covariates measure aspects of obesity, an important risk factor in type 2 diabetes.

Original languageEnglish (US)
Pages (from-to)813-827
Number of pages15
JournalJournal of Statistical Computation and Simulation
Volume78
Issue number9
DOIs
StatePublished - 2008

Keywords

  • Covariate adjusted regression
  • Local polynomial regression
  • Multiplicative effect
  • Varying-coefficient models

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty

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