Semiparametrically efficient estimation in quantile regression of secondary analysis

Liang Liang, Yanyuan Ma, Ying Wei, Raymond J. Carroll

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Analysing secondary outcomes is a common practice for case–control studies. Traditional secondary analysis employs either completely parametric models or conditional mean regression models to link the secondary outcome to covariates. In many situations, quantile regression models complement mean-based analyses and provide alternative new insights on the associations of interest. For example, biomedical outcomes are often highly asymmetric, and median regression is more useful in describing the ‘central’ behaviour than mean regressions. There are also cases where the research interest is to study the high or low quantiles of a population, as they are more likely to be at risk. We approach the secondary quantile regression problem from a semiparametric perspective, allowing the covariate distribution to be completely unspecified. We derive a class of consistent semiparametric estimators and identify the efficient member. The asymptotic properties of the resulting estimators are established. Simulation results and a real data analysis are provided to demonstrate the superior performance of our approach with a comparison with the only existing approach so far in the literature.

Original languageEnglish (US)
Pages (from-to)625-648
Number of pages24
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume80
Issue number4
DOIs
StatePublished - Sep 1 2018

Fingerprint

Quantile Regression
Efficient Estimation
Covariates
Regression Model
Median Regression
Estimator
Case-control Study
Parametric Model
Quantile
Asymptotic Properties
Data analysis
Complement
Regression
Likely
Alternatives
Demonstrate
Efficient estimation
Quantile regression
Simulation
Regression model

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Semiparametrically efficient estimation in quantile regression of secondary analysis. / Liang, Liang; Ma, Yanyuan; Wei, Ying; Carroll, Raymond J.

In: Journal of the Royal Statistical Society. Series B: Statistical Methodology, Vol. 80, No. 4, 01.09.2018, p. 625-648.

Research output: Contribution to journalArticle

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AB - Analysing secondary outcomes is a common practice for case–control studies. Traditional secondary analysis employs either completely parametric models or conditional mean regression models to link the secondary outcome to covariates. In many situations, quantile regression models complement mean-based analyses and provide alternative new insights on the associations of interest. For example, biomedical outcomes are often highly asymmetric, and median regression is more useful in describing the ‘central’ behaviour than mean regressions. There are also cases where the research interest is to study the high or low quantiles of a population, as they are more likely to be at risk. We approach the secondary quantile regression problem from a semiparametric perspective, allowing the covariate distribution to be completely unspecified. We derive a class of consistent semiparametric estimators and identify the efficient member. The asymptotic properties of the resulting estimators are established. Simulation results and a real data analysis are provided to demonstrate the superior performance of our approach with a comparison with the only existing approach so far in the literature.

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