Quantile regression with measurement error

Regression quantiles can be substantially biased when the covariates are measured with error. In this paper we propose a new method that produces consistent linear quantile estimation in the presence of covariate measurement error. The method corrects the measurement error induced bias by constructing joint estimating equations that simultaneously hold for all the quantile levels. An iterative EM-type estimation algorithm to obtain the solutions to such joint estimation equations is provided. The finite sample performance of the proposed method is investigated in a simulation study, and compared to the standard regression calibration approach. Finally, we apply our methodology to part of the National Collaborative Perinatal Project growth data, a longitudinal study with an unusual measurement error structure. KEY WORDS: Correction for attenuation: Growth curves; Longitudinal data; Measurement error; Quantile regression; Regression calibration; Regression quantiles.