Estimation of sparse functional quantile regression with measurement error: a SIMEX approach. (31st May 2022)

• Record Type: Journal Article
• Authors: Tekwe, Carmen D; Zhang, Mengli; Carroll, Raymond J; Luan, Yuanyuan; Xue, Lan; Zoh, Roger S; Carter, Stephen J; Allison, David B; Geraci, Marco
• Is Part Of: Biostatistics. Volume 23:Number 4(2022)
• Page Start: 1218
• Page End: 1241
• Publication Date: 2022-05-31
• Subjects: Functional data analysis -- Obesity -- Physical activity -- Spline basis splines -- Wearable accelerometer; Medical statistics -- Periodicals; Biometry -- Periodicals; Health risk assessment -- Periodicals; Medicine -- Research -- Statistical methods -- Periodicals; 610.727
• DOI: 10.1093/biostatistics/kxac017
• Languages: English
• ISSNs: 1465-4644

Abstract

Summary: Quantile regression is a semiparametric method for modeling associations between variables. It is most helpful when the covariates have complex relationships with the location, scale, and shape of the outcome distribution. Despite the method's robustness to distributional assumptions and outliers in the outcome, regression quantiles may be biased in the presence of measurement error in the covariates. The impact of function-valued covariates contaminated with heteroscedastic error has not yet been examined previously; although, studies have investigated the case of scalar-valued covariates. We present a two-stage strategy to consistently fit linear quantile regression models with a function-valued covariate that may be measured with error. In the first stage, an instrumental variable is used to estimate the covariance matrix associated with the measurement error. In the second stage, simulation extrapolation (SIMEX) is used to correct for measurement error in the function-valued covariate. Point-wise standard errors are estimated by means of nonparametric bootstrap. We present simulation studies to assess the robustness of the measurement error corrected for functional quantile regression. Our methods are applied to National Health and Examination Survey data to assess the relationship between physical activity and body mass index among adults in the United States.