Department of Epidemiology and Biostatistics, Indiana University, Bloomington, IN 47405, USA.
Department of Statistics, Oregon State University, Corvallis, OR 97331, USA.
Biostatistics. 2022 Oct 14;23(4):1218-1241. doi: 10.1093/biostatistics/kxac017.
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.
分位数回归是一种用于建模变量之间关联的半参数方法。当协变量与结果分布的位置、规模和形状之间存在复杂关系时，它最有帮助。尽管该方法对结果中的分布假设和异常值具有稳健性，但在协变量存在测量误差的情况下，回归分位数可能会存在偏差。以前尚未研究过具有异方差误差的函数型协变量的影响；尽管已经研究了标量协变量的情况。我们提出了一种两阶段策略，以一致地拟合具有可能存在测量误差的函数型协变量的线性分位数回归模型。在第一阶段，使用工具变量来估计与测量误差相关的协方差矩阵。在第二阶段，使用模拟外推（SIMEX）来校正函数型协变量中的测量误差。通过非参数自举法估计逐点标准误差。我们进行了模拟研究，以评估功能分位数回归中测量误差校正的稳健性。我们的方法应用于国家健康和体检调查数据，以评估美国成年人中身体活动与体重指数之间的关系。
