While extensive work has been done to correct for biases due to measurement error in scalar-valued covariates prone to errors in generalized linear regression models, limited work has been done to address biases associated with functional covariates prone to errors or the combination of scalar and functional covariates prone to errors in these models. We propose Simulation Extrapolation (SIMEX) and Regression Calibration approaches to correct measurement errors associated with a mixture of functional and scalar covariates prone to classical measurement errors in generalized functional linear regression. The simulation extrapolation method is developed to handle the functional and scalar covariates prone to errors. We also develop methods based on regression calibration extended to our current measurement error settings. Extensive simulation studies are conducted to assess the finite sample performance of our developed methods. The methods are applied to the 2011-2014 cycles of the National Health and Examination Survey data to assess the relationship between physical activity and total caloric intake with type 2 diabetes among community-dwelling adults living in the United States. We treat the device-based measures of physical activity as error-prone functional covariates prone to complex arbitrary heteroscedastic errors, while the total caloric intake is considered a scalar-valued covariate prone to error. We also examine the characteristics of observed measurement errors in device-based physical activity by important demographic subgroups including age, sex, and race.

翻译：已有大量研究针对广义线性回归模型中易受误差影响的标量型协变量进行偏差校正，但关于函数型协变量或函数型与标量型协变量组合在模型中易受误差影响的偏差研究仍然有限。本文针对广义函数线性回归中混合函数型和标量型协变量在经典测量误差下的问题，提出了模拟外推（SIMEX）和回归校准两种方法来校正测量误差。我们开发了处理易受误差影响的函数型和标量型协变量的模拟外推方法，同时扩展了回归校准方法以适应当前的测量误差设定。通过大量模拟研究评估了所提方法的有限样本性能。我们将方法应用于2011-2014年周期的美国国家健康与营养调查数据，旨在评估美国社区居住成年人的体力活动与总热量摄入对2型糖尿病的影响。其中，设备测量的体力活动被视为易受复杂任意异方差误差影响的函数型协变量，而总热量摄入则被视为易受误差影响的标量型协变量。我们还按年龄、性别和种族等重要人口统计学亚组，分析了设备测量体力活动中观测测量误差的特征。