Generalized functional linear regression models with a mixture of complex function-valued and scalar-valued covariates prone to measurement error

Abstract: 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.