Generalized Functional Linear Regression Models With Functional and Scalar Covariates Prone to Measurement Error

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Generalized linear regression models often struggle with measurement error in covariates.
• Existing methods primarily address scalar covariates, leaving a gap for mixed functional and scalar covariate scenarios.

Purpose of the Study:

• To develop and evaluate novel methods for adjusting measurement error in generalized functional linear regression with mixed covariate types.
• To compare the performance of joint functional simulation extrapolation (FSIMEX) and mixed effects model-based (MEM) approaches against existing methods and an Oracle estimator.

Main Methods:

• Development of joint FSIMEX and MEM estimators for generalized functional linear regression with classical measurement errors in functional and scalar covariates.
• Extensive simulations were conducted to compare the proposed methods with Oracle, PACE, Naive_ave, and Naive_one estimators.
• Application of the methods to NHANES data to assess the relationship between physical activity, caloric intake, and type 2 diabetes status.

Main Results:

• Joint FSIMEX and MEM estimators demonstrated low bias, closely approximating the Oracle estimator.
• SIMEX and MEM methods significantly outperformed Naive_one estimators lacking measurement error adjustment.
• Naive_ave and PACE estimators showed limitations in handling heteroscedasticity and scalar predictors, respectively.

Conclusions:

• Failing to account for measurement error in functional and scalar covariates leads to biased estimations in generalized functional linear regression.
• The developed joint FSIMEX and MEM methods provide effective bias adjustment for mixed covariate types.
• Accurate covariate measurement error adjustment is crucial for reliable statistical inference, as demonstrated in the NHANES diabetes analysis.