Novel Bayesian assessments of device-based physical activity and self-reported dietary intake in joint models of all-cause mortality and type 2 diabetes in a cohort of biracial older US adults

Biomedical research often involves the collection of error-prone, complex, high-dimensional functional and scalar data. Functional data analysts typically treat functional data as smooth latent curves obtained at discrete time intervals and regard the error terms as homoscedastic and independent random noise, ignoring potential serial correlations. Although measurement error attenuates coefficients in classical regression, the impacts of heteroscedastic, error-prone functional covariates and the combination of error-prone functional and scalar covariates in survival models, censored quantile regression, and joint models of censored and uncensored data remain unknown. Failing to account for measurement error and serial correlations in functional covariates in linear regression leads to severely biased estimates, influencing conclusions drawn from such models. Although researchers have worked extensively to correct for error-prone scalar covariates in survival models, they have not addressed measurement error in complex, high-dimensional functional data and the mixture of errors in combined scalar and functional data in survival and censored quantile regression models. We will develop novel approaches to survival analysis using Bayesian and frequentist frameworks to address the complexities introduced by measurement errors in longitudinal, high-dimensional, device-based physical activity (PA) and self-reported dietary intake (DI) data. Current wearable devices monitor PA objectively, but generate complex data with poorly understood, heteroscedastic, and systematic errors. Also, researchers often assess DI with self- reports, which are prone to recall bias and variations in seasonal and day-to-day intake. We will build and evaluate new models with data from the Reasons for Geographic and Racial Differences in Stroke (REGARDS) Study, a biracial cohort of adults aged 45 years or older (n=30,239). All models will correct for error in device- measured PA and self-reported DI. We will pursue three aims. Aim 1: Develop latent group semiparametric models for survival time correcting for measurement error in DI and PA. Aim 2: Develop model-based approaches to correct for measurement error in PA and DI data and determine the relationships of error- corrected PA and DI data with joint quantile functions of censored survival time. Aim 3: Develop models to estimate the average treatment effect (ATE) of T2D on survival time after correcting for measurement error in PA and DI in the presence of endogeneity and potential asymmetric dependency. Our models will inform personalized recommendations for PA and DI and address health disparities in vulnerable populations. We will make public use software that implements our models and allows other researchers to apply our methods in diverse biomedical settings.