A Bayesian Varying-effect Scalar-on-function Survival Model with Measurement Error

Music City Center 

Scalar-on-function regression (SoFR) has become a commonly used method for modeling the relationship between scalar outcomes and functional predictors, such as physical activity (PA) patterns from wearable devices. Recent extensions of SoFR to survival analysis also correct for measurement error in functional covariates. However, these approaches often do not simultaneously address the heterogeneity of the effect across individuals. More specifically, they assume that the effect of the functional predictor is constant across individuals, which may obscure variation driven by subject-specific characteristics. We develop a semi-parametric Bayesian SoFR accelerated failure time (AFT) model that corrects for measurement error within functional covariates and includes an instrumental variable that allows nonlinear relationships with the functional covariate. We also introduce a varying functional coefficient that depends on a scalar covariate through a flexible Gaussian process single-index structure. For inference, we compare traditional Markov chain Monte Carlo sampling with the integrated nested Laplace approximation (INLA) to highlight trade-offs between computational efficiency and flexibility.

Bayesian

Scalar-on-function

Physical activity

Measurement error

Instrumental variables

Varying effect 

Biometrics Section