A Functional Cure Model with Heterogeneous Competing Causes for Cancer Mortality Analysis in NHANES

Thomas M. Menino Convention & Exhibition Center 

Most existing cure models assume homogeneous latent cause structures and rely primarily on scalar covariates. We propose a functional two-component cure model that incorporates functional covariates and allows heterogeneous latent cause distributions through a mixture of power series distributions. This model generalizes both the mixture cure model and the promotion time cure model to functional data with a cured fraction. We employ an expectation–maximization algorithm and a semiparametric penalized spline approach to estimate dynamic functional coefficients for both incidence and latency components, enforcing smoothness via roughness penalties. Simulation studies show satisfactory performance in parameter and baseline survival estimation. The clinical utility of the proposed method is illustrated using National Health and Nutrition Examination Survey 2003–2006 data, where minute-level physical activity trajectories were analyzed in relation to all-cancer mortality through 2019, adjusting for biological factors. The results highlight how latent mixing structures capture unobserved population heterogeneity and how daily activity patterns are associated with cancer mortality risk.

Survival Analysis

Functional Data Analysis

Cancer Mortality

Physical Activity 

Biometrics Section