Date of Award
Spring 2026
Document Type
Open Access Dissertation
Department
Epidemiology and Biostatistics
First Advisor
Jiajia Zhang
Abstract
This dissertation develops a class of semiparametric cure models that integrate scalar and high-dimensional functional covariates measured at baseline into both the incidence and latency components of survival analysis. Modern biomedical studies increasingly collect complex longitudinal data, such as wearable sensor measurements and biomarker trajectories, yet existing cure models are not well designed to incorporate such information. By explicitly modeling functional covariates within a complex cure framework, this work enables more realistic and informative modelling in the presence of long-term survivors.
In the first project, a Functional Promotion Time Cure Model (FPTCM) with scalar and functional covariates measured at baseline is introduced. Extending the promotion time cure model to functional data with a cured fraction, we employ an Expectation–Maximization (EM) 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 method’s clinical utility is illustrated using National Health and Nutrition Examination Survey (NHANES) 2003–2006 data, where minute-level physical activity (PA) trajectories were analyzed in relation to all-cancer mortality through 2019, adjusting for biological factors. Findings highlight novel epidemiological evidence on how daily PA patterns influence cancer mortality.
The second project proposes a Functional Cure Model with Heterogeneous Competing Causes (FCMHCC) that relaxes the assumption of a homogeneous latent cause distribution by allowing the number of competing causes to follow a mixture of two power series (PS) distributions. This model generalizes both the mixture cure model and the promotion time cure model as special cases, while accommodating baseline functional covariates through a functional principal component (FPC) representation that effectively handles poorly observed functional data. Smoothness in the functional coefficients is imposed using rich spline bases with automated smoothing parameter selection, resulting in flexible yet stable estimation. Simulation studies show satisfactory performance in parameter and baseline survival estimation and applications to cancer mortality in NHANES and COVID-19 outcomes among people with HIV (PWH) from South Carolina illustrate how the mixing structure captures population heterogeneity.
The third project further extends cure modeling by introducing a Functional Semiparametric Mixture Cure Frailty Model (FSMCFM), which incorporates subjectspecific frailty to account for unobserved heterogeneity beyond observed covariates. An EM-based estimation procedure combined with penalized functional regression is developed. The proposed method is computationally efficient and simultaneously incorporates smoothness in the estimated functional coefficients through roughness penalties with automated smoothing parameter selection. Simulation studies confirm stable and accurate estimation across varying frailty variance levels. Application to NHANES data suggests that, for this dataset, incorporating frailty does not substantially improve model fit or predictive performance, indicating limited unobserved heterogeneity after accounting for baseline scalar and functional covariates.
Overall, this dissertation advances the methodology of survival analysis by unifying cure modeling, functional data analysis, and frailty modeling within flexible semiparametric frameworks. The proposed methods provide interpretable decompositions of long-term survival, latent susceptibility, and dynamic functional effects, and offer practical tools for analyzing complex biomedical data with heterogeneous populations and high-dimensional predictors.
Rights
© 2026, Jiayang Xiao
Recommended Citation
Xiao, J.(2026). Semiparametric Estimation for Complex Cure Models With Functional Components. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/8946