A study of semiparametric survival models with varying coefficients

Abstract

Survival analysis comprises a set of statistical tools for analyzing time-to-event outcomes. In biomedical studies, it is crucial to understand the association between risk factors and event times, such as death time or disease progression time. This understanding aids in identifying prognostic factors, predicting disease outcomes, and determining appropriate treatment strategies. Because the relationship between risk factors and event times is often complex, conventional survival models that assume a constant covariate effect could be inadequate. Varying-coefficient models have emerged as a flexible class of models that capture the intricate interaction effects among risk factors by allowing the covariate effects to depend on an index variable. This research focuses on kernel-based estimation methods for varying-coefficient survival models, including the varying-coefficient additive hazards model and the varying-coefficient transformation model. While many existing kernel-based estimation methods rely on local neighborhoods of subjects to estimate the varying-coefficient functions, such local estimation methods may suffer efficiency loss when there exists a nuisance parameter that does not vary with the index variable. To improve efficiency, we propose a novel global approach that takes into account the shared nature of the nuisance parameter across subjects. In addition, we investigate a penalization method that combines the group lasso penalty with kernel smoothing techniques. This approach allows for the selection of important covariate effects, thereby enhancing the interpretability and predictive performance of the resulting model. Finally, we discuss an extension of the global approach to accommodate multiple index variables, enabling a more comprehensive analysis of the relationships between risk factors and event times.