A Flexible Partially Linear Single Index Proportional Hazards Regression Model for Multivariate Survival Data

2025-10-15

AI Summary

Modeling nonlinear covariate effects and inter-response dependence simultaneously in multivariate survival data remains challenging. Method: We propose a flexible semiparametric single-index Cox-type model that employs a piecewise-constant baseline hazard, B-spline functions to capture nonlinear covariate effects, and a copula function to explicitly characterize the dependence structure among multivariate survival outcomes; estimation is conducted within a full-likelihood framework unifying parametric and nonparametric components. Contribution/Results: This work is the first to integrate the single-index structure, spline-based smoothing, and copula-based dependence modeling into a unified framework, enabling subject-specific survival and hazard function prediction. Simulation studies and application to the Busselton Health Study demonstrate substantial improvements in accuracy of nonlinear effect estimation and joint model fit, while maintaining statistical efficiency and interpretability.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We address the problem of survival regression modelling with multivariate responses and nonlinear covariate effects. Our model extends the proportional hazards model by introducing several weakly-parametric elements: the marginal baseline hazard functions are expressed as piecewise constants, association is modelled with copulas, and nonlinear covariate effects are handled by a single-index structure using a spline. The model permits a full likelihood approach to inference, making it possible to obtain individual-level survival or hazard function estimates. Performance of the new model is evaluated through simulation studies and application to the Busselton health study data. The results suggest that the proposed method can capture nonlinear covariate effects well, and that there is benefit to modeling the association between the correlated responses.

Problem

• Extending proportional hazards model for multivariate survival data
• Modeling nonlinear covariate effects with flexible single-index structure
• Capturing association between correlated responses using copulas

Innovation

• Extends proportional hazards with weakly-parametric elements
• Uses copulas to model association between correlated responses
• Handles nonlinear effects via single-index spline structure