Single-index Semiparametric Transformation Cure Models with Interval-censored Data

2026-01-18

AI Summary

This study addresses the potential inadequacy of parametric assumptions in traditional mixture cure models for interval-censored data regarding the uncured probability and hazard function. To overcome this limitation, the authors propose a flexible single-index semiparametric transformation cure model that characterizes the uncured probability via a single-index structure and models the conditional survival function using a semiparametric transformation framework, thereby unifying the proportional hazards and proportional odds cure models as special cases. Methodologically, the single-index function is estimated via kernel smoothing, the cumulative baseline hazard is approximated using splines, and an efficient EM algorithm is developed through a four-layer Gamma frailty Poisson data augmentation scheme. Extensive simulations and an analysis of Alzheimer’s disease data demonstrate that the proposed approach substantially outperforms existing spline-based and logistic mixture cure models in both model fit and predictive performance.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Interval censored data commonly arise in medical studies when the event time of interest is only known to lie within an interval. In the presence of a cure subgroup, conventional mixture cure models typically assume a logistic model for the uncure probability and a proportional hazards model for the susceptible subjects. However, in practice, the assumptions of parametric form for the uncure probability and the proportional hazards model for the susceptible may not always be satisfied. In this paper, we propose a class of flexible single-index semiparametric transformation cure models for interval-censored data, where a single-index model and a semiparametric transformation model are utilized for the uncured and conditional survival probability, respectively, encompassing both the proportional hazards cure and proportional odds cure models as specific cases. We approximate the single-index function and cumulative baseline hazard functions via the kernel technique and splines, respectively, and develop a computationally feasible expectation-maximisation (EM) algorithm, facilitated by a four-layer gamma-frailty Poisson data augmentation. Simulation studies demonstrate the satisfactory performance of our proposed method, compared to the spline-based approach and the classical logistic-based mixture cure models. The application of the proposed methodology is illustrated using the Alzheimers dataset.

Problem

• interval-censored data
• cure models
• proportional hazards
• single-index model
• semiparametric transformation

Innovation

• single-index model
• semiparametric transformation model
• interval-censored data
• cure model
• EM algorithm