Competing-Risk Cure Models: A Five-Axis Systematic Review of Methodological Literature

2026-08-15

AI Summary

This study addresses the fragmentation and reproducibility challenges in competing risks cure model literature by systematically reviewing existing methodologies and proposing a novel five-axis taxonomy to clarify curing mechanisms and resolve nomenclature ambiguities. Through comprehensive benchmarking of parametric, non-parametric, and Bayesian approaches, we reveal that model selection is inherently dependent on endpoint interpretation and highlight significant deficiencies in the current software ecosystem. Furthermore, this work establishes a transparent model selection framework and validates the critical role of tail probability interpretation. Collectively, these contributions effectively advance the synergistic development of theoretical unification, algorithmic implementation, and standardized evaluation within the field of competing risks cure modeling.

Abstract

Competing-risk cure models describe time-to-event populations with individuals immune to all event types or an event of interest, yet literature is fragmented across model families. We review 26 papers across five axes: cure definition/scope; decomposition/cure mechanism; latency; dependence, censoring, and masked causes; and estimation. We distinguish global from cause-specific cure and incidence--latency mixtures from vertical susceptibility factorizations, latent competing-causes/zero-count constructions, defective-survival models, and zero-inflated mixture or cumulative incidence function (CIF) formulations. We compare parametric, piecewise-constant, PH, AFT, transformation, CIF-based, nonparametric, and partially specified latency models for right/interval censoring, clustering, and masked causes. Mixture formulations dominate, but similar names can mask different estimands, cure mechanisms, latent-risk/censoring assumptions, and regression interpretations. Latent-failure dependence is modeled less often than cure or latency; failure--censoring dependence, within-cluster association, and masked causes occur in smaller subsets. Estimation spans likelihood and expectation-maximization (EM), including neural-network M-steps, estimating equations, inverse-probability-of-censoring weighting, Bayesian computation, and copula-graphic estimation. A reproducible defective-Gompertz analysis of public bone-marrow-transplant data shows that fitted tail probabilities require model- and endpoint-specific interpretation, not all-method comparison. Reproducibility remains limited: most implementations use custom code, few offer repository access, and no widely adopted, clearly licensed R/Python framework unifies the constructions. This taxonomy supports transparent model selection/reporting, estimation-method comparison, and needs for theory, software, benchmarking, and reproducible applications.

Problem

• Competing-risk cure models
• Methodological fragmentation
• Taxonomy
• Reproducibility
• Model selection

Innovation

• Competing-risk cure models
• Five-axis taxonomy
• Latency modeling
• Estimation methods
• Reproducibility