Introduction
In clinical studies evaluating therapies for major diseases such as cancer, overall survival (OS) is a gold standard endpoint. Yet OS blends multiple failure causes and can obscure the actual burden of disease- or treatment-related events. In long follow-ups, competing risks (e.g., non-disease death) influence observed outcomes and make crude cumulative incidence (CIF) a more informative metric for the event of interest. This article outlines modeling strategies for flexible CIF estimation, choosing appropriate models, and rigorously evaluating predictive ability to support evidence-based decision making.
Why crude cumulative incidence matters in long follow-ups
Crude cumulative incidence estimates the probability that a specific event occurs by a given time, accounting for competing events that preclude the event of interest. In cancer research, CIF helps clinicians compare therapies not only on survival but also on disease-specific risk trajectories, enabling better patient counseling, trial design, and health technology assessments. Long follow-ups intensify censoring and dynamic risk profiles, underscoring the need for models that are robust, interpretable, and capable of extrapolating beyond observed data when appropriate.
Model choices for flexible estimation
Several modeling paradigms address CIF in the presence of competing risks. The choice depends on the research aim (estimation vs. prediction), the need for extrapolation, interpretability, and data structure.
Non-parametric and semi-parametric estimators
The Aalen-Johansen estimator provides a non-parametric, model-free approach to CIF in multi-state models. It yields consistent CIF estimates under censoring without assuming a particular hazard form. For long follow-ups, the Aalen-Johansen estimator can be complemented with bootstrap methods to quantify uncertainty and to compare CIF curves across treatment groups.
Fine-Gray subdistribution hazards models
The Fine-Gray model directly targets the subdistribution hazard associated with the CIF. It is particularly useful when the aim is to assess covariate effects on the incidence of the event of interest while accounting for competing risks. Limitations include potential misinterpretation of hazard parameters as cause-specific risks and the need for careful model checking in long follow-ups where hazards may evolve over time.
Cause-specific hazard models
Cause-specific hazard models estimate the instantaneous risk of each event type separately, treating other events as censoring. They are valuable for understanding etiological processes and for scenarios where extrapolation beyond observed times is feasible. When the primary goal is CIF prediction, the interpretation must be related back to the cumulative incidence via appropriate transformation.
Pseudo-values and regression approaches
Pseudo-value regression translates CIF estimation into a regression framework suitable for covariate adjustment, dynamic prediction, and time-varying effects. This approach can accommodate flexible modeling choices and provides straightforward interpretation for clinicians interested in risk at fixed time horizons.
Flexible parametric and multi-state models
Flexible parametric survival models (e.g., Royston-Parmar-type models) and multi-state frameworks accommodate smooth hazard shapes and time-varying effects. These are particularly advantageous in long follow-ups where hazards may change substantially over time, enabling more accurate extrapolation and CIF estimation beyond the observed window.
Evaluating predictive ability and model performance
Model evaluation should address discrimination, calibration, and overall predictive accuracy, with attention to competing risks and censoring.
Discrimination and time-dependent measures
Discrimination can be assessed with time-dependent AUC or C-index adapted for competing risks. These metrics quantify how well the model ranks individuals by their risk of the event of interest over time. Dynamic or cumulative AUCs reflect predictive performance at various follow-up horizons, informing model selection for different clinical decision points.
Calibration and scoring rules
Calibration assesses how closely predicted CIFs agree with observed probabilities across risk strata and time points. Calibration plots and statistical tests provide a visual and quantitative check. Proper scoring rules like the Brier score for cumulative incidence offer an overall measure of accuracy by combining discrimination and calibration into a single metric.
Validation strategies
Robust assessment requires internal validation (e.g., bootstrap or cross-validation) and, when possible, external validation using independent data. In long-term studies, temporal validation—splitting data by calendar time or follow-up period—helps gauge model transportability to future cohorts and evolving practice patterns.
Model comparison and selection
Beyond predictive performance, consider model parsimony, interpretability, and computational feasibility. Information criteria (AIC/BIC) and likelihood-based metrics aid comparison, but should be weighed against clinical relevance and the ability to provide reliable CIF estimates across the time horizon of interest.
Practical guidelines for analysis and reporting
Key steps include: (1) clearly define the event of interest and competing risks; (2) choose a CIF estimation approach aligned with the study goal; (3) assess time-varying effects and, if needed, adopt flexible modeling of hazards; (4) evaluate discrimination, calibration, and overall accuracy with appropriate time-dependent methods; (5) transparently report model assumptions, validation results, and uncertainty in CIF estimates. Present CIF curves with confidence bands, report covariate effects on CIF (via subdistribution hazards or pseudo-values), and provide guidance on clinical interpretation for long-term follow-ups.
Conclusion
Flexible estimation of crude cumulative incidence in the presence of competing risks is essential for accurate prognosis and decision-making in long-term cancer studies. By carefully selecting modeling approaches and rigorously evaluating predictive ability, researchers can deliver CIF estimates that are both scientifically sound and clinically actionable, supporting better patient care and policy decisions in the era of extended follow-ups.
