Introduction: Why crude cumulative incidence matters in long follow-ups
In clinical studies evaluating therapeutic interventions, overall survival is a well-established endpoint. However, crude cumulative incidence (CCI) offers a direct view of event probabilities when competing risks are present. When follow-up is prolonged, standard methods can misestimate CCI due to time-varying hazards and changing risk profiles. This article outlines modeling strategies for flexible estimation of CCI in long follow-ups, emphasizing model choice and predictive ability evaluation.
Modeling approaches for CCI in long follow-up studies
Flexible and robust modeling is essential to capture evolving risk patterns over time. Under competing risks, researchers must choose between cause-specific hazards and subdistribution hazards, depending on the clinical question and interpretability needs. Flexible parametric survival models (FPSMs) with splines provide a versatile framework to model the baseline hazard and time-varying effects, enabling smooth estimates of CCI across the follow-up horizon. Extensions of FPSMs to competing risks contexts (e.g., subdistribution or cause-specific formulations) support accurate and interpretable CCI curves.
Pseudo-values offer another valuable approach, converting survival or cumulative incidence problems into regression tasks on pseudo-observations. This semi-parametric method supports straightforward model comparison and accommodates long follow-ups where hazards may depart from simple parametric shapes. In addition, non-parametric or spline-based hazard models give flexibility without forcing rigid functional forms, which helps when risk trajectories are complex or non-monotone over time.
Key model-choice considerations
Model selection should balance flexibility, sample size, and clinical interpretability. More flexible specifications can capture time-varying effects and late-onset risk but risk overfitting in smaller samples. Clinicians often prefer summaries that are easy to interpret, such as CCI estimates at clinically relevant time points. Practical criteria for comparing models include cross-validation performance, information criteria (AIC/BIC), and, where possible, external validation to assess transportability of CCI estimates in different cohorts.
Practical modeling options
Practical options include FPSMs with restricted cubic splines for the baseline hazard and time-varying effects, Fine-Gray subdistribution hazard models for direct CCI interpretation, and cause-specific hazard models when the clinical question targets a particular cause. For long follow-ups, joint modeling of longitudinal covariates that evolve over time (e.g., biomarkers) with survival outcomes can improve CCI estimation when these covariates influence risk dynamics.
Evaluating predictive ability and calibration
Predictive performance should be assessed with time-dependent metrics that reflect follow-up duration. Time-dependent AUC (or C-index) measures discrimination across time, while the Brier score captures overall accuracy and calibration. Calibration plots compare observed versus predicted CCI at multiple horizons, highlighting potential miscalibration in the tail of follow-up. Resampling methods such as bootstrap or cross-validation provide robust estimates of predictive performance and uncertainty, reducing the risk of overoptimistic conclusions from flexible models.
Clinical usefulness and decision support
Beyond statistical metrics, evaluating clinical usefulness is essential. Decision-curve analysis can quantify net benefit across risk thresholds, translating CCI estimates into actionable information for patient counseling and treatment planning. Clear reporting of modeling choices, assumptions about competing risks, and sensitivity analyses strengthens the credibility of the estimated CCI curves.
Guidelines for reporting and practical takeaways
When presenting estimates of crude cumulative incidence in long follow-ups, document the chosen modeling approach, rationale for time-varying effects, and the regularization or penalty strategies used to prevent overfitting. Provide CCI curves with uncertainty bands, and, if feasible, validate the model in an independent cohort to demonstrate generalizability. In summary, flexible estimation of CCI benefits from thoughtful model choice, rigorous evaluation of predictive ability, and transparent reporting to support informed clinical decisions.
