Discrimination performance in illness-death models with interval-censored disease data

In clinical studies, the illness-death model is often used to describe disease progression. A subject starts disease-free, may develop the disease and then die, or die directly. In clinical practice, disease can only be diagnosed at pre-specified follow-up visits, so the exact time of disease onset is often unknown, resulting in interval-censored data. This study examines the impact of ignoring this interval-censored nature of disease data on the discrimination performance of illness-death models, focusing on the time-specific Area Under the receiver operating characteristic Curve (AUC) in both incident/dynamic and cumulative/dynamic definitions. A simulation study with data simulated from Weibull transition hazards and disease state censored at regular intervals is conducted. Estimates are derived using different methods: the Cox model with a time-dependent binary disease marker, which ignores interval-censoring, and the illness-death model for interval-censored data estimated with three implementations - the piecewise-constant model from the msm package, the Weibull and M-spline models from the SmoothHazard package. These methods are also applied to a dataset of 2232 patients with high-grade soft tissue sarcoma, where the interval-censored disease state is the post-operative development of distant metastases. The results suggest that, in the presence of interval-censored disease times, it is important to account for interval-censoring not only when estimating the parameters of the model but also when evaluating the discrimination performance of the disease.

💡 Research Summary

This paper investigates how interval‑censoring of disease onset times influences the discrimination performance of illness‑death models, focusing on time‑specific area under the receiver operating characteristic curve (AUC) under both incident/dynamic and cumulative/dynamic definitions. In many clinical studies disease can only be diagnosed at scheduled follow‑up visits, so the exact time of transition from the disease‑free state to the disease state is unknown and only known to lie within an interval. While previous work has shown that ignoring this censoring biases regression coefficients, baseline hazards, and survival estimates, the impact on predictive discrimination has not been systematically examined.

The authors first formalize the illness‑death process with three states (0 = disease‑free, 1 = diseased, 2 = death) and define transition intensities λ₀₁(t), λ₀₂(t), λ₁₂(t). They treat the disease status X(t) as a time‑dependent binary marker and extend the standard time‑dependent AUC to incorporate the multi‑state transition probabilities. Two AUC concepts are considered: (i) incident/dynamic AUC, which evaluates the ability of X(t) to predict a future disease event between times s and t among subjects who are disease‑free and alive at s; and (ii) cumulative/dynamic AUC, which evaluates the ability to predict whether disease occurs at any time in the interval