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

Marta Spreafico, Anja J. Rueten-Budde, Hein Putter, Marta Fiocco

TL;DR

This study tackles discrimination assessment for illness-death models when disease onset is interval-censored, a common situation in clinical follow-up. It compares Cox models with time-dependent markers to three interval-censored illness-death estimators (piecewise-constant, Weibull, M-spline) using time-specific AUCs for incident/dynamic and cumulative/dynamic definitions, under simulation and real soft tissue sarcoma data. Results show that ignoring interval-censoring biases parameter estimates and misrepresents discrimination; among methods, Weibull generally performs best when appropriate, but convergence and distributional fit matter, and piecewise-constant may be less flexible; M-splines offer flexibility but can face convergence issues. The findings stress incorporating interval-censoring into both estimation and discrimination evaluation to obtain reliable prognostic assessments in interval-observed disease settings, with practical implications for dynamic prediction in oncology and similar fields.

Abstract

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.

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

TL;DR

This study tackles discrimination assessment for illness-death models when disease onset is interval-censored, a common situation in clinical follow-up. It compares Cox models with time-dependent markers to three interval-censored illness-death estimators (piecewise-constant, Weibull, M-spline) using time-specific AUCs for incident/dynamic and cumulative/dynamic definitions, under simulation and real soft tissue sarcoma data. Results show that ignoring interval-censoring biases parameter estimates and misrepresents discrimination; among methods, Weibull generally performs best when appropriate, but convergence and distributional fit matter, and piecewise-constant may be less flexible; M-splines offer flexibility but can face convergence issues. The findings stress incorporating interval-censoring into both estimation and discrimination evaluation to obtain reliable prognostic assessments in interval-observed disease settings, with practical implications for dynamic prediction in oncology and similar fields.

Abstract

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.
Paper Structure (21 sections, 23 equations, 6 figures, 4 tables)

This paper contains 21 sections, 23 equations, 6 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Illness-death models
  3. Cox model with time-dependent covariate
  4. Piecewise-constant model accounting for interval-censoring
  5. Weibull model accounting for interval-censoring
  6. M-spline model accounting for interval-censoring
  7. Discrimination for time-dependent marker and survival data
  8. Incident cases and dynamic controls
  9. Estimation.
  10. Cumulative cases and dynamic controls
  11. Estimation.
  12. Simulation study
  13. Data generation and methods
  14. Results
  15. Estimated models.
  16. ...and 6 more sections

Figures (6)

  • Figure 1: Illness-death model.
  • Figure 2: Estimated time-specific incident/dynamic AUC for scenario A (3 months; left panels), B (6 months; middle panels) and C (12 months; right panels) using different models (Cox, PW-const, Weibull, M-spline). The x-axis represents time $t$ in years; the y-axis represents $\widehat{\text{AUC}}^{\text{I/D}}(t)$. The blue line in each panel represents the true values over time. Estimates for Cox ROC are based on risksetAUC function for Cox model. Estimates for Cox prob are based on transition probabilities of Cox model via mstate package.
  • Figure 3: Estimated time-specific cumulative/dynamic AUC for scenario A (3 months; left panels), B (6 months; middle panels) and C (12 months; right panels) using different models (Cox, PW-const, Weibull, M-spline). The x-axis represents the prediction time $t$ in years. The prediction window is set to 5 years, so the y-axis represents $\widehat{\text{AUC}}^{\text{C/D}}(t,t+5)$. The blue line in each panel represents the true values over time.
  • Figure 4: Soft tissue sarcoma illness-death model ($N$ = 2232). State 0 (disease-free): surgery with curative intent; state 1 (disease): development of distant metastases (DM); state 2: death. The numbers indicate the number of patients moving from one state to the other.
  • Figure 5: Left panel: Cumulative transition hazards. Right panel: plot of logarithm of cumulative transition hazards versus logarithm of time (in years) to empirically check the fit of the Weibull distribution.
  • ...and 1 more figures