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Clustered flexible calibration plots for binary outcomes using random effects modeling.

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Summary
This summary is machine-generated.

Evaluating clinical prediction models requires assessing calibration across different data clusters. This study introduces three methods—clustered group calibration, two-stage meta-analysis calibration, and mixed model calibration—to account for this clustering, improving model evaluation.

Keywords:
Binary OutcomesCalibrationClustered DataMeta-analysisModel validationprediction models

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Area of Science:

  • Biostatistics
  • Clinical Epidemiology
  • Health Informatics

Background:

  • Clinical prediction models are increasingly evaluated across multiple clusters (centers or datasets).
  • Model calibration, assessing agreement between predicted risks and observed outcomes, is crucial for clinical decision-making.
  • Calibration performance often varies significantly between clusters.

Purpose of the Study:

  • To present and evaluate three novel approaches for assessing calibration that explicitly account for clustered data.
  • To compare the performance of these methods using a case study, simulation, and synthetic data.
  • To provide practical recommendations and tools for robust calibration assessment in multi-center studies.

Main Methods:

  • Three methods were developed: clustered group calibration (CG-C), two-stage meta-analysis calibration (2MA-C), and mixed model calibration (MIX-C).
  • Methods were evaluated using an external validation of an ovarian tumor malignancy risk model (N=2489).
  • Simulation and synthetic data studies were conducted to assess performance under known data structures.

Main Results:

  • Mixed model calibration (MIX-C) and two-stage meta-analysis calibration (2MA-C) with splines produced overall curves closest to the true curve in simulations.
  • MIX-C generated cluster-specific curves closest to the truth in the synthetic data study.
  • Two-stage meta-analysis calibration (2MA-C) with splines demonstrated the best prediction interval coverage.

Conclusions:

  • Recommend 2MA-C with splines for overall curve estimation and prediction intervals, and MIX-C for cluster-specific curves, especially with limited per-cluster sample sizes.
  • These methods facilitate flexible calibration plots with confidence and prediction intervals to assess calibration heterogeneity.
  • Ready-to-use code is provided to aid in the construction of summary flexible calibration curves.