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A Note on Calibration of Clinical Prediction Models with Copas Statistics.

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This study evaluates Copas statistics for assessing clinical prediction model calibration. A simulation showed a Cornish-Fisher approximation adequately estimated Copas statistics, proving useful for calibration studies.

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Area of Science:

  • Statistics
  • Biostatistics
  • Epidemiology

Background:

  • Clinical prediction models require goodness-of-fit assessment.
  • Independent, non-identically distributed Bernoulli random variables are often used.
  • Copas statistics are investigated for this calibration setting.

Purpose of the Study:

  • To investigate and compare the operating characteristics of two Copas statistics.
  • To evaluate their performance in calibration studies.

Main Methods:

  • Distribution theory and a simulation study were employed.
  • Comparison of Copas statistics' operating characteristics.
  • Illustration using a calibration study for atherosclerotic cardiovascular disease risk prediction.

Main Results:

  • A Cornish-Fisher approximation for tail quantiles of Copas statistics performed adequately in simulations with small sample sizes.
  • Power properties reflected differential observation weighting, similar to other goodness-of-fit statistics.
  • The statistics were effective in a cardiovascular disease risk prediction calibration study.

Conclusions:

  • Copas statistics are easily implemented and valuable for calibration studies.
  • They are underutilized and should be standard tools for researchers.
  • Their use enhances the assessment of clinical prediction model calibration.