External validation of clinical prediction models: simulation-based sample size calculations were more reliable than rules-of-thumb

Snell KIE, Archer L, Ensor J, Bonnett LJ, Debray TPA, Phillips B, Collins GS, Riley RD

Introduction: Sample size 'rules-of-thumb' for external validation of clinical prediction models suggest at least 100 events and 100 non-events. Such blanket guidance is imprecise, and not specific to the model or validation setting. We investigate factors affecting precision of model performance estimates upon external validation, and propose a more tailored sample size approach.

Methods: Simulation of logistic regression prediction models to investigate factors associated with precision of performance estimates. Then, explanation and illustration of a simulation-based approach to calculate the minimum sample size required to precisely estimate a model's calibration, discrimination and clinical utility.

Results: Precision is affected by the model's linear predictor (LP) distribution, in addition to number of events and total sample size. Sample sizes of 100 (or even 200) events and non-events can give imprecise estimates, especially for calibration. The simulation-based calculation accounts for the LP distribution and (mis)calibration in the validation sample. Application identifies 2430 required participants (531 events) for external validation of a deep vein thrombosis diagnostic model.

Conclusion: Where researchers can anticipate the distribution of the model's LP (e.g. based on development sample, or a pilot study), a simulation-based approach for calculating sample size for external validation offers more flexibility and reliability than rules-of-thumb.

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