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Meta-analysis of prediction model performance across multiple studies: Which scale helps ensure between-study normality for the C-statistic and calibration measures?

Meta-analysis of prediction model performance across multiple studies: Which scale helps ensure between-study normality for the C-statistic and calibration measures? Thumbnail


Abstract

If individual participant data are available from multiple studies or clusters, then a prediction model can be externally validated multiple times. This allows the model's discrimination and calibration performance to be examined across different settings. Random-effects meta-analysis can then be used to quantify overall (average) performance and heterogeneity in performance. This typically assumes a normal distribution of 'true' performance across studies. We conducted a simulation study to examine this normality assumption for various performance measures relating to a logistic regression prediction model. We simulated data across multiple studies with varying degrees of variability in baseline risk or predictor effects and then evaluated the shape of the between-study distribution in the C-statistic, calibration slope, calibration-in-the-large, and E/O statistic, and possible transformations thereof. We found that a normal between-study distribution was usually reasonable for the calibration slope and calibration-in-the-large; however, the distributions of the C-statistic and E/O were often skewed across studies, particularly in settings with large variability in the predictor effects. Normality was vastly improved when using the logit transformation for the C-statistic and the log transformation for E/O, and therefore we recommend these scales to be used for meta-analysis. An illustrated example is given using a random-effects meta-analysis of the performance of QRISK2 across 25 general practices.

Citation

(2018). Meta-analysis of prediction model performance across multiple studies: Which scale helps ensure between-study normality for the C-statistic and calibration measures?. Statistical Methods in Medical Research, 3505-3522. https://doi.org/10.1177/0962280217705678

Acceptance Date May 8, 2017
Publication Date Nov 1, 2018
Journal Stat Methods Med Res
Print ISSN 0962-2802
Publisher SAGE Publications
Pages 3505-3522
DOI https://doi.org/10.1177/0962280217705678
Keywords validation, performance statistics, C-statistic, discrimination, calibration, meta-analysis, between-study distribution, heterogeneity, simulation
Publisher URL https://doi.org/10.1177/0962280217705678

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