Empirical Evidence That There Is No Such Thing As A Validated Prediction Model
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| Format: | Preprint |
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2024
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| _version_ | 1866913389853278208 |
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| author | van Leeuwen, Florian D. Steyerberg, Ewout W. van Klaveren, David Wessler, Ben Kent, David M. van Zwet, Erik W. |
| author_facet | van Leeuwen, Florian D. Steyerberg, Ewout W. van Klaveren, David Wessler, Ben Kent, David M. van Zwet, Erik W. |
| contents | Background: External validations are essential to assess clinical prediction models (CPMs) before deployment. Apart from model misspecification, differences in patient population and other factors influence a model's AUC (c-statistic). We aimed to quantify variation in AUCs across external validation studies and adjust expectations of a model's performance in a new setting.
Methods: The Tufts-PACE CPM Registry contains CPMs for cardiovascular disease prognosis. We analyzed the AUCs of 469 CPMs with a total of 1,603 external validations. For each CPM, we performed a random effects meta-analysis to estimate the between-study standard deviation $τ$ among the AUCs. Since the majority of these meta-analyses has only a handful of validations, this leads to very poor estimates of $τ$. So, we estimated a log normal distribution of $τ$ across all CPMs and used this as an empirical prior. We compared this empirical Bayesian approach with frequentist meta-analyses using cross-validation.
Results: The 469 CPMs had a median of 2 external validations (IQR: [1-3]). The estimated distribution of $τ$ had a mean of 0.055 and a standard deviation of 0.015. If $τ$ = 0.05, the 95% prediction interval for the AUC in a new setting is at least +/- 0.1, regardless of the number of validations. Frequentist methods underestimate the uncertainty about the AUC in a new setting. Accounting for $τ$ in a Bayesian approach achieved near nominal coverage.
Conclusion: Due to large heterogeneity among the validated AUC values of a CPM, there is great irreducible uncertainty in predicting the AUC in a new setting. This uncertainty is underestimated by existing methods. The proposed empirical Bayes approach addresses this problem which merits wide application in judging the validity of prediction models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_08628 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Empirical Evidence That There Is No Such Thing As A Validated Prediction Model van Leeuwen, Florian D. Steyerberg, Ewout W. van Klaveren, David Wessler, Ben Kent, David M. van Zwet, Erik W. Methodology Background: External validations are essential to assess clinical prediction models (CPMs) before deployment. Apart from model misspecification, differences in patient population and other factors influence a model's AUC (c-statistic). We aimed to quantify variation in AUCs across external validation studies and adjust expectations of a model's performance in a new setting. Methods: The Tufts-PACE CPM Registry contains CPMs for cardiovascular disease prognosis. We analyzed the AUCs of 469 CPMs with a total of 1,603 external validations. For each CPM, we performed a random effects meta-analysis to estimate the between-study standard deviation $τ$ among the AUCs. Since the majority of these meta-analyses has only a handful of validations, this leads to very poor estimates of $τ$. So, we estimated a log normal distribution of $τ$ across all CPMs and used this as an empirical prior. We compared this empirical Bayesian approach with frequentist meta-analyses using cross-validation. Results: The 469 CPMs had a median of 2 external validations (IQR: [1-3]). The estimated distribution of $τ$ had a mean of 0.055 and a standard deviation of 0.015. If $τ$ = 0.05, the 95% prediction interval for the AUC in a new setting is at least +/- 0.1, regardless of the number of validations. Frequentist methods underestimate the uncertainty about the AUC in a new setting. Accounting for $τ$ in a Bayesian approach achieved near nominal coverage. Conclusion: Due to large heterogeneity among the validated AUC values of a CPM, there is great irreducible uncertainty in predicting the AUC in a new setting. This uncertainty is underestimated by existing methods. The proposed empirical Bayes approach addresses this problem which merits wide application in judging the validity of prediction models. |
| title | Empirical Evidence That There Is No Such Thing As A Validated Prediction Model |
| topic | Methodology |
| url | https://arxiv.org/abs/2406.08628 |