Empirical evaluation of internal validation methods for prediction in large-scale clinical data with rare-event outcomes: a case study in suicide risk prediction

Abstract

Abstract Background There is increasing interest in clinical prediction models for rare outcomes such as suicide, psychiatric hospitalizations, and opioid overdose. Accurate model validation is needed to guide model selection and decisions about whether and how prediction models should be used. Split-sample estimation and validation of clinical prediction models, in which data are divided into training and testing sets, may reduce predictive accuracy and precision of validation. Using all data for estimation and validation increases sample size for both procedures, but validation must account for overfitting, or optimism. Our study compared split-sample and entire-sample methods for estimating and validating a suicide prediction model. Methods We compared performance of random forest models estimated in a sample of 9,610,318 mental health visits (“entire-sample”) and in a 50% subset (“split-sample”) as evaluated in a prospective validation sample of 3,754,137 visits. We assessed optimism of three internal validation approaches: for the split-sample prediction model, validation in the held-out testing set and, for the entire-sample model, cross-validation and bootstrap optimism correction. Results The split-sample and entire-sample prediction models showed similar prospective performance; the area under the curve, AUC, and 95% confidence interval was 0.81 (0.77–0.85) for both. Performance estimates evaluated in the testing set for the split-sample model (AUC = 0.85 [0.82–0.87]) and via cross-validation for the entire-sample model (AUC = 0.83 [0.81–0.85]) accurately reflected prospective performance. Validation of the entire-sample model with bootstrap optimism correction overestimated prospective performance (AUC = 0.88 [0.86–0.89]). Measures of classification accuracy, including sensitivity and positive predictive value at the 99th, 95th, 90th, and 75th percentiles of the risk score distribution, indicated similar conclusions: bootstrap optimism correction overestimated classification accuracy in the prospective validation set. Conclusions While previous literature demonstrated the validity of bootstrap optimism correction for parametric models in small samples, this approach did not accurately validate performance of a rare-event prediction model estimated with random forests in a large clinical dataset. Cross-validation of prediction models estimated with all available data provides accurate independent validation while maximizing sample size.

Keywords

• Bootstrap
• Clinical prediction
• Cross-validation
• Machine learning
• Optimism
• Random forest