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Multivariable predictive models are important statistical tools for providingsynthetic diagnosis and prognostic algorithms based on multiple patients'characteristics. Their apparent discriminant and calibration measures usuallyhave overestimation biases (known as 'optimism') relative to the actualperformances for external populations. Existing statistical evidence andguidelines suggest that three bootstrap-based bias correction methods arepreferable in practice, namely Harrell's bias correction and the .632 and .632+estimators. Although Harrell's method has been widely adopted in clinicalstudies, simulation-based evidence indicates that the .632+ estimator mayperform better than the other two methods. However, there is limited evidenceand these methods' actual comparative effectiveness is still unclear. In thisarticle, we conducted extensive simulations to compare the effectiveness ofthese methods, particularly using the following modern regression models:conventional logistic regression, stepwise variable selections, Firth'spenalized likelihood method, ridge, lasso, and elastic-net. Under relativelylarge sample settings, the three bootstrap-based methods were comparable andperformed well. However, all three methods had biases under small samplesettings, and the directions and sizes of the biases were inconsistent. Ingeneral, the .632+ estimator is recommended, but we provide several notesconcerning the operating characteristics of each method.

bmc medical research methodology

Re-evaluation of the comparative effectiveness of bootstrap-based  optimism correction methods in the development of multivariable clinical  prediction models