Developing a Clinical Prediction Score: Comparing Prediction Accuracy of Integer Scores to Statistical Regression Models

Abstract

Researchers often convert prediction tools built on statistical regression models into integer scores and risk classification systems in the name of simplicity. However, this workflow discards useful information and reduces prediction accuracy. We, therefore, investigated the impact on prediction accuracy when researchers simplify a regression model into an integer score using a simulation study and an example clinical data set. Simulated independent training and test sets (n = 1000) were randomly generated such that a logistic regression model would perform at a specified target area under the receiver operating characteristic curve (AUC) of 0.7, 0.8, or 0.9. After fitting a logistic regression with continuous covariates to each data set, continuous variables were dichotomized using data-dependent cut points. A logistic regression was refit, and the coefficients were scaled and rounded to create an integer score. A risk classification system was built by stratifying integer scores into low-, intermediate-, and high-risk tertiles. Discrimination and calibration were assessed by calculating the AUC and index of prediction accuracy (IPA) for each model. The optimism in performance between the training set and test set was calculated for both AUC and IPA. The logistic regression model using the continuous form of covariates outperformed all other models. In the simulation study, converting the logistic regression model to an integer score and subsequent risk classification system incurred an average decrease of 0.057–0.094 in AUC, and an absolute 6.2%–17.5% in IPA. The largest decrease in both AUC and IPA occurred in the dichotomization step. The dichotomization and risk stratification steps also increased the optimism of the resulting models, such that they appeared to be able to predict better than they actually would on new data. In the clinical data set, converting the logistic regression with continuous covariates to an integer score incurred a decrease in externally validated AUC of 0.06 and a decrease in externally validated IPA of 13%. Converting a regression model to an integer score decreases model performance considerably. Therefore, we recommend developing a regression model that incorporates all available information to make the most accurate predictions possible, and using the unaltered regression model when making predictions for individual patients. In all cases, researchers should be mindful that they correctly validate the specific model that is intended for clinical use.

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