Assessing the performance of prediction models: a framework for traditional and novel measures

Abstract

The performance of prediction models can be assessed using a variety of methods and metrics. Traditional measures for binary and survival outcomes include the Brier score to indicate overall model performance, the concordance (or c) statistic for discriminative ability (or area under the receiver operating characteristic [ROC] curve), and goodness-of-fit statistics for calibration.Several new measures have recently been proposed that can be seen as refinements of discrimination measures, including variants of the c statistic for survival, reclassification tables, net reclassification improvement (NRI), and integrated discrimination improvement (IDI). Moreover, decision-analytic measures have been proposed, including decision curves to plot the net benefit achieved by making decisions based on model predictions.We aimed to define the role of these relatively novel approaches in the evaluation of the performance of prediction models. For illustration, we present a case study of predicting the presence of residual tumor versus benign tissue in patients with testicular cancer (n = 544 for model development, n = 273 for external validation).We suggest that reporting discrimination and calibration will always be important for a prediction model. Decision-analytic measures should be reported if the predictive model is to be used for clinical decisions. Other measures of performance may be warranted in specific applications, such as reclassification metrics to gain insight into the value of adding a novel predictor to an established model.

Fig 1

Receiver operating characteristic (ROC) curves for the predicted probabilities without (solid line) and with the tumor marker LDH (dashed line) in the development data set (left) and for the predicted probabilities without the tumor marker LDH from the development data set in the validation data set (right). Threshold probabilities are indicated.

Fig 2

Box plots of predicted probabilities without and with the tumor marker LDH. The discrimination slope is calculated as the difference between the mean predicted probability with and without residual tumor (solid dots indicate means). The difference between discrimination slopes is equivalent to integrated discrimination index (IDI=0.04).

Fig 3

Scatter plot of predicted probabilities without and with the tumor marker LDH (+: tumor; o: necrosis). Some patients with necrosis have higher predicted risks of tumor according to the model without LDH than according to the model with LDH (circles in right lower corner of the graph). For example, we note a patient with necrosis and an original prediction of nearly 60%, who is reclassified as less than 20% risk.

Fig 4

Decision curves for the predicted probabilities without (solid line) and with the tumor marker LDH (dashed line) in the development data set (left) and for the predicted probabilities without the tumor marker LDH from the development data set in the validation data set (right).

Fig 5

Validation plots of prediction models for residual masses in patients with testicular cancer without and with the tumor marker LDH. The arrow indicates the decision threshold of 20% risk of residual tumor.