Partial summary measures of the predictiveness curve

In the evaluation of a biomarker for risk prediction, one can assess the performance of the biomarker in the population of interest by displaying the predictiveness curve. In conjunction with an assessment of the classification accuracy of a biomarker, the predictiveness curve is an important tool for assessing the usefulness of a risk prediction model. Inference for a single biomarker or for multiple biomarkers can be performed using summary measures of the predictiveness curve. We propose two partial summary measures, the partial total gain and the partial proportion of explained variation, that summarize the predictiveness curve over a restricted range of risk. The methods we describe can be used to compare two biomarkers when there are existing thresholds for risk stratification. We describe inferential tools for one and two samples that are shown to have adequate power in a simulation study. The methods are illustrated by assessing the accuracy of a risk score for predicting the onset of Alzheimer's disease.

[1]  D. Freedman,et al.  Some Asymptotic Theory for the Bootstrap , 1981 .

[2]  Nancy R Cook,et al.  Comments on ‘Evaluating the added predictive ability of a new marker: From area under the ROC curve to reclassification and beyond’ by M. J. Pencina et al., Statistics in Medicine (DOI: 10.1002/sim.2929) , 2008, Statistics in medicine.

[3]  Richard Mayeux,et al.  A summary risk score for the prediction of Alzheimer disease in elderly persons. , 2010, Archives of neurology.

[4]  J. Cummings,et al.  Effective pharmacologic management of Alzheimer's disease. , 2007, The American journal of medicine.

[5]  M S Pepe,et al.  A Parametric Roc Model Based Approach for Evaluating the Predictiveness of Continuous Markers in Case-control Studies Suggested Citation , 2022 .

[6]  M Schemper,et al.  Explained variation for logistic regression. , 1996, Statistics in medicine.

[7]  Margaret Sullivan Pepe,et al.  Semiparametric methods for evaluating risk prediction markers in case-control studies. , 2009, Biometrika.

[8]  Debashis Ghosh,et al.  Spline-based models for predictiveness curves and surfaces. , 2010, Statistics and its interface.

[9]  P. Qiu The Statistical Evaluation of Medical Tests for Classification and Prediction , 2005 .

[10]  Margaret Pepe,et al.  Measures to Summarize and Compare the Predictive Capacity of Markers , 2009, The international journal of biostatistics.

[11]  M. Kenward,et al.  An Introduction to the Bootstrap , 2007 .

[12]  J. Morris,et al.  The Uniform Data Set (UDS): Clinical and Cognitive Variables and Descriptive Data From Alzheimer Disease Centers , 2006, Alzheimer disease and associated disorders.

[13]  Margaret Sullivan Pepe,et al.  Assessing risk prediction models in case–control studies using semiparametric and nonparametric methods , 2010, Statistics in medicine.

[14]  Mari Palta,et al.  Properties of R2 statistics for logistic regression , 2006, Statistics in medicine.

[15]  M S Pepe,et al.  Comments on ‘Evaluating the added predictive ability of a new marker: From area under the ROC curve to reclassification and beyond’ by M. J. Pencina et al., Statistics in Medicine (DOI: 10.1002/sim.2929) , 2008, Statistics in medicine.

[16]  J. Haines,et al.  Gene dose of apolipoprotein E type 4 allele and the risk of Alzheimer's disease in late onset families. , 1993, Science.

[17]  Ziding Feng,et al.  Evaluating the Predictiveness of a Continuous Marker , 2007, Biometrics.

[18]  Yingye Zheng,et al.  Integrating the predictiveness of a marker with its performance as a classifier. , 2007, American journal of epidemiology.

[19]  M. Pencina,et al.  Evaluating the added predictive ability of a new marker: From area under the ROC curve to reclassification and beyond , 2008, Statistics in medicine.

[20]  Joseph L. Gastwirth,et al.  The binary regression quantile plot : Assessing the importance of predictors in binary regression visually , 2001 .