On Combination of Elliptically Distributed Biomarkers to Improve Diagnostic Accuracy
Open AccessDiagnostic biomarkers play a critical role in biomedical research such as diagnosis and prediction of diseases, selection of treatments for patients, etc. It has been widely accepted by medical researchers that diagnosis based on one single biomarker may not provide sufficient accuracy. To improve the diagnostic performance, researchers proposed methods to combine multiple biomarkers and the corresponding measurements to help clinicians make better diagnostic judgment. Considerable research results have been derived based on the multivariate normal distribution, especially for the combination based on AUC values. In chapter 2, the properties of the ROC curve function under the multivariate normal distribution are discussed. We find that if the case and control group have different covariance matrices for the binormal model, there would always exist a segment of ROC curve which is lower than the chance line.In addition, the normality is indeed a hard assumption in diagnostic medicine. It is common in practice that many biomarkers follow distributions that are far from normality, even after popular transformations. To make the combination method more useful in practice, we extend the combination of multiple biomarkers to a broader distribution family -- elliptical distributions. It is well known that the likelihood ratio combination is the optimal combination but it's sensitive to the distribution assumption and complicated to calculate. Based on the assumption of elliptical distribution, we study the ROC curve function of likelihood ratio combination in chapter 4. The empirical estimation of elliptical likelihood ratio combination is proposed. Except for the optimal combination, we also extend the best linear combination AUC to the elliptical distribution and derive the linear combination ROC curve function of elliptically distributed biomarkers. We find that the best linear combination only depends on the Mahalanobis distance of elliptical distributions. Many researchers focused on combinations to improve the resulting AUC value while the AUC still has drawbacks. Therefore, we research the combination of more indices besides AUC in order to improve the diagnosis performance. We develop the linear combination based on projected length (PLC) of ROC curves in the chapter 6. It is concluded that the best linear coefficient of PLC is the same as the combination coefficient of AUC under elliptical distribution assumption.The proposed methods are applied to two case-control studies. The first example is predicting autism in children. Compared with the empirical best linear combination, the AUC value of elliptical likelihood ratio combination is increased by 7.69% in predicting autism, and the PLC value is improved by 16.78%. The AUC and PLC value of elliptical likelihood ratio combination is increased by 1.85% and 5.15% from normal likelihood ratio combination. Another application is the diagnosis of neural tube defects. We find that our method improve by 11.43% and 23.29% from normal likelihood ratio combined AUC value and empirical best linear combination, respectively.
- All rights reserved
Notice to Authors
If you are the author of this work and you have any questions about the information on this page, please use the Contact form to get in touch with us.