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Combining multiple biomarkers linearly to maximize the partial area under the ROC curve.

ABSTRACT: It is now common in clinical practice to make clinical decisions based on combinations of multiple biomarkers. In this paper, we propose new approaches for combining multiple biomarkers linearly to maximize the partial area under the receiver operating characteristic curve (pAUC). The parametric and nonparametric methods that have been developed for this purpose have limitations. When the biomarker values for populations with and without a given disease follow a multivariate normal distribution, it is easy to implement our proposed parametric approach, which adopts an alternative analytic expression of the pAUC. When normality assumptions are violated, a kernel-based approach is presented, which handles multiple biomarkers simultaneously. We evaluated the proposed as well as existing methods through simulations and discovered that when the covariance matrices for the disease and nondisease samples are disproportional, traditional methods (such as the logistic regression) are more likely to fail to maximize the pAUC while the proposed methods are more robust. The proposed approaches are illustrated through application to a prostate cancer data set, and a rank-based leave-one-out cross-validation procedure is proposed to obtain a realistic estimate of the pAUC when there is no independent validation set available.

SUBMITTER: Yan Q

PROVIDER: S-EPMC6469690 | biostudies-literature | 2018 Feb

REPOSITORIES: biostudies-literature

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Combining multiple biomarkers linearly to maximize the partial area under the ROC curve.

Yan Qingxiang Q Bantis Leonidas E LE Stanford Janet L JL Feng Ziding Z

Statistics in medicine 20171030 4

It is now common in clinical practice to make clinical decisions based on combinations of multiple biomarkers. In this paper, we propose new approaches for combining multiple biomarkers linearly to maximize the partial area under the receiver operating characteristic curve (pAUC). The parametric and nonparametric methods that have been developed for this purpose have limitations. When the biomarker values for populations with and without a given disease follow a multivariate normal distribution, ...[more]

PMID: 29082535

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Project description:BACKGROUND: The receiver operating characteristic (ROC) curve is a fundamental tool to assess the discriminant performance for not only a single marker but also a score function combining multiple markers. The area under the ROC curve (AUC) for a score function measures the intrinsic ability for the score function to discriminate between the controls and cases. Recently, the partial AUC (pAUC) has been paid more attention than the AUC, because a suitable range of the false positive rate can be focused according to various clinical situations. However, existing pAUC-based methods only handle a few markers and do not take nonlinear combination of markers into consideration. RESULTS: We have developed a new statistical method that focuses on the pAUC based on a boosting technique. The markers are combined componentially for maximizing the pAUC in the boosting algorithm using natural cubic splines or decision stumps (single-level decision trees), according to the values of markers (continuous or discrete). We show that the resulting score plots are useful for understanding how each marker is associated with the outcome variable. We compare the performance of the proposed boosting method with those of other existing methods, and demonstrate the utility using real data sets. As a result, we have much better discrimination performances in the sense of the pAUC in both simulation studies and real data analysis. CONCLUSIONS: The proposed method addresses how to combine the markers after a pAUC-based filtering procedure in high dimensional setting. Hence, it provides a consistent way of analyzing data based on the pAUC from maker selection to marker combination for discrimination problems. The method can capture not only linear but also nonlinear association between the outcome variable and the markers, about which the nonlinearity is known to be necessary in general for the maximization of the pAUC. The method also puts importance on the accuracy of classification performance as well as interpretability of the association, by offering simple and smooth resultant score plots for each marker.

Project description:BackgroundIncremental value (IncV) evaluates the performance change between an existing risk model and a new model. Different IncV metrics do not always agree with each other. For example, compared with a prescribed-dose model, an ovarian-dose model for predicting acute ovarian failure has a slightly lower area under the receiver operating characteristic curve (AUC) but increases the area under the precision-recall curve (AP) by 48%. This phenomenon of disagreement is not uncommon, and can create confusion when assessing whether the added information improves the model prediction accuracy.MethodsIn this article, we examine the analytical connections and differences between the AUC IncV (ΔAUC) and AP IncV (ΔAP). We also compare the true values of these two IncV metrics in a numerical study. Additionally, as both are semi-proper scoring rules, we compare them with a strictly proper scoring rule: the IncV of the scaled Brier score (ΔsBrS) in the numerical study.ResultsWe demonstrate that ΔAUC and ΔAP are both weighted averages of the changes (from the existing model to the new one) in separating the risk score distributions between events and non-events. However, ΔAP assigns heavier weights to the changes in higher-risk regions, whereas ΔAUC weights the changes equally. Due to this difference, the two IncV metrics can disagree, and the numerical study shows that their disagreement becomes more pronounced as the event rate decreases. In the numerical study, we also find that ΔAP has a wide range, from negative to positive, but the range of ΔAUC is much smaller. In addition, ΔAP and ΔsBrS are highly consistent, but ΔAUC is negatively correlated with ΔsBrS and ΔAP when the event rate is low.ConclusionsΔAUC treats the wins and losses of a new risk model equally across different risk regions. When neither the existing or new model is the true model, this equality could attenuate a superior performance of the new model for a sub-region. In contrast, ΔAP accentuates the change in the prediction accuracy for higher-risk regions.

Project description:Rationale and objectivesThe "binormal" model is the most frequently used tool for parametric receiver operating characteristic (ROC) analysis. The binormal ROC curves can have "improper" (non-concave) shapes that are unrealistic in many practical applications, and several tools (eg, PROPROC) have been developed to address this problem. However, due to the general robustness of binormal ROCs, the improperness of the fitted curves might carry little consequence for inferences about global summary indices, such as the area under the ROC curve (AUC). In this work, we investigate the effect of severe improperness of fitted binormal ROC curves on the reliability of AUC estimates when the data arise from an actually proper curve.Materials and methodsWe designed theoretically proper ROC scenarios that induce severely improper shape of fitted binormal curves in the presence of well-distributed empirical ROC points. The binormal curves were fitted using maximum likelihood approach. Using simulations, we estimated the frequency of severely improper fitted curves, bias of the estimated AUC, and coverage of 95% confidence intervals (CIs). In Appendix S1, we provide additional information on percentiles of the distribution of AUC estimates and bias when estimating partial AUCs. We also compared the results to a reference standard provided by empirical estimates obtained from continuous data.ResultsWe observed up to 96% of severely improper curves depending on the scenario in question. The bias in the binormal AUC estimates was very small and the coverage of the CIs was close to nominal, whereas the estimates of partial AUC were biased upward in the high specificity range and downward in the low specificity range. Compared to a non-parametric approach, the binormal model led to slightly more variable AUC estimates, but at the same time to CIs with more appropriate coverage.ConclusionsThe improper shape of the fitted binormal curve, by itself, ie, in the presence of a sufficient number of well-distributed points, does not imply unreliable AUC-based inferences.

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Combining multiple biomarkers linearly to maximize the partial area under the ROC curve.

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Combining multiple biomarkers linearly to maximize the partial area under the ROC curve.

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