Menu Back to Poster-Presentations-Details

P235: Linear Biomarker Combinations to Minimize the Distance of the Closest Point on the ROC Surface to the Perfection Corner

Poster Presenter

Brian Mosier

Biostatistician
EMB Statistical Solutions, LLC
United States

Objectives

Our objective is to improve diagnostic accuracy for biomarkers discriminating three groups by combining multiple biomarkers linearly to minimize the shortest Euclidean distance from the ROC surface to the perfection corner and to provide smaller variance than combinations based on the Youden index.

Method

We conducted an extensive simulation study to evaluate the performance of our methods. We used various sample sizes, correlations between markers, and distributions to generate data. We evaluated our methods based on performance in independent testing data.

Results

Our proposed methods of combining biomarkers to minimize the Euclidean distance are: (1) normality assumption, (2) Box-Cox transformation, (3) kernel-based approach, (4) stepwise procedure, (5) ordinal logistic regression. We generated data from normal, lognormal, and gamma distributions. When data are generated from normal distributions, the normality assumption provides the best performance in terms of diagnostic accuracy (sum of TCRs) and bias, variance, and MSE of the estimated TCRs. We see comparable diagnostic accuracy when compared to a Youden-based approach based on the normality assumption. Sums of TCRs were generally within 0.5% compared to the Youden combination. Almost all normal scenarios saw smaller bias, variance, and MSE for the TCRs for our proposed methods compared to those for the Youden index, making the confidence of our estimates higher than for those from the Youden index, especially for smaller sample sizes. When data are generated from lognormal distributions, the Box-Cox approach has the best performance with regard to diagnostic accuracy of the combination, as well as variance of the estimated TCRs. When compared to the Youden-based combination, our method sees slightly smaller sum of TCRs, but has smaller variance in the estimated TCRs across the board. When data are generated from gamma distributions, the kernel-based approach has the best performance. The combination based on logistic regression had a comparable sum of TCRs, but had much higher variance for the estimated TCRs. The sum of TCRs is higher for several scenarios for our proposed method compared to the Youden-based approach. Overall, we see comparable diagnostic accuracy for our proposed method compared to the Youden-based approach, and in several scenarios, our methods outperform the Youden-based approach. Additionally, our methods provide a smaller variance for the estimated TCRs.

Conclusion

We provide an attractive alternative to the Youden index for combining biomarkers in the three-class setting. We include various parametric and nonparametric approaches under the Euclidean distance framework to accommodate a wide variety of data. Our simulations show a comparable sum of TCRs for our methods when compared to the Youden-based combinations. Additionally, our methods see smaller variances for the estimated TCRs (and bias/MSE where evaluable) than the Youden index does. Interestingly, when data are generated from normal or gamma distributions, the ordinal logistic model in conjunction with the Euclidean distance objective function provide a higher sum of TCRs than the Youden-based approach. This is particularly important because logistic regression is the most popular method of combining biomarkers, largely due to its availability and ease of use with various statistical softwares. As such, when investigators choose to use logistic regression to combine markers, our method will likely outperform the Youden index for cutoff selection for the combined marker derived from the logistic model. Additionally, for the proposed kernel-based approach, when the data are generated from gamma distributions, our method provides a higher sum of TCRs than the Youden-based approach, while still having smaller variances for the estimated TCRs. In conclusion, our proposed methods are an attractive alternative to Youden-based combinations in the three-class setting. We provide full estimation and inferential frameworks for the various proposed approaches. We see comparable diagnostic accuracy for our proposed combinations and oftentimes are able to outperform those derived by the Youden index in terms of both diagnostic accuracy and variance of our estimates.