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Smooth ROC curve estimation via Bernstein polynomials.

ABSTRACT: The receiver operating characteristic (ROC) curve is commonly used to evaluate the accuracy of a diagnostic test for classifying observations into two groups. We propose two novel tuning parameters for estimating the ROC curve via Bernstein polynomial smoothing of the empirical ROC curve. The new estimator is very easy to implement with the naturally selected tuning parameter, as illustrated by analyzing both real and simulated data sets. Empirical performance is investigated through extensive simulation studies with a variety of scenarios where the two groups are both from a single family of distributions (symmetric or right skewed) or one from a symmetric and the other from a right skewed distribution. The new estimator is uniformly more efficient than the empirical ROC estimator, and very competitive to eleven other existing smooth ROC estimators in terms of mean integrated square errors.

SUBMITTER: Wang D

PROVIDER: S-EPMC8148335 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature

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Smooth ROC curve estimation via Bernstein polynomials.

Wang Dongliang D Cai Xueya X

PloS one 20210525 5

The receiver operating characteristic (ROC) curve is commonly used to evaluate the accuracy of a diagnostic test for classifying observations into two groups. We propose two novel tuning parameters for estimating the ROC curve via Bernstein polynomial smoothing of the empirical ROC curve. The new estimator is very easy to implement with the naturally selected tuning parameter, as illustrated by analyzing both real and simulated data sets. Empirical performance is investigated through extensive s ...[more]

PMID: 34032801

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Project description:BackgroundNovel molecular and statistical methods are in rising demand for disease diagnosis and prognosis with the help of recent advanced biotechnology. High-resolution mass spectrometry (MS) is one of those biotechnologies that are highly promising to improve health outcome. Previous literatures have identified some proteomics biomarkers that can distinguish healthy patients from cancer patients using MS data. In this paper, an MS study is demonstrated which uses glycomics to identify ovarian cancer. Glycomics is the study of glycans and glycoproteins. The glycans on the proteins may deviate between a cancer cell and a normal cell and may be visible in the blood. High-resolution MS has been applied to measure relative abundances of potential glycan biomarkers in human serum. Multiple potential glycan biomarkers are measured in MS spectra. With the objection of maximizing the empirical area under the ROC curve (AUC), an analysis method was considered which combines potential glycan biomarkers for the diagnosis of cancer.ResultsMaximizing the empirical AUC of glycomics MS data is a large-dimensional optimization problem. The technical difficulty is that the empirical AUC function is not continuous. Instead, it is in fact an empirical 0-1 loss function with a large number of linear predictors. An approach was investigated that regularizes the area under the ROC curve while replacing the 0-1 loss function with a smooth surrogate function. The constrained threshold gradient descent regularization algorithm was applied, where the regularization parameters were chosen by the cross-validation method, and the confidence intervals of the regression parameters were estimated by the bootstrap method. The method is called TGDR-AUC algorithm. The properties of the approach were studied through a numerical simulation study, which incorporates the positive values of mass spectrometry data with the correlations between measurements within person. The simulation proved asymptotic properties that estimated AUC approaches the true AUC. Finally, mass spectrometry data of serum glycan for ovarian cancer diagnosis was analyzed. The optimal combination based on TGDR-AUC algorithm yields plausible result and the detected biomarkers are confirmed based on biological evidence.ConclusionThe TGDR-AUC algorithm relaxes the normality and independence assumptions from previous literatures. In addition to its flexibility and easy interpretability, the algorithm yields good performance in combining potential biomarkers and is computationally feasible. Thus, the approach of TGDR-AUC is a plausible algorithm to classify disease status on the basis of multiple biomarkers.

Dataset Information

Smooth ROC curve estimation via Bernstein polynomials.

Publications

Smooth ROC curve estimation via Bernstein polynomials.

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