A semiparametric separation curve approach for comparing correlated ROC data from multiple markers

Modeling conditional reference regions: Application to glycemic markers

Many clinical decisions are taken based on the results of continuous diagnostic tests. Usually, only the results of one single test is taken into consideration, the interpretation of which requires a reference range for the healthy population. However, the use of two different tests, can be necessary in the diagnosis of certain diseases. This obliges a bivariate reference region be available for their interpretation. It should also be remembered that reference regions may depend on patient variables (eg, age and sex) independent of the suspected disease. However, few proposals have been made regarding the statistical modeling of such reference regions, and those put forward have always assumed a Gaussian distribution, which can be rather restrictive. The present work describes a new statistical method that allows such reference regions to be estimated with no insistence on the results being normally distributed. The proposed method is based on a bivariate location-scale model that provides probabilistic regions covering a specific percentage of the bivariate data, dependent on certain covariates. The reference region is estimated nonparametrically and the nonlinear effects of continuous covariates via polynomial kernel smoothers in additive models. The bivariate model is estimated using a backfitting algorithm, and the optimal smoothing parameters of the kernel smoothers selected by cross-validation. The model performed satisfactorily in simulation studies under the assumption of non-Gaussian conditions. Finally, the proposed methodology was found to be useful in estimating a reference region for two continuous diagnostic tests for diabetes (fasting plasma glucose and glycated hemoglobin), taking into account the age of the patient.

Unified Least Squares Methods for the Evaluation of Diagnostic Tests With the Gold Standard

The article proposes a unified least squares method to estimate the receiver operating characteristic (ROC) parameters for continuous and ordinal diagnostic tests, such as cancer biomarkers. The method is based on a linear model framework using the empirically estimated sensitivities and specificities as input "data." It gives consistent estimates for regression and accuracy parameters when the underlying continuous test results are normally distributed after some monotonic transformation. The key difference between the proposed method and the method of Tang and Zhou lies in the response variable. The response variable in the latter is transformed empirical ROC curves at different thresholds. It takes on many values for continuous test results, but few values for ordinal test results. The limited number of values for the response variable makes it impractical for ordinal data. However, the response variable in the proposed method takes on many more distinct values so that the method yields valid estimates for ordinal data. Extensive simulation studies are conducted to investigate and compare the finite sample performance of the proposed method with an existing method, and the method is then used to analyze 2 real cancer diagnostic example as an illustration.

Least squares regression methods for clustered ROC data with discrete covariates

The receiver operating characteristic (ROC) curve is a popular tool to evaluate and compare the accuracy of diagnostic tests to distinguish the diseased group from the nondiseased group when test results from tests are continuous or ordinal. A complicated data setting occurs when multiple tests are measured on abnormal and normal locations from the same subject and the measurements are clustered within the subject. Although least squares regression methods can be used for the estimation of ROC curve from correlated data, how to develop the least squares methods to estimate the ROC curve from the clustered data has not been studied. Also, the statistical properties of the least squares methods under the clustering setting are unknown. In this article, we develop the least squares ROC methods to allow the baseline and link functions to differ, and more importantly, to accommodate clustered data with discrete covariates. The methods can generate smooth ROC curves that satisfy the inherent continuous property of the true underlying curve. The least squares methods are shown to be more efficient than the existing nonparametric ROC methods under appropriate model assumptions in simulation studies. We apply the methods to a real example in the detection of glaucomatous deterioration. We also derive the asymptotic properties of the proposed methods.

An additive selection of markers to improve diagnostic accuracy based on a discriminatory measure

RATIONALE AND OBJECTIVES

The estimation of the area under the receiver operating characteristic (ROC) curve (AUC) often relies on the assumption that the truly positive population tends to have higher marker results than the truly negative population. The authors propose a discriminatory measure to relax such an assumption and apply the measure to identify the appropriate set of markers for combination.

MATERIALS AND METHODS

The proposed measure is based on the maximum of the AUC and 1-AUC. The existing methods are applied to estimate the measure. The subset of markers is selected using a combination method that maximizes a function of the proposed discriminatory score with the number of markers as a penalty in the function.

RESULTS

The properties of the estimators for the proposed measure were studied through large-scale simulation studies. The application was illustrated through a real example to identify the set of markers to combine.

CONCLUSION

Simulation results showed excellent small-sample performance of the estimators for the proposed measure. The application in the example yielded a reasonable subset of markers for combination.