Bayesian ROC curve estimation under binormality using an ordinal category likelihood

Receiver operating characteristic (ROC) curve has been widely used in medical diagnosis. Various methods are proposed to estimate ROC curve parameters under the binormal model. In this paper, we propose a Bayesian estimation method from the continuously distributed data which is constituted by the truth-state-runs in the rank-ordered data. By using an ordinal category data likelihood and following the Metropolis–Hastings (M–H) procedure, we compute the posterior distribution of the binormal parameters, as well as the group boundaries parameters. Simulation studies and real data analysis are conducted to evaluate our Bayesian estimation method.     

ROC curve estimation based on local smoothing

ROC curve is a graphical representation of the relationship between sensitivity and specificity of a diagnostic test. It is a popular tool for evaluating and comparing different diagnostic tests in medical sciences. In the literature,the ROC curve is often estimated empirically based on an empirical distribution function estimator and an empirical quantile function estimator. In this paper an alternative nonparametric procedure to estimate the ROC Curve is suggested which is based on local smoothing techniques. Several numerical examples are presented to evaluate the performance of this procedure.     

A test for crossing receiver operating characteristic (roc) curves

The receiver operating characteristic (ROC) curve gives a graphical representation of sensitivity and specificity of a prediction model when varying the decision treshold on a diagnostic criterion. A classical test for comparing the overall accuracies for two models -1 and 2- is based on the difference between ROC curves areas - related to its standard error. This test is designed for the situation where ROC curve 1 caps ROC curve 2. Often both curves cross :in this paper, a new test, based on the integrated difference between the curves, is proposed to deal with this situation. In a simulation experiment, the new test was less powerful than the old test for detecting an overall superiority, but much more powerfull against the crossing alternative.     

Nonparametric estimation of the ROC curve for length-biased and right-censored data

Abstract

ROC curve is a fundamental evaluation tool in medical researches and survival analysis. The estimation of ROC curve has been studied extensively with complete data and right-censored survival data. However, these methods are not suitable to analyze the length-biased and right-censored data. Since this kind of data includes the auxiliary information that truncation time and residual time share the same distribution, the two new estimators for the ROC curve are proposed by taking into account this auxiliary information to improve estimation efficiency. Numerical simulation studies with different assumed cases and real data analysis are conducted.     

An alternative method for global and partial comparison of two diagnostic systems based on ROC curves

In this paper, an alternative method for the comparison of two diagnostic systems based on receiver operating characteristic (ROC) curves is presented. ROC curve analysis is often used as a statistical tool for the evaluation of diagnostic systems. However, in general, the comparison of ROC curves is not straightforward, in particular, when they cross each other. A similar difficulty is also observed in the multi-objective optimization field where sets of solutions defining fronts must be compared with a multi-dimensional space. Thus, the proposed methodology is based on a procedure used to compare the performance of distinct multi-objective optimization algorithms. In general, methods based on the area under the ROC curves are not sensitive to the existence of crossing points between the curves. The new approach can deal with this situation and also allows the comparison of partial portions of ROC curves according to particular values of sensitivity and specificity of practical interest. Simulations results are presented. For illustration purposes, considering real data from newborns with very low birthweight, the new method was applied in order to discriminate the better index for evaluating the risk of death.     

Combining ROC curves using MAMSE weighted distributions

The receiver operating characteristic (ROC) curve can be used to evaluate the properties of a diagnostic test from the distribution of a variable on the healthy and diseased populations. The minimum averaged mean squared error (MAMSE) weights were developed to handle data from different sources by adjusting the relative contribution of each data source. The authors use the MAMSE weights to infer the ROC curve of a diagnostic test based on raw data from multiple studies. The proposed estimates are consistent and Monte Carlo simulations show favourable finite sample performance. The method is illustrated in a case study where progesterone level is used to detect ectopic pregnancies and abortions from other natural causes. The Canadian Journal of Statistics 46: 298–315; 2018 © 2018 Statistical Society of Canada     

Nonparametric estimation of the ROC curve based on smoothed empirical distribution functions

The receiver operating characteristic (ROC) curve is a graphical representation of the relationship between false positive and true positive rates. It is a widely used statistical tool for describing the accuracy of a diagnostic test. In this paper we propose a new nonparametric ROC curve estimator based on the smoothed empirical distribution functions. We prove its strong consistency and perform a simulation study to compare it with some other popular nonparametric estimators of the ROC curve. We also apply the proposed method to a real data set.     

ROC Curves in Non‐Parametric Location‐Scale Regression Models

Abstract. The receiver operating characteristic (ROC) curve is a tool of extensive use to analyse the discrimination capability of a diagnostic variable in medical studies. In certain situations, the presence of a covariate related to the diagnostic variable can increase the discriminating power of the ROC curve. In this article, we model the effect of the covariate over the diagnostic variable by means of non‐parametric location‐scale regression models. We propose a new non‐parametric estimator of the conditional ROC curve and study its asymptotic properties. We also present some simulations and an illustration to a data set concerning diagnosis of diabetes.     

The diagnostic accuracy of a composite index increases as the number of partitions of the components increases and when specific weights are assigned to each component

The aim of this work was to evaluate whether the number of partitions of index components and the use of specific weights for each component influence the diagnostic accuracy of a composite index. Simulation studies were conducted in order to compare the sensitivity, specificity and area under the ROC curve (AUC) of indices constructed using equal number of components but different number of partitions for all components. Moreover, the odds ratio obtained from the univariate logistic regression model for each component was proposed as potential weight. The current simulation results showed that the sensitivity, specificity and AUC of an index increase as the number of partitions of components increases. However, the rate that the diagnostic accuracy increases is reduced as the number of partitions increases. In addition, it was found that the diagnostic accuracy of the weighted index developed using the proposed weights is higher compared with that of the corresponding un-weighted index. The use of large-scale index components and the use of effect size measures (i.e. odds ratios, ORs) of index components as potential weights are proposed in order to obtain indices with high diagnostic accuracy for a particular binary outcome.     

Nonparametric and semiparametric estimation of the three way receiver operating characteristic surface

In many situations the diagnostic decision is not limited to a binary choice. Binary statistical tools such as receiver operating characteristic (ROC) curve and area under the ROC curve (AUC) need to be expanded to address three-category classification problem. Previous authors have suggest various ways to model the extension of AUC but not the ROC surface. Only simple parametric approaches are proposed for modeling the ROC measure under the assumption that test results all follow normal distributions. We study the estimation methods of three-dimensional ROC surfaces with nonparametric and semiparametric estimators. Asymptotical results are provided as a basis for statistical inference. Simulation studies are performed to assess the validity of our proposed methods in finite samples. We consider an Alzheimer's disease example from a clinical study in the US as an illustration. The nonparametric and semiparametric modelling approaches for the three way ROC analysis can be readily generalized to diagnostic problems with more than three classes.     

Prediction of disease status: A regressive model approach for repeated measures

In this paper, regressive models are proposed for modeling a sequence of transitions in longitudinal data. These models are employed to predict the future status of the outcome variable of the individuals on the basis of their underlying background characteristics or risk factors. The estimation of parameters and also estimates of conditional and unconditional probabilities are shown for repeated measures. The goodness of fit tests are extended in this paper on the basis of the deviance and the Hosmer–Lemeshow procedures and generalized to repeated measures. In addition, to measure the suitability of the proposed models for predicting the disease status, we have extended the ROC curve approach to repeated measures. The procedure is shown for the conditional models for any order as well as for the unconditional model, to predict the outcome at the end of the study. The test procedures are also suggested. For testing the differences between areas under the ROC curves in subsequent follow-ups, two different test procedures are employed, one of which is based on permutation test. In this paper, an unconditional model is proposed on the basis of conditional models for the disease progression of depression among the elderly population in the USA on the basis of the Health and Retirement Survey data collected longitudinally. The illustration shows that the disease progression observed conditionally can be employed to predict the outcome and the role of selected variables and the previous outcomes can be utilized for predictive purposes. The results show that the percentage of correct predictions of a disease is quite high and the measures of sensitivity and specificity are also reasonably impressive. The extended measures of area under the ROC curve show that the models provide a reasonably good fit in terms of predicting the disease status during a long period of time. This procedure will have extensive applications in the field of longitudinal data analysis where the objective is to obtain estimates of unconditional probabilities on the basis of series of conditional transitional models.     

An application of lomax distributions in receiver operating characteristic(roc)curve analysis

Receiver operating characteristic(ROC)curves are useful for studying the performance of diagnostic tests. ROC curves occur in many fields of applications including psychophysics, quality control and medical diagnostics. In practical situations, often the responses to a diagnostic test are classified into a number of ordered categories. Such data are referred to as ratings data. It is typically assumed that the underlying model is based on a continuous probability distribution. The ROC curve is then constructed from such data using this probability model. Properties of the ROC curve are inherited from the model. Therefore, understanding the role of different probability distributions in ROC modeling is an interesting and important area of research. In this paper the Lomax distribution is considered as a model for ratings data and the corresponding ROC curve is derived. The maximum likelihood estimation procedure for the related parameters is discussed. This procedure is then illustrated in the analysis of a neurological data example.     

Semi-empirical likelihood inference for the ROC curve with missing data

The receiver operating characteristic (ROC) curve is one of the most commonly used methods to compare the diagnostic performance of two or more laboratory or diagnostic tests. In this paper, we propose semi-empirical likelihood based confidence intervals for ROC curves of two populations, where one population is parametric and the other one is non-parametric and both have missing data. After imputing missing values, we derive the semi-empirical likelihood ratio statistic and the corresponding likelihood equations. It is shown that the log-semi-empirical likelihood ratio statistic is asymptotically scaled chi-squared. The estimating equations are solved simultaneously to obtain the estimated lower and upper bounds of semi-empirical likelihood confidence intervals. We conduct extensive simulation studies to evaluate the finite sample performance of the proposed empirical likelihood confidence intervals with various sample sizes and different missing probabilities.     

Fitting Roc Curves Using Non-linear Binomial Regression

The performance of a diagnostic test is summarized by its receiver operating characteristic (ROC) curve. Empirical data on a test's performance often come in the form of observed true positive and false positive relative frequencies, under varying conditions. This paper describes a family of models for analysing such data. The underlying ROC curves are specified by a shift parameter, a shape parameter and a link function. Both the position along the ROC curve and the shift parameter are modelled linearly. The shape parameter enters the model non-linearly but in a very simple manner. One simple application is to the meta-analysis of independent studies of the same diagnostic test, illustrated on some data of Moses, Shapiro & Littenberg (1993). A second application to so-called vigilance data is given, where ROC curves differ across subjects, and modelling of the position along the ROC curve is of primary interest.     

The average area under correlated receiver operating characteristic curves: a nonparametric approach based on generalized two-sample Wilcoxon statistics

It is well known that, when sample observations are independent, the area under the receiver operating characteristic (ROC) curve corresponds to the Wilcoxon statistics if the area is calculated by the trapezoidal rule. Correlated ROC curves arise often in medical research and have been studied by various parametric methods. On the basis of the Mann–Whitney U-statistics for clustered data proposed by Rosner and Grove, we construct an average ROC curve and derive nonparametric methods to estimate the area under the average curve for correlated ROC curves obtained from multiple readers. For the more complicated case where, in addition to multiple readers examining results on the same set of individuals, two or more diagnostic tests are involved, we derive analytic methods to compare the areas under correlated average ROC curves for these diagnostic tests. We demonstrate our methods in an example and compare our results with those obtained by other methods. The nonparametric average ROC curve and the analytic methods that we propose are easy to explain and simple to implement.     

Non‐parametric estimation for time-dependent AUC

The area under the receiver operating characteristic (ROC) curve (AUC) is one of the commonly used measure to evaluate or compare the predictive ability of markers to the disease status. Motivated by an angiographic coronary artery disease (CAD) study, our objective is mainly to evaluate and compare the performance of several baseline plasma levels in the prediction of CAD-related vital status over time. Based on censored survival data, the non-parametric estimators are proposed for the time-dependent AUC. The limiting Gaussian processes of the estimators and the estimated asymptotic variance–covariance functions enable us to further construct confidence bands and develop testing procedures. Applications and finite sample properties of the proposed estimation methods and inference procedures are demonstrated through the CAD-related death data from the British Columbia Vital Statistics Agency and Monte Carlo simulations.     

Compare diagnostic tests using transformation-invariant smoothed ROC curves()

Receiver operating characteristic (ROC) curve, plotting true positive rates against false positive rates as threshold varies, is an important tool for evaluating biomarkers in diagnostic medicine studies. By definition, ROC curve is monotone increasing from 0 to 1 and is invariant to any monotone transformation of test results. And it is often a curve with certain level of smoothness when test results from the diseased and non-diseased subjects follow continuous distributions. Most existing ROC curve estimation methods do not guarantee all of these properties. One of the exceptions is Du and Tang (2009) which applies certain monotone spline regression procedure to empirical ROC estimates. However, their method does not consider the inherent correlations between empirical ROC estimates. This makes the derivation of the asymptotic properties very difficult. In this paper we propose a penalized weighted least square estimation method, which incorporates the covariance between empirical ROC estimates as a weight matrix. The resulting estimator satisfies all the aforementioned properties, and we show that it is also consistent. Then a resampling approach is used to extend our method for comparisons of two or more diagnostic tests. Our simulations show a significantly improved performance over the existing method, especially for steep ROC curves. We then apply the proposed method to a cancer diagnostic study that compares several newly developed diagnostic biomarkers to a traditional one.     

Detecting diagnostic accuracy of two biomarkers through a bivariate log-normal ROC curve

In biomedical research, two or more biomarkers may be available for diagnosis of a particular disease. Selecting one single biomarker which ideally discriminate a diseased group from a healthy group is confront in a diagnostic process. Frequently, most of the people use the accuracy measure, area under the receiver operating characteristic (ROC) curve to choose the best diagnostic marker among the available markers for diagnosis. Some authors have tried to combine the multiple markers by an optimal linear combination to increase the discriminatory power. In this paper, we propose an alternative method that combines two continuous biomarkers by direct bivariate modeling of the ROC curve under log-normality assumption. The proposed method is applied to simulated data set and prostate cancer diagnostic biomarker data set.     

Two transformation models for estimating an ROC curve derived from continuous data

A receiver operating characteristic (ROC) curve is a plot of two survival functions, derived separately from the diseased and healthy samples. A special feature is that the ROC curve is invariant to any monotone transformation of the measurement scale. We propose and analyse semiparametric and parametric transformation models for this two-sample problem. Following an unspecified or specified monotone transformation, we assume that the healthy and diseased measurements have two normal distributions with different means and variances. Maximum likelihood algorithms for estimating ROC curve parameters are developed. The proposed methods are illustrated on the marker CA125 in the diagnosis of gastric cancer.     

A Flexible Method for Estimating the ROC Curve

In this paper we propose a flexible method for estimating a receiver operating characteristic (ROC) curve that is based on a continuous-scale test. The approach is easily understood and efficiently computed, and robust to the smooth parameter selection, which needs intensive computation when using local polynomial and smoothing spline techniques. The results from our simulation experiment indicate that the moderate-sample numerical performance of our estimator is better than the empirical ROC curve estimator and comparable to the local linear estimator. The availability of easy implementation is also illustrated by our simulation. We apply the proposed method to two real data sets.