Two-sample survival probability curves: A graphical approach for the analysis of time to event data in clinical trials

With the aim to improve the communication of trial results, we introduce a novel graphical approach that complements the analysis of time to event outcomes in two-arm randomized trials. We define the so-called two-sample survival probability curve and propose a nonparametric estimator of the curve based on a random walk using Kaplan-Meier survival estimates for the two arms. We then use the estimated curve to visualize treatment effect as well as potential effect modification of factors of interest. We also propose to estimate two-sample survival probability curves within the framework of the Cox model to graphically assess model fit. The proposed two-sample survival probability plot puts trials in a standardized [0,1] × [0,1] space, allowing for a simple visualization of the main effect, effect modification, and the adequacy of a model fit.

Accuracy and cut-off point selection in three-class classification problems using a generalization of the Youden index

We study properties of the index J(3), defined as the accuracy, or the maximum correct classification, for a given three-class classification problem. Specifically, using J(3) one can assess the discrimination between the three distributions and obtain an optimal pair of cut-off points c(1)<c(2) in the sense that the sum of the correct classification proportions will be maximized. It also serves as the generalization of the Youden index in three-class problems. Parametric and non-parametric approaches for estimation and testing are considered and methods are applied to data from an MRS study on human immunodeficiency virus (HIV) patients.

Lehmann family of ROC curves

Receiver operating characteristic (ROC) curves evaluate the discriminatory power of a continuous marker to predict a binary outcome. The most popular parametric model for an ROC curve is the binormal model, which assumes that the marker, after a monotone transformation, is normally distributed conditional on the outcome. Here, the authors present an alternative to the binormal model based on the Lehmann family, also known as the proportional hazards specification. The resulting ROC curve and its functionals (such as the area under the curve and the sensitivity at a given level of specificity) have simple analytic forms. Closed-form expressions for the functional estimates and their corresponding asymptotic variances are derived. This family accommodates the comparison of multiple markers, covariate adjustments, and clustered data through a regression formulation. Evaluation of the underlying assumptions, model fitting, and model selection can be performed using any off-the-shelf proportional hazards statistical software package.

Childhood predictors of young-onset type 2 diabetes

OBJECTIVE

Optimal prevention of young-onset type 2 diabetes requires identification of the early-life modifiable risk factors. We aimed to do this using longitudinal data in 1,604 5- to 19-year-old initially nondiabetic American Indians.

RESEARCH DESIGN AND METHODS

For type 2 diabetes prediction, we derived an optimally weighted, continuously distributed, standardized multivariate score (zMS) comprising commonly measured metabolic, anthropometric, and vascular traits (i.e., fasting and 2-h glucose, A1C, BMI, waist circumference, fasting insulin, HDL cholesterol, triglycerides, and blood pressures) and compared the predictive power for each feature against zMS.

RESULTS

In separate Cox proportional hazard models, adjusted for age, sex, and ethnicity, zMS and each of its component risk factors were associated with incident type 2 diabetes. Stepwise proportional hazards models selected fasting glucose, 2-h glucose, HDL cholesterol, and BMI as independent diabetes predictors; individually, these were weaker predictors than zMS (P < 0.01). However, a parsimonious summary score combining only these variables had predictive power similar to that of zMS (P = 0.33). Although intrauterine diabetes exposure or parental history of young-onset diabetes increased a child's absolute risk of developing diabetes, the magnitude of the diabetes-risk relationships for zMS and the parsimonious score were similar irrespective of familial risk factors.

CONCLUSIONS

We have determined the relative value of the features of the metabolic syndrome in childhood for the prediction of subsequent type 2 diabetes. Our findings suggest that strategies targeting obesity, dysregulated glucose homeostasis, and low HDL cholesterol during childhood and adolescence may have the most success in preventing diabetes.

Matching in studies of classification accuracy: implications for analysis, efficiency, and assessment of incremental value

In case-control studies evaluating the classification accuracy of a marker, controls are often matched to cases with respect to factors associated with the marker and disease status. In contrast with matching in epidemiologic etiology studies, matching in the classification setting has not been rigorously studied. In this article, we consider the implications of matching in terms of the choice of statistical analysis, efficiency, and assessment of the incremental value of the marker over the matching covariates. We find that adjustment for the matching covariates is essential, as unadjusted summaries of classification accuracy can be biased. In many settings, matching is the most efficient covariate-dependent sampling scheme, and we provide an expression for the optimal matching ratio. However, we also show that matching greatly complicates estimation of the incremental value of the marker. We recommend that matching be carefully considered in the context of these findings.

A solution for the most basic optimization problem associated with an ROC curve

In a few cases, such as early pregnancy tests, the test results are dichotomous; many diagnostic tests, however, give results which are not binary. In the diagnosis of prostate cancer, prostate-specific antigen test result is on a continuous scale; or, in radiology, assessment of mammograms is on an ordinal scale. In such cases, the accuracy of the marker or test is often first summarized in a receiver operating characteristic (ROC) curve and then as the area under that curve. The area under the ROC curve, however, only shows the 'potential' of a marker; sooner or later, for practical uses, we still need to dichotomize the test result so that we can classify subjects as 'diseased' or 'healthy'. Finding an 'optimal' cutpoint to dichotomize a continuous marker is desirable and is a very basic problem but, in all or most cases, cutpoints used in practice are arbitrary. The difficulty lies in our failure to define and justify a criterion for optimality. In this paper, we will propose a solution by maximizing a well-known parameter--the Youden's Index--within the framework of the ROC curve.

Adding in Vivo Quantitative1H MR Spectroscopy to Improve Diagnostic Accuracy of Breast MR Imaging: Preliminary Results of Observer Performance Study at 4.0 T

PURPOSE

To determine whether the addition of in vivo quantitative hydrogen 1 (1H) magnetic resonance (MR) spectroscopy can improve the radiologist's diagnostic accuracy in interpreting breast MR images to distinguish benign from malignant lesions.

MATERIALS AND METHODS

The study was approved by the institutional review board and, where appropriate, was compliant with the Health Insurance Portability and Accountability Act. All patients provided written informed consent. Fifty-five breast MR imaging cases-one lesion each in 55 patients aged 24-66 years with biopsy-confirmed findings-were retrospectively evaluated by four radiologists. Patients were examined with contrast material-enhanced fat-suppressed T1-weighted 4.0-T MR imaging. The concentration of total choline-containing compounds (tCho) was quantified by using single-voxel 1H MR spectroscopy. For each case, the radiologists were asked to give the percentage probability of malignancy, the Breast Imaging and Reporting Data System category, and a recommendation for patient treatment. Two interpretations were performed for each case: The initial interpretation was based on the lesion's morphologic features and time-signal intensity curve, and the second interpretation was based on the lesion's morphologic features, time-signal intensity curve, and tCho concentration. Receiver operating characteristic (ROC), Wilcoxon signed rank, kappa statistic, and accuracy (based on the area under the ROC curve) analyses were performed.

RESULTS

Of the 55 lesions evaluated, 35 were invasive carcinomas and 20 were benign. The addition of 1H MR spectroscopy resulted in higher sensitivity, specificity, accuracy, and interobserver agreement for all four radiologists. More specifically, two of the four radiologists achieved a significant improvement in sensitivity (P=.03, P=.03), and all four radiologists achieved a significant improvement in accuracy (P = .01, P = .05, P = .009, P < .001).

CONCLUSION

Current study results suggest that the addition of quantitative 1H MR spectroscopy to the breast MR imaging examination may help to improve the radiologist's ability to distinguish benign from malignant breast lesions.

An interpretation for the ROC curve and inference using GLM procedures

The accuracy of a medical diagnostic test is often summarized in a receiver operating characteristic (ROC) curve. This paper puts forth an interpretation for each point on the ROC curve as being a conditional probability of a test result from a random diseased subject exceeding that from a random nondiseased subject. This interpretation gives rise to new methods for making inference about ROC curves. It is shown that inference can be achieved with binary regression techniques applied to indicator variables constructed from pairs of test results, one component of the pair being from a diseased subject and the other from a nondiseased subject. Within the generalized linear model (GLM) binary regression framework, ROC curves can be estimated, and we highlight a new semiparametric estimator. Covariate effects can also be evaluated with the GLM models. The methodology is applied to a pancreatic cancer dataset where we use the regression framework to compare two different serum biomarkers. Asymptotic distribution theory is developed to facilitate inference and to provide insight into factors influencing variability of estimated model parameters.

The interpretation of diagnostic tests

Laboratory diagnostic tests are central in the practice of modern medicine. Common uses include screening a specific population for evidence of disease and confirming or ruling out a tentative diagnosis in an individual patient. The interpretation of a diagnostic test result depends on both the ability of the test to distinguish diseased from nondiseased subjects and the particular characteristics of the patient and setting in which the test is being used. This article reviews statistical methodology for assessing laboratory diagnostic test accuracy and interpreting individual test results, with an emphasis on diagnostic tests that yield a continuous measurement. The article begins with a summary of basic concepts and terminology, then briefly discusses study design and reviews methods for assessing the accuracy of a single diagnostic test, comparing the accuracy of two or more diagnostic tests and interpreting individual test results.