A Marginal Model Approach for Analysis of Multi-reader Multi-test Receiver Operating Characteristic (ROC) Data

The receiver operating characteristic (ROC) curve is a popular tool to characterize the capabilities of diagnostic tests with continuous or ordinal responses. One common design for assessing the accuracy of diagnostic tests is to have each patient examined by multiple readers with multiple tests; this design is most commonly used in a radiology setting, where the results of diagnostic tests depend on a radiologist\u27s subjective interpretation. The most widely used approach for analyzing data from such a study is the Dorfman-Berbaum-Metz (DBM) method (Dorfman, Berbaum and Metz, 1992) which utilizes a standard analysis of variance (ANOVA) model for the jackknife pseudovalues of the AUCs. Although the DBM method performs well in previous simulation studies, there is no clear theoretical basis for this approach. In this paper, focusing on continuous outcomes, we investigate the theoretical basis of this approach. Our result indicates that the DBM method does not satisfy the regular assumptions for standard ANOVA models, and thus might lead to erroneous inference. We then propose a marginal model approach based on the AUCs which can adjust for covariates as well. We derive consistent and asymptotically normal estimators for the regression coe±cients. We compare our approach with the DBM method via simulation and by an application to data from a breast cancer study. The simulation results show that both our new method and the DBM method perform well when the accuracy of tests under the study is the same and that our new method outperforms the DBM method when the accuracy of tests is not the same. The marginal model approach can be easily extended to ordinal outcomes

Semi-parametric Single-index Two-Part Regression Models

In this paper, we proposed a semi-parametric single-index two-part regression model to weaken assumptions in parametric regression methods that were frequently used in the analysis of skewed data with additional zero values. The estimation procedure for the parameters of interest in the model was easily implemented. The proposed estimators were shown to be consistent and asymptotically normal. Through a simulation study, we showed that the proposed estimators have reasonable finite-sample performance. We illustrated the application of the proposed method in one real study on the analysis of health care costs

Evaluating Markers for Treatment Selection Based on Survival Time

For many medical conditions several treatment options may be available for treating patients. We consider evaluating markers based on a simple treatment selection policy that incorporates information on the patient\u27s marker value exceeding a threshold. For example, colon cancer patients may be treated by surgery alone or surgery plus chemotherapy. The c-myc gene expression level may be used as a biomarker for treatment selection. Although traditional regression methods may assess the effect of the marker and treatment on outcomes, it is appealing to quantify more directly the potential impact on the population of using the marker to select treatment. A useful tool is the selection impact (SI) curve proposed by Song and Pepe (2004, Biometrics 60, 874-883) for binary outcomes. However, the current SI method does not deal with continuous outcomes, nor does it allow to adjust for other covariates that are important for treatment selection. In this paper, we extend the SI curve for general outcomes, with a specific focus on survival time. We further propose the covariate specific SI curve to incorporate covariate information in treatment selection. Nonparametric and semiparametric estimators are developed accordingly. We show that the proposed estimators are consistent and asymptotically normal. The performance is illustrated by simulation studies and through an application to data from a cancer clinical trial

COVARIATE SPECIFIC ROC CURVE WITH SURVIVAL OUTCOME

The receiver operating characteristic (ROC) curve has been extended to survival data recently, including the nonparametric approach by Heagerty, Lumley and Pepe (2000) and the semiparametric approach by Heagerty and Zheng (2005) using standard survival analysis techniques based on two different time-dependent ROC curve definitions. However, both approaches cannot adjust for the effect of covariates on the accuracy of the biomarker. To account for the covariate effect, we propose semiparametric models for covariate specific ROC curves corresponding to the two time-dependent ROC curve definitions, respectively. We show that the estimators are consistent and converge to Gaussian processes. In the case of no covariates, the estimators are demonstrated to be more efficient than the Heagerty-Lumley-Pepe estimator and the Heagerty-Zheng estimator via simulation studies. In addition, the estimators can be easily extended to other survival models. We apply these estimators to an HIV dataset

Empirical Likelihood Intervals for the Mean Difference of Two Skewed Populations with Additional Zero Values

We considered the problem of constructing nonparametric confidence intervals for the difference in the means of two independent skewed populations which contain zero values. To account for zero values, we used a two-part model to separately estimate the probability of having any non-zero value and the expected value of positive observations. Under such a two-part model we developed the empirical likelihood (EL) based interval for the difference in the two population means. We then derived asymptotic properties of the proposed method. In a simulation study, we showed that the EL-based interval outperforms the existing normal approximation method and the bootstrap method. Finally, we illustrated the application of the proposed method in a study that assessed the relationship between the excess charges among older patients and the burden of their medical illness

Novel Non-equilibrium Phase Transition Caused by Non-linear Hadronic-quark Phase Structure

We consider how the occurrence of first-order phase transitions in non-constant pressure differs from those at constant pressure. The former has shown the non-linear phase structure of mixed matter, which implies a particle number dependence of the binding energies of the two species. If the mixed matter is mixed hadron-quark phase, nucleon outgoing from hadronic phase and ingoing to quark phase probably reduces the system to a non-equilibrium state, in other words, there exists the imbalance of the two phases when deconfinement takes place. This novel non-equilibrium process is very analogous to the nuclear reactions that nuclei emit neutrons and absorb them under appropriate conditions. We present self-consistent thermodynamics in description for the processes and identify the microphysics responsible for the processes. The microphysics is an inevitable consequence of non-linear phase structure instead of the effect of an additional dissipation force. When applying our findings to the neutron star containing mixed hadron-quark matter, it is found that the newly discovered energy release might strongly change the thermal evolution behavior of the star.Comment: 18pages,3figures;to be accepted for publication in Physics Letters

Semi-Parametric Maximum Likelihood Estimates for ROC Curves of Continuous-Scale Tests

In this paper, we propose a semi-parametric maximum likelihood estimate of an ROC curve that satisfies the property of invariance of the ROC curve. In our simulation studies, we demonstrate that the proposed estimator has the best performance among all the existing semi-parametric estimators considered here. Finally, we illustrate the application of the proposed estimator using a real data set

The consistency of estimator under fixed design regression model with NQD errors

In this article, basing on NQD samples, we investigate the fixed design nonparametric regression model, where the errors are pairwise NQD random errors, with fixed design points, and an unknown function. Nonparametric weighted estimator will be introduced and its consistency is studied. As special case, the consistency result for weighted kernel estimators of the model is obtained. This extends the earlier work on independent random and dependent random errors to NQD case