| dc.description.abstract | In this paper, we are mainly interested in using the receiver operating characteristic (ROC) curve to determine which biomarker has better disease prediction. We consider the data that patient’s covariates and their disease status are both time dependent and, in general, this kind of data is justified by the Area under ROC curve (AUC). However, due to the time-dependent covariates, AUC values may vary (under different time points), which make us difficult to make inference (or decide which biomarker has better disease prediction). Thus, we adapt the volume under the ROC surface (VUS) approach instead－the larger the volume, the better the disease prediction. Here, we use the nearest neighbor estimation for a bivariate distribution to estimate the ROC curve. In simulation, we generate two biomarkers, and we are interested in which biomarker has better prediction. From the AUC values, we can know that the biomarker one is better than biomarker two, we compare biomarker one to the combination of biomarker one and biomarker two and by the AUC values, we can know that the linear combination of biomarkers has better prediction. We also use the VUS, we know the linear combination of biomarkers has better prediction. In the practical data analysis, two examples (cases) are given. First, we are interested in the biomarkers CD4 counts and viral load, which one has better prediction for the AIDS. From the AUC values, we can know that the CD4 counts is better than viral load. Second, we are interested in the biomarkers total number of eggs laid during lifetime, the time of maximum eggs laid and number of eggs laid daily, which one has more influence to medfly lifetime. From the AUC values, we can know that the total number of eggs laid during lifetime and number of eggs laid daily are better, but by volume under the ROC surface, number of eggs laid daily has more influence to medfly lifetime. | en_US |