Time‐dependent classification accuracy curve under marker‐dependent sampling

Evaluating the classification accuracy of a candidate biomarker signaling the onset of disease or disease status is essential for medical decision making. A good biomarker would accurately identify the patients who are likely to progress or die at a particular time in the future or who are in urgent need for active treatments. To assess the performance of a candidate biomarker, the receiver operating characteristic (ROC) curve and the area under the ROC curve (AUC) are commonly used. In many cases, the standard simple random sampling (SRS) design used for biomarker validation studies is costly and inefficient. In order to improve the efficiency and reduce the cost of biomarker validation, marker‐dependent sampling (MDS) may be used. In a MDS design, the selection of patients to assess true survival time is dependent on the result of a biomarker assay. In this article, we introduce a nonparametric estimator for time‐dependent AUC under a MDS design. The consistency and the asymptotic normality of the proposed estimator is established. Simulation shows the unbiasedness of the proposed estimator and a significant efficiency gain of the MDS design over the SRS design.     

Polysaccharides from the brown seaweed Padina tetrastromatica: Characterization of a sulfated fucan

Sulfated fucans, the complex polysaccharides from brown seaweeds, possess various biological activities. To understand the structure activity relationship of sulfated fucans, we have investigated the structural features of one such polymer from Padina tetrastromatica using standard methods of carbohydrate structural analysis. We report a novel structural motif for this polymer. The average structure of this macromolecule that has a molecular mass of 25 kDa differs from the previous models in three respects. First, the core region of this macromolecule is composed primarily of α-(1 → 2)- and α-(1 → 3)-linked fucopyranosyl residues. Sulfate groups, when present are located at position 4 and 2 of fucosyl residues. Secondly, fucose and xylose is attached to this polymer to form branch points, one for every two residues within the chain. Finally, this macromolecule contained smaller amount of sulfate (0.21 mol of sulfate per mol of deoxyhexose).