Statistical Methods for Evaluating Biomarkers Subject to Detection Limit

As a cost effective diagnostic tool, numerous candidate biomarkers have been emerged for different diseases. The increasing effort of discovering informative biomarkers highlights the need for valid statistical modeling and evaluation. Our focus is on the biomarker data which are both measured repeatedly over time and censored by the sensitivity of given assay. Inappropriate handling of these types of data can cause biased results, resulting in erroneous medical decision.In the first topic, we extend the discriminant analysis to censored longitudinal biomarker data based on linear mixed models and modified likelihood function. The performance of biomarker is evaluated by area under the receiver operation characteristic (ROC) curve (AUC). The simulation study shows that the proposed method improves both parameter and AUC estimation over substitution methods when normality assumption is satisfied for biomarker data. Our method is applied to the biomarker study for acute kidney injury patients. In the second topic, we introduce a simple and practical evaluation method for censored longitudinal biomarker data. A modification of the linear combination approach by Su and Liu enables us to calculate the optimum AUC as well as relative importance of measurements from each time point. The simulation study demonstrates that the proposed method performs well in a practical situation. The application to real-world data is provided. In the third topic, we consider censored time-invariant biomarker data to discriminate time to event or cumulative events by a particular time point. C-index and time dependent ROC curve are often used to measure the discriminant potential of survival model. We extend these methods to censored biomarker data based on joint likelihood approach. Simulation study shows that the proposed methods result in accurate discrimination measures. The application to a biomarker study is provided. Both early detection and accurate prediction of disease are important to manage serious public health problems. Because many of diagnostic tests are based on biomarkers, discovery of informative biomarker is one of the active research areas in public health. Our methodology is important for public health researchers to identify promising biomarkers when the measurements are censored by detection limits