Optimal combination of biomarkers for time-dependent receiver operating characteristic estimation and related problems.

The receiver operating characteristic curve is commonly used for assessing diagnostic test accuracy and for discriminatory ability of a medical diagnostic test in distinguishing between diseases and non-diseased individuals. With the advance of technology, many genetic variables and biomarker variables are easily collected. The most challenging problem is how to combine clinical, genetic, and biomarker variables together to predict disease status. If one is interested in predicting t-year survival, however, the status of "case" (death) and "control" (survival) at the given t-year is unknown for those individuals who were censored before t-year. To conduct a receiver operating characteristic analysis, one has to impute those ambiguous statuses. In this paper, we study a maximum pseudo likelihood method to estimate the underlying parameters and baseline distribution functions. The proposed approach produces more efficient and smoother estimate of the optimal time-dependent receiver operating characteristic curve and more stable estimation of the prediction rule for the t-year survivors. More importantly, the proposal is equipped with a goodness-of-fit test for the model assumption based on the bootstrap method. Two real medical data sets are used for illustration.