Robust combination of multiple diagnostic tests for classifying censored event times

Recent advancement in technology promises to yield a multitude of tests for disease diagnosis and prognosis. When there are multiple sources of information available, it is often of interest to construct a composite score that can provide better classification accuracy than any individual measurement. In this paper, we consider robust procedures for optimally combining tests when test results are measured prior to disease onset and disease status evolves over time. To account for censoring of disease onset time, the most commonly used approach to combining tests to detect subsequent disease status is to fit a proportional hazards model (Cox, 1972) and use the estimated risk score. However, simulation studies suggested that such a risk score may have poor accuracy when the proportional hazards assumption fails. We propose the use of a nonparametric transformation model (Han, 1987) as a working model to derive an optimal composite score with theoretical justification. We demonstrate that the proposed score is the optimal score when the model holds and is optimal "on average" among linear scores even if the model fails. Time-dependent sensitivity, specificity, and receiver operating characteristic curve functions are used to quantify the accuracy of the resulting composite score. We provide consistent and asymptotically Gaussian estimators of these accuracy measures. A simple model-free resampling procedure is proposed to obtain all consistent variance estimators. We illustrate the new proposals with simulation studies and an analysis of a breast cancer gene expression data set.