The diagnostic likelihood ratio function and modified test for trend: Identifying, evaluating, and validating nontraditional biomarkers in case‐control studies

Abstract

The ROC curve and its associated summary statistic, the AUC, are used to identify informative diagnostic biomarkers under the assumption that risk of disease is a monotone function of the biomarker. We refer to biomarkers that meet this assumption as traditional, and those that do not as nontraditional. Nontraditional biomarkers most often arise when both low and high biomarker values are associated with an outcome of interest, such as blood pressure with medical complications or leukocyte count with ICU prognosis. Since nontraditional biomarkers do not meet the assumptions for ROC‐based analyses, we propose using the discrete diagnostic likelihood ratio (DLR) function to evaluate a wider class of informative biomarkers. We obtain the DLR function using the multinomial logistic regression (MLR) model to improve upon existing estimation techniques, and implement a likelihood ratio test to identify candidate informative traditional and nontraditional biomarkers. We propose a modification of the Cochran‐Armitage test for trend that separates biomarkers deemed informative into traditional and nontraditional categories. The statistical properties of the likelihood ratio test and modified test for trend are explored under simulation. Together, these methods achieve the identification, evaluation, and validation of biomarkers from early discovery research. Finally, we show that incorporating covariates into the MLR model results in a covariate‐adjusted DLR function that is useful for integrating multiple sources of information in clinical decision making. The methods are applied to gene expression data from subjects with high grade serous ovarian cancer, where stage, early stage vs late stage, is the outcome of interest.