An overview of methods for receiver operating characteristic analysis, with an application to SARS-CoV-2 vaccine-induced humoral responses in solid organ transplant recipients

Receiver operating characteristic (ROC) analysis is a tool to evaluate the capacity of an ordinal or numeric measure to distinguish between states, often employed in the evaluation of diagnostic tests. Assumptions regarding the nature of the data or the structure of the ROC curve can improve efficiency of estimation for the ROC curve itself or its associated area under the curve (a measure of stochastic ordering closely related to the target parameter of a Mann-Whitney <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>U</mml:mi></mml:math> test). Despite recent interest in methods to conduct comparisons by way of stochastic ordering, ROC modeling strategies are not widely known but may be appreciated by practitioners of these methods. The major goals of this manuscript are to (1) provide an overview of non-parametric, parametric, and semiparametric frameworks for ROC curve estimation, (2) guide the practice of ROC analysis by offering considerations regarding methodological trade-offs, and (3) supply sample R code to further guide implementation. We utilize simulations to demonstrate various features of the methods we discuss. As an illustrative example, we analyze data from a recent cohort study in order to compare responses to SARS-CoV-2 vaccination between solid organ transplant recipients and healthy individuals.