Transformation models for ROC analysis

TL;DR

This paper introduces a flexible regression framework for ROC analysis that handles complex medical data features, providing efficient inference and practical software tools for improved diagnostic test evaluation.

Contribution

It proposes a novel transformation model for ROC analysis that accommodates covariates, ordinal data, censored data, and correlated biomarkers, with guaranteed asymptotic efficiency.

Findings

Estimates are unbiased and have correct coverage in simulations.

The model effectively handles complex data features in ROC analysis.

Software implementation is available in the 'tram' R package.

Abstract

Receiver operating characteristic (ROC) analysis is one of the most popular approaches for evaluating and comparing the accuracy of medical diagnostic tests. Although various methodologies have been developed for estimating ROC curves and its associated summary indices, there is no consensus on a single framework that can provide consistent statistical inference whilst handling the complexities associated with medical data. Such complexities might include covariates that influence the diagnostic potential of a test, ordinal test data, censored data due to instrument detection limits or correlated biomarkers. We propose a regression model for the transformed test results which exploits the invariance of ROC curves to monotonic transformations and naturally accommodates these features. Our use of maximum likelihood inference guarantees asymptotic efficiency of the resulting estimators and associated confidence intervals. Simulation studies show that the estimates based on transformation models are unbiased and yield coverage at nominal levels. The methodology is applied to a cross-sectional study of metabolic syndrome where we investigate the covariate-specific performance of weight-to-height ratio as a non-invasive diagnostic test. Software implementations for all the methods described in the article are provided in the "tram" R package.