Classification using longitudinal trajectory of biomarker in the presence of detection limits

Discriminant analysis is commonly used to evaluate the ability of candidate biomarkers to separate patients into pre-defined groups. Recent extension of discriminant analysis to longitudinal data enables us to improve the classification accuracy based on biomarker profiles rather than on a single biomarker measurement. However, the biomarker measurement is often limited by the sensitivity of the given assay, resulting in data that are censored at either the lower or the upper limit of detection. Inappropriate handling of censored data may affect the classification accuracy of biomarker and hinder the evaluation of its potential discrimination power. We develop a discriminant analysis method for censored longitudinal biomarker data based on mixed models and evaluate its performance by area under the receiver operation characteristic curve. Through the simulation study, we show that our method is better than the simple substitution methods in terms of parameter estimation and evaluating biomarker performance. Application to a biomarker study of patients with acute kidney injury demonstrates that our method may shed light on the potential clinical utility of biomarkers by taking into account both longitudinal trajectory and limit of detection issues.