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

Abstract

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.

Keywords

AUC censored biomarker discriminant analysis limit of detection longitudinal

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References

de Leon

DeSanti

Zinkowski

. Longitudinal CSF and MRI biomarkers improve the diagnosis of mild cognitive impairment. Neurobiol Aging 2006; 27: 394–401.

Parretti

Mealli

Magrini

. Cross-sectional and longitudinal evaluation of uterine artery Doppler velocimetry for the prediction of pre-eclampsia in normotensive women with specific risk factors. Ultrasound Obstet Gynecol: Off J Int Soc Ultrasound Obstet Gynecol 2003; 22: 160–165.

Helsel

. Less than obvious – statistical treatment of data below the detection limit. Environ Sci Technol 1990; 24: 1766–1774.

Perkins

Schisterman

Vexler

. Receiver operating characteristic curve inference from a sample with a limit of detection. Am J Epidemiol 2007; 165: 325–333.

Vexler

Liu

Eliseeva

. Maximum likelihood ratio tests for comparing the discriminatory ability of biomarkers subject to limit of detection. Biometrics 2008; 64: 895–903.

Schisterman

Vexler

Whitcomb

. The limitations due to exposure detection limits for regression models. Am J Epidemiol 2006; 163: 374–383.

Tomasko

Helms

Snapinn

. A discriminant analysis extension to mixed models. Stat Med 1999; 18: 1249–1260.

Marshall

Baron

. Linear discriminant models for unbalanced longitudinal data. Stat Med 2000; 19: 1969–1981.

Wernecke

Kalb

Schink

. A mixed model approach to discriminant analysis with longitudinal data. Biometric J 2004; 46: 246–254.

10.

Roy

Khattree

. On discrimination and classification with multivariate repeated measures data. J Stat Plan Infer 2005; 134: 462–485.

11.

Marshall

De la Cruz-Mesia

Quintana

. Discriminant analysis for longitudinal data with multiple continuous responses and possibly missing data. Biometrics 2009; 65: 69–80.

12.

Kohlmann

Held

Grunert

. Classification of therapy resistance based on longitudinal biomarker profiles. Biometric J Biometrische Zeitschrift 2009; 51: 610–626.

13.

Hughes

. Mixed effects models with censored data with application to HIV RNA levels. Biometrics 1999; 55: 625–629.

14.

Lyles

Taylor

. Random regression models for human immunodeficiency virus ribonucleic acid data subject to left censoring and informative drop-outs. J Roy Stat Soc: Ser C (Appl Stat) 2000; 49: 485–497.

15.

Thiebaut

Jacqmin-Gadda

. Mixed models for longitudinal left-censored repeated measures. Comput Meth Programs Biomed 2004; 74: 255–260.

16.

Vexler

Hutson

. Likelihood testing populations modeled by autoregressive process subject to the limit of detection in applications to longitudinal biomedical data. J Appl Stat 2011; 38: 1333–1346.

17.

Langdon

Taylor

West

. Classification of type I-censored bivariate data. Comput Stat & Data Anal 2007; 51: 4562–4576.

18.

Perkins

Schisterman

Vexler

. ROC curve inference for best linear combination of two biomarkers subject to limits of detection. Biometric J 2011; 53: 464–476.

19.

Littell

. SAS for mixed models, 2nd ed. Cary, NC: SAS Institute, 2006xii, 814.

20.

McClish

. Analyzing a portion of the ROC curve. Med Decis Making: Int J Soc Med Decis Making 1989; 9: 190–195.

21.

DeLong

Clarke-Pearson

. Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach. Biometrics 1988; 44: 837–845.

22.

Palevsky

Zhang

O’Connor

. Intensity of renal support in critically ill patients with acute kidney injury. N Eng J Med 2008; 359: 7–20.

23.

Whitcomb

Schisterman

. Assays with lower detection limits: implications for epidemiological investigations. Paediatr Perinat Epidemiol 2008; 22: 597–602.

24.

Han

Kronmal

. Box–Cox transformation of left-censored data with application to the analysis of coronary artery calcification and pharmacokinetic data. Stat Med 2004; 23: 3671–3679.

25.

Hamasaki

Kim

. Box and Cox power-transformation to confined and censored nonnormal responses in regression. Comput Stat & Data Anal 2007; 51: 3788–3799.

26.

Shi

. Marginal versus joint Box–Cox transformation with applications to percentile curve construction for IgG subclasses and blood pressures. Stat Med 2003; 22: 397–408.

27.

Gurka

Edwards

Muller

. Extending the Box–Cox transformation to the linear mixed model. J Roy Stat Soc: Ser A (Stat Soc) 2006; 169: 273–288.