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Semiparametric estimation of the covariate-specific ROC curve in presence of ignorable verification bias. (English) Zbl 1226.62031
Summary: Covariate-specific receiver operating characteristic (ROC) curves are often used to evaluate the classification accuracy of a medical diagnostic test or a biomarker, when the accuracy of the test is associated with certain covariates. In many large-scale screening tests, the gold standard is subject to missingness due to high cost or harmfulness to the patient. We propose a semiparametric estimation of the covariate-specific ROC curves with a partial missing gold standard. A location-scale model is constructed for the test result to model the covariates’ effect, but the residual distributions are left unspecified. Thus the baseline and link functions of the ROC curve both have flexible shapes. With the gold standard missing at random (MAR) assumption, we consider weighted estimating equations for the location-scale parameters, and weighted kernel estimating equations for the residual distributions. Three ROC curve estimators are proposed and compared, namely, imputation-based, inverse probability weighted, and doubly robust estimators. We derive the asymptotic normality of the estimated ROC curve, as well as the analytical form of the standard error estimator. The proposed method is motivated and applied to the data in an Alzheimer’s disease research.

MSC:
62G05 Nonparametric estimation
62P10 Applications of statistics to biology and medical sciences; meta analysis
92C50 Medical applications (general)
62G20 Asymptotic properties of nonparametric inference
62N02 Estimation in survival analysis and censored data
65C60 Computational problems in statistics (MSC2010)
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[1] Alonzo, Assessing accuracy of a continuous screening test in the presence of verification bias, Journal of the Royal Statistical Society-Series C (Applied Statistics) 54 pp 173– (2005) · Zbl 05188679 · doi:10.1111/j.1467-9876.2005.00477.x
[2] Begg, Assessment of diagnostic tests when disease verification is subject to verification bias, Biometrics 39 pp 207– (1983) · doi:10.2307/2530820
[3] Cai, Semiparametric receiver operating characteristic analysis to evaluate biomarkers for disease, Journal of the American Statistical Association 97 pp 1099– (2002) · Zbl 1041.62086 · doi:10.1198/016214502388618915
[4] Fluss, Estimation of the ROC curve under verification bias, Biometrical Journal 51 pp 475– (2009) · Zbl 1179.62143 · doi:10.1002/bimj.200800128
[5] Gary, Construction of receiver operating characteristic curves when disease verification is subject to selection bias, Medical Decision Making 4 pp 151– (1983) · doi:10.1177/0272989X8400400204
[6] Isella, Discriminative and predictive power of an informant report in mild cognitive impairment, Journal of Neurology, Neurosurgery and Psychiatry 77 pp 166– (2006) · doi:10.1136/jnnp.2005.069765
[7] Kim, Diagnostic accuracy of mini-mental status examination and revised hasegawa dementia scale for Alzheimer’s disease, Dementia and Geriatric Cognitive Disorders 19 pp 324– (2005) · doi:10.1159/000084558
[8] Lipsitz, A weighted estimating equation for missing covariate data with properties similar to maximum likelihood, Journal of the American Statistical Association 94 pp 1147– (1999) · Zbl 1072.62532 · doi:10.2307/2669931
[9] Liu, A model for adjusting for nonignorable verification bias in estimation of ROC curve and its area with likelihood-based approach, Biometrics 66 pp 1119– (2010) · Zbl 1233.62183 · doi:10.1111/j.1541-0420.2010.01397.x
[10] McDowell, Community screening for dementia: The Mini Mental State Exam (MMSE) and modified Mini-Mental State Exam (3MS) compared, Journal of Clinical Epidemiology 50 pp 377– (1997) · doi:10.1016/S0895-4356(97)00060-7
[11] Nadaraya, Some new estimates for distribution functions, Theory of Probability and its Applications 9 pp 497– (1964) · Zbl 0152.17605 · doi:10.1137/1109069
[12] Page, Estimation of the disease-specific diagnostic marker distribution under verification bias, Computational Statistics and Data Analysis 53 pp 707– (2009) · Zbl 1452.62837 · doi:10.1016/j.csda.2008.06.021
[13] Pepe, Three approaches to regression analysis of receiver operating characteristic curves for continuous test results, Biometrics 54 pp 124– (1998) · Zbl 1058.62643 · doi:10.2307/2534001
[14] Pepe, Statistical Evaluation of Medical Tests for Classification and Prediction (2003) · Zbl 1039.62105
[15] Punglia, Effect of verification bias on screening for prostate cancer by measurement of prostate-specific antigen, New England Journal of Medicine 349 pp 335– (2003) · doi:10.1056/NEJMoa021659
[16] Rodenberg, ROC curve estimation when covariates affect the verification process, Biometrics 56 pp 1256– (2000) · Zbl 1060.62661 · doi:10.1111/j.0006-341X.2000.01256.x
[17] Rotnitzky, Doubly robust estimation of the area under the receiver-operating characteristic curve in the presence of verification bias, Journal of the American Statistical Association 101 pp 1276– (2006) · Zbl 1120.62336 · doi:10.1198/016214505000001339
[18] Zheng, Assessing accuracy of mannography in the presence of verification bias and intrareader correlation, Biometrics 61 pp 259– (2005) · doi:10.1111/j.0006-341X.2005.031139.x
[19] Zhou, A nonparametric ML estimate of an ROC curve area corrected for verification bias, Biometrics 52 pp 310– (1996) · Zbl 0876.62030 · doi:10.2307/2533165
[20] Zhou, Comparing correlated areas under the ROC curves of two diagnostic tests in the presence of verification bias, Biometrics 54 pp 453– (1998) · Zbl 1058.62674 · doi:10.2307/3109755
[21] Zhou, Statistical Methods in Diagnostic Medicine (2002) · doi:10.1002/9780470317082
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