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Estimation of the disease-specific diagnostic marker distribution under verification bias

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  • Page, John H.
  • Rotnitzky, Andrea

Abstract

We consider the estimation of the parameters indexing a parametric model for the conditional distribution of a diagnostic marker given covariates and disease status. Such models are useful for the evaluation of whether and to what extent a marker's ability to accurately detect or discard disease depends on patient characteristics. A frequent problem that complicates the estimation of the model parameters is that estimation must be conducted from observational studies. Often, in such studies not all patients undergo the gold standard assessment of disease. Furthermore, the decision as to whether a patient undergoes verification is not controlled by study design. In such scenarios, maximum likelihood estimators based on subjects with observed disease status are generally biased. In this paper, we propose estimators for the model parameters that adjust for selection to verification that may depend on measured patient characteristics and additionally adjust for an assumed degree of residual association. Such estimators may be used as part of a sensitivity analysis for plausible degrees of residual association. We describe a doubly robust estimator that has the attractive feature of being consistent if either a model for the probability of selection to verification or a model for the probability of disease among the verified subjects (but not necessarily both) is correct.

Suggested Citation

  • Page, John H. & Rotnitzky, Andrea, 2009. "Estimation of the disease-specific diagnostic marker distribution under verification bias," Computational Statistics & Data Analysis, Elsevier, vol. 53(3), pages 707-717, January.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:3:p:707-717
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    References listed on IDEAS

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    1. Alicia Y. Toledano & Constantine Gatsonis, 1999. "Generalized Estimating Equations for Ordinal Categorical Data: Arbitrary Patterns of Missing Responses and Missingness in a Key Covariate," Biometrics, The International Biometric Society, vol. 55(2), pages 488-496, June.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Rotnitzky, Andrea & Faraggi, David & Schisterman, Enrique, 2006. "Doubly Robust Estimation of the Area Under the Receiver-Operating Characteristic Curve in the Presence of Verification Bias," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1276-1288, September.
    4. Cindy Rodenberg & Xiao-Hua Zhou, 2000. "ROC Curve Estimation When Covariates Affect the Verification Process," Biometrics, The International Biometric Society, vol. 56(4), pages 1256-1262, December.
    5. Robert Gray & Colin B. Begg & Robert A. Greenes, 1984. "Construction of Receiver Operating Characteristic Curves when Disease Verification Is Subject to Selection Bias," Medical Decision Making, , vol. 4(2), pages 151-164, June.
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    Cited by:

    1. Danping Liu & Xiao-Hua Zhou, 2011. "Semiparametric Estimation of the Covariate-Specific ROC Curve in Presence of Ignorable Verification Bias," Biometrics, The International Biometric Society, vol. 67(3), pages 906-916, September.
    2. Chinyereugo M Umemneku Chikere & Kevin Wilson & Sara Graziadio & Luke Vale & A Joy Allen, 2019. "Diagnostic test evaluation methodology: A systematic review of methods employed to evaluate diagnostic tests in the absence of gold standard – An update," PLOS ONE, Public Library of Science, vol. 14(10), pages 1-25, October.
    3. Danping Liu & Xiao-Hua Zhou, 2013. "Covariate Adjustment in Estimating the Area Under ROC Curve with Partially Missing Gold Standard," Biometrics, The International Biometric Society, vol. 69(1), pages 91-100, March.

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