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 markerâ€™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 additonally 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.
doi:10.1016/j.csda.2008.06.021
PMCID: PMC3475507
PMID: 23087495
Missing at Random; Nonignorable; Missing Covariate; Sensitivity Analysis; Semiparametric; Diagnosis
Summary
The ROC (Receiver Operating Characteristic) curve is the most commonly used statistical tool for describing the discriminatory accuracy of a diagnostic test. Classical estimation of the ROC curve relies on data from a simple random sample from the target population. In practice, estimation is often complicated due to not all subjects undergoing a definitive assessment of disease status (verification). Estimation of the ROC curve based on data only from subjects with verified disease status may be badly biased. In this work we investigate the properties of the doubly robust (DR) method for estimating the ROC curve under verification bias originally developed by Rotnitzky et al. (2006) for estimating the area under the ROC curve. The DR method can be applied for continuous scaled tests and allows for a non ignorable process of selection to verification. We develop the estimator's asymptotic distribution and examine its finite sample properties via a simulation study. We exemplify the DR procedure for estimation of ROC curves with data collected on patients undergoing electron beam computer tomography, a diagnostic test for calcification of the arteries.
doi:10.1002/bimj.200800128
PMCID: PMC3475535
PMID: 19588455
Diagnostic test; Nonignorable; Semiparametric model; Sensitivity analysis; Sensitivity; Specificity
We consider the doubly robust estimation of the parameters in a semiparametric conditional odds ratio model. Our estimators are consistent and asymptotically normal in a union model that assumes either of two variation independent baseline functions is correctly modelled but not necessarily both. Furthermore, when either outcome has finite support, our estimators are semiparametric efficient in the union model at the intersection submodel where both nuisance functions models are correct. For general outcomes, we obtain doubly robust estimators that are nearly efficient at the intersection submodel. Our methods are easy to implement as they do not require the use of the alternating conditional expectations algorithm of Chen (2007).
doi:10.1093/biomet/asp062
PMCID: PMC3412601
PMID: 23049119
Doubly robust; Generalized odds ratio; Locally efficient; Semiparametric logistic regression