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Table 1 Summary of the proposed statistical models, their assumptions regarding the diagnostic method, and the additional data required to fit these models

From: Bias in logistic regression due to imperfect diagnostic test results and practical correction approaches

Model Additional data requirement Assumptions related to detection
Standard logistic regression None Perfect detection (i.e., sensitivity and specificity equal to 100 %)
Bayesian model 1 Estimate of sensitivity \(\widehat{SN}\) and specificity \(\widehat{SP}\) based on external study Sensitivity and specificity are perfectly known constants, equal to the estimates from external study
Bayesian model 2 Data on sensitivity and specificity (i.e., \(N_{ + } ,T_{ + } ,N_{ - } ,T_{ - }\)) from external study Sensitivity and specificity are constants and external study provides reasonable prior information on sensitivity and specificity for the target study
Bayesian model 3 Subset of individuals diagnosed with the regular and the gold standard method Sensitivity and specificity can vary as a function of covariates. This model does not rely on data from external study (i.e., does not rely on transportability assumption)