ObjectiveTo systematically review methods developed and employed to evaluate the diagnostic accuracy of medical test when there is a missing or no gold standard.Study design and settingsArticles that proposed or applied any methods to evaluate the diagnostic accuracy of medical test(s) in the absence of gold standard were reviewed. The protocol for this review was registered in PROSPERO (CRD42018089349).ResultsIdentified methods were classified into four main groups: methods employed when there is a missing gold standard; correction methods (which make adjustment for an imperfect reference standard with known diagnostic accuracy measures); methods employed to evaluate a medical test using multiple imperfect reference standards; and other methods, like agreement studies, and a mixed group of alternative study designs. Fifty-one statistical methods were identified from the review that were developed to evaluate medical test(s) when the true disease status of some participants is unverified with the gold standard. Seven correction methods were identified and four methods were identified to evaluate medical test(s) using multiple imperfect reference standards. Flow-diagrams were developed to guide the selection of appropriate methods.ConclusionVarious methods have been proposed to evaluate medical test(s) in the absence of a gold standard for some or all participants in a diagnostic accuracy study. These methods depend on the availability of the gold standard, its’ application to the participants in the study and the availability of alternative reference standard(s). The clinical application of some of these methods, especially methods developed when there is missing gold standard is however limited. This may be due to the complexity of these methods and/or a disconnection between the fields of expertise of those who develop (e.g. mathematicians) and those who employ the methods (e.g. clinical researchers). This review aims to help close this gap with our classification and guidance tools.

Background Staquet et al. and Brenner both developed correction methods to estimate the sensitivity and specificity of a binary-response index test when the reference standard is imperfect and its sensitivity and specificity are known. However, to our knowledge, no study has compared the statistical properties of these methods, despite their long application in diagnostic accuracy studies. Aim To compare the correction methods developed by Staquet et al. and Brenner. Methods Simulations techniques were employed to compare the methods under assumptions that the new test and the reference standard are conditionally independent or dependent given the true disease status of an individual. Three clinical datasets were analysed to understand the impact of using each method to inform clinical decision-making. Results Under the assumption of conditional independence, the Staquet et al. correction method outperforms the Brenner correction method irrespective of the prevalence of disease and whether the performance of the reference standard is better or worse than the index test. However, when the prevalence of the disease is high (> 0.9) or low (< 0.1), the Staquet et al. correction method can produce illogical results (i.e. results outside [0,1]). Under the assumption of conditional dependence; both methods failed to estimate the sensitivity and specificity of the index test especially when the covariance terms between the index test and the reference standard is not close to zero. Conclusion When the new test and the imperfect reference standard are conditionally independent, and the sensitivity and specificity of the imperfect reference standard are known, the Staquet et al. correction method outperforms the Brenner method. However, where the prevalence of the target condition is very high or low or the two tests are conditionally dependent, other statistical methods such as latent class approaches should be considered.