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Open Access Technical advance

A Bayesian framework for estimating the incremental value of a diagnostic test in the absence of a gold standard

Daphne I Ling1, Madhukar Pai1, Ian Schiller2 and Nandini Dendukuri12*

Author Affiliations

1 Department of Epidemiology and Biostatistics, McGill University, 1020 Pine Ave West, Montreal H3A 1A2, QC, Canada

2 Division of Clinical Epidemiology, McGill University Health Centre–Research Institute, 687 Pine Avenue West, Room R4.09, Montreal H3A 1A1, QC, Canada

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BMC Medical Research Methodology 2014, 14:67  doi:10.1186/1471-2288-14-67

Published: 15 May 2014

Abstract

Background

The absence of a gold standard, i.e., a diagnostic reference standard having perfect sensitivity and specificity, is a common problem in clinical practice and in diagnostic research studies. There is a need for methods to estimate the incremental value of a new, imperfect test in this context.

Methods

We use a Bayesian approach to estimate the probability of the unknown disease status via a latent class model and extend two commonly-used measures of incremental value based on predictive values [difference in the area under the ROC curve (AUC) and integrated discrimination improvement (IDI)] to the context where no gold standard exists. The methods are illustrated using simulated data and applied to the problem of estimating the incremental value of a novel interferon-gamma release assay (IGRA) over the tuberculin skin test (TST) for latent tuberculosis (TB) screening. We also show how to estimate the incremental value of IGRAs when decisions are based on observed test results rather than predictive values.

Results

We showed that the incremental value is greatest when both sensitivity and specificity of the new test are better and that conditional dependence between the tests reduces the incremental value. The incremental value of the IGRA depends on the sensitivity and specificity of the TST, as well as the prevalence of latent TB, and may thus vary in different populations.

Conclusions

Even in the absence of a gold standard, incremental value statistics may be estimated and can aid decisions about the practical value of a new diagnostic test.

Keywords:
Area under the curve; Bayesian estimation; Incremental value; Informative priors; Integrated discrimination improvement; Imperfect diagnostic tests; Latent class models; Tuberculosis