EVIDENCE SYNTHESIS FOR DIAGNOSTIC TESTS WITH PARTIALLY ORDERED PERFORMANCE AND NO REFERENCE STANDARD

Purpose:    Mathematical models of test and treat strategies typically require estimates of the sensitivity and specificity of tests. We develop evidence synthesis models for obtaining such estimates from independent studies, when the true disease status is unknown (no error-free reference standard exists), which is a common situation. To explicate, we estimate the performance of tuberculin skin test (TST) and interferon-gamma release assays (IGRA) to diagnose Latent Tuberculosis Infection (LTBI) for a cost-effectiveness analysis of screening of immigrants for LTBI.

Methods:    We develop a Bayesian hierarchical random effects model that (1) treats the unobserved disease status (LTBI) as a latent variable; (2) allows for between-study heterogeneity in disease prevalence, and in the sensitivities and specificities of tests (TST, IGRA); (3) accounts for threshold effects across studies; (4) accommodates covariates; (5) allows test results to be correlated conditional on disease status. The model also (6) allows for partial ordering of test performance, because information elicited from 9 context experts, suggests that IGRA cannot have worse specificity that TST. While for each study the model has more parameters than independent data points, identification is attained and estimation becomes possible through “borrowing of strength” across studies, and from the expert-provided ordering of the specificities.

Results:    We present the model, and provide intuition about how it identifies parameters by presenting feasible regions for parameters under various constraints (Figure, panel A). We apply the model in 76 studies that report the cross-classification of TST and IGRA results in various populations, and obtain estimates for the prevalence of LTBI, and the sensitivities and specificities of TST for scenarios defined by whether immigrants come from a country with high tuberculosis incidence; have had BCG vaccination; have chronic diseases; have HIV infection; or are 30 versus 50 years old. The Figure (panel B) shows posterior densities for the sensitivities of TST and IGRA for an example scenario of 30-year-old immigrants from a high-incidence country, without history of BCG vaccination or diseases.

Conclusions:    We developed a meta-analysis model that estimates test performance measures in the absence of an error-free reference standard, which is a very common situation in decision and economic analyses of test-and-treat strategies.