Estimating Diagnostic Error without a Gold Standard: A Mixed Membership Approach
Résumé
Evaluation of sensitivity and specificity of diagnostic tests in the absence of a gold standard typically
relies on latent structure models. For example, two extensions of latent class models in the
biostatistics literature, Gaussian random effects (Qu et al., 1996) and finite mixture (Albert and
Dodd, 2004), form the basis of several recent approaches to estimating sensitivity and specificity
of diagnostic tests when no (or partial) gold standard evaluation is available. These models attempt
to account for additional item dependencies that cannot be explained with traditional latent class
models, where the classes typically correspond to healthy and diseased individuals.
We propose an alternative latent structure model, namely, the extended mixture Grade of Membership
(GoM) model, for evaluation of diagnostic tests without a gold standard. The extended
mixture GoM model allows for test results to be dependent on latent degree of disease severity,
while also allowing for the presence of some individuals with deterministic response patterns such
as all-positive and all-negative test results. We formulate and estimate the model in a hierarchical
Bayesian framework. We use a simulation study to compare recovery of true sensitivity and specificity
parameters with the extended mixture GoM model, and the latent class, Gaussian random
effects, and finite mixture models.
Our findings indicate that when the true generating model contains deterministic mixture components
and the sample size is large, all four models tend to underestimate sensitivity and overestimate
specificity parameters. These results emphasize the need for sensitivity analyses in real life
applications when the data generating model is unknown. Employing a number of latent structure
models and examining how the assumptions on latent structure affect conclusions about accuracy of
diagnostic tests is a crucial step in analyzing test performance without a gold standard. We illustrate
the sensitivity analysis approach using data on screening for Chlamydia trachomatis. This example
demonstrates that the extended mixture GoM model not only provides us with new latent structure
and the corresponding interpretation to mechanisms that give rise to test results, but also provides
new insights for estimating test accuracy without a gold standard.