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. 2021 Sep 30;40(22):4751-4763.
doi: 10.1002/sim.8999. Epub 2021 May 14.

On the robustness of latent class models for diagnostic testing with no gold standard

Matthew R Schofield  1 , Michael J Maze  2   3 , John A Crump  4 , Matthew P Rubach  5 , Renee Galloway  6 , Katrina J Sharples  1
Affiliations

On the robustness of latent class models for diagnostic testing with no gold standard

Matthew R Schofield et al. Stat Med. .

Abstract

It is difficult to estimate sensitivity and specificity of diagnostic tests when there is no gold standard. Latent class models have been proposed as a potential solution as they provide estimates without the need for a gold standard. Using a motivating example of the evaluation of point of care tests for leptospirosis in Tanzania, we show how a realistic violation of assumptions underpinning the latent class model can lead directly to substantial bias in the estimates of the parameters of interest. In particular, we consider the robustness of estimates of sensitivity, specificity, and prevalence, to the presence of additional latent states when fitting a two-state latent class model. The violation is minor in the sense that it cannot be routinely detected with goodness-of-fit procedures, but is major with regard to the resulting bias.

Keywords: Bayes; leptospirosis; model sensitivity; sensitivity; specificity.

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Figures

FIGURE 1
FIGURE 1
The vertical lines represent the central 90% credible intervals for sensitivity (black) and specificity (gray) for each of the four tests for the Tanzania data using a two-state latent class model, where are tests are conditionally independent. The horizontal line represents the median of the posterior distribution
FIGURE 2
FIGURE 2
Posterior predictive distributions for the counts n. Each entry in n is referenced by the corresponding combination of test results given in the plot title. The vertical blue line gives the observed count [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 3
FIGURE 3
The difference between the true sensitivity/specificity and estimated sensitivity/specificity in each of the 1000 simulations when the true model had two-states (M = 2) and three-states (M = 3)
FIGURE 4
FIGURE 4
The difference between the true sensitivity/specificity and estimated sensitivity/specificity of the 1000 simulations when the true model has three-states (M = 3). We assess the sensitivity of the test to diagnose any disease (either state 1 or state 3)
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