Meta-analysis of diagnostic test accuracy with multiple disease stages: combining stage-specific and merged-stage data

For many conditions, it is of clinical importance to know not just the ability of a test to distinguish between those with and without the disease, but also the sensitivity to detect disease at different stages: in particular, the test’s ability to detect disease at a stage most amenable to treatment. In a systematic review of test accuracy, pooled stage-specific estimates can be produced using subgroup analysis or meta-regression. However, this requires stage-specific data from each study, which is often not reported. Studies may however report test sensitivity for merged stage categories (e.g. stages I-II) or merged across all stages, together with information on the proportion of patients with disease at each stage. We demonstrate how to incorporate studies reporting merged stage data alongside studies reporting stage-specific data, to allow the inclusion of more studies in the meta-analysis. We consider both meta-analysis of tests with binary results, and meta-analysis of tests with continuous results, where the sensitivity to detect disease of each stage across the whole range of observed thresholds is estimated. The methods are demonstrated using a series of simulated datasets and applied to data from a systematic review of the accuracy of tests used to screen for hepatocellular carcinoma in people with liver cirrhosis. We show that incorporating studies with merged stage data can lead to more precise estimates and, in some cases, corrects biologically implausible results that can arise when the availability of stage-specific data is limited.

💡 Research Summary

The paper addresses a common problem in diagnostic test accuracy meta‑analyses: clinicians often need stage‑specific sensitivity estimates (e.g., early‑stage cancer detection) rather than a single overall sensitivity. Traditional meta‑analysis methods require each primary study to report sensitivity for every disease stage, but in practice many studies only provide overall sensitivity together with the proportion of cases in each stage, or they merge several stages (e.g., stages I‑II). The authors propose a Bayesian hierarchical model that can simultaneously incorporate (1) fully stage‑specific 2 × 2 tables, (2) overall sensitivity together with stage‑proportion covariates, and (3) merged‑stage sensitivity counts.

For binary tests, the model treats the false‑positive fraction (1‑specificity) and the sensitivities for each stage as latent probabilities. After a logit transformation, these probabilities follow a multivariate normal distribution with means m_j and a full covariance matrix Σ, allowing study‑level correlations and heterogeneity across stages. When only overall sensitivity is available, the observed count is modeled as a binomial draw from a weighted average of the stage‑specific sensitivities, where the weights are the reported stage proportions. For merged‑stage data, a similar weighted‑average formulation is used, with the appropriate grouping of stages.

The framework is extended to continuous‑outcome tests that report results at multiple thresholds. Using a Bayesian multiple‑threshold model, each threshold’s sensitivity and specificity are linked to the same latent stage‑specific sensitivities, and stage proportions can be entered as covariates affecting the location parameter of the threshold‑specific distributions. This permits estimation of the full receiver‑operating‑characteristic curve for each disease stage.

The authors evaluate the approach through simulation studies, showing that when stage‑specific data are sparse, the combined model yields substantially lower mean‑squared error and narrower credible intervals compared with analyses that ignore merged data or that treat overall sensitivity as if it applied uniformly to all stages. They also apply the method to a systematic review of hepatocellular carcinoma (HCC) screening tests in cirrhotic patients. Five tests (ultrasound, MRI, CT, AFP, AFP‑L3) were examined; only a few studies reported stage‑specific sensitivities, while many provided overall or merged sensitivities together with stage‑distribution information. Incorporating all available data produced more precise and biologically plausible stage‑specific sensitivity estimates. For example, the overall AFP sensitivity appeared unrealistically high when analyzed alone, but after adjusting for the proportion of very‑early‑stage tumors, the estimated sensitivity for that stage decreased to a more credible level.

Key strengths of the proposed methodology include: (1) efficient use of all reported information, reducing waste of data; (2) explicit modeling of between‑study heterogeneity and correlation across stages via the covariance matrix; (3) applicability to both binary and continuous tests with multiple thresholds; and (4) the ability to produce stage‑specific ROC curves useful for health‑economic modelling and clinical decision‑making. Limitations involve the need for Bayesian expertise, careful prior specification, and computational intensity due to MCMC sampling.

In summary, the paper delivers a flexible, statistically rigorous solution for meta‑analysing diagnostic test accuracy when disease stages matter, enabling researchers to combine fully stage‑specific, merged, and overall data within a single coherent framework. This advancement has the potential to improve evidence synthesis for a wide range of diseases where early detection is critical.