Testing and Quantifying Site-Level Variability in Diagnostic Sensitivity of an Anchor Variable

In multi-site clinical research, diagnostic assessments can vary across sites even when standardized criteria and instruments are used, leading to inconsistent disease classification. This issue is examined in settings with an anchor variable that confidently identifies disease when positive but provides no information when negative. A random effects model is introduced for site-specific sensitivity, along with likelihood-based methods for estimation and hypothesis testing. The approach addresses two objectives: testing whether diagnostic sensitivity varies across sites, and quantifying the magnitude of such variability. Validation data is incorporated to establish parameter identifiability. Laplace approximation and the Expectation-Maximization (EM) algorithm are further engaged to address the computational challenge caused by an intractable integral in the likelihood function. Likelihood ratio and score tests are constructed to account for the boundary constraint that arises when the null hypothesis places the variance component at zero. Simulation studies demonstrate the good performance in finite samples, with accurate parameter estimates and appropriate test size and power. Application to a multi-site Huntington disease cohort for diagnosing mild cognitive impairment reveals differences in diagnostic sensitivity across sites, with tests providing strong evidence of heterogeneity. This framework offers a principled approach for testing and quantifying site-level variability in diagnostic sensitivity, supporting more consistent inference in multi-site studies.