Insights into latent class analysis of diagnostic test performance

Area of Science:

• Biostatistics
• Epidemiology
• Diagnostic Test Evaluation

Background:

• Assessing diagnostic test accuracy often requires a gold standard, which is not always available.
• Multiple imperfect diagnostic tests can be used to infer disease status and test performance.
• Latent class analysis provides a statistical framework for such scenarios.

Purpose of the Study:

• To derive and present closed-form maximum likelihood parameter estimates for latent class analysis in a 3-test setting.
• To investigate the impact of conditional independence assumptions on parameter estimates.
• To provide intuition for bias introduced by violations of conditional independence.

Main Methods:

• Latent class analysis with maximum likelihood estimation.
• Derivation of closed-form expressions for parameter estimates under conditional independence.
• Expectation-Maximization (EM) algorithm for calculating estimates.

Main Results:

• Explicit formulas show how test result associations inform disease prevalence and test accuracy (true/false positive rates).
• Estimates are shown to be unreliable when the conditional independence assumption fails.
• Analytic expressions and EM approach provide intuition for bias from conditional dependence.

Conclusions:

• Accurate estimation of disease prevalence and test operating characteristics requires careful justification of test dependence assumptions.
• Clinical definitions of disease and biological knowledge are crucial for validating these assumptions.
• Results inform the application of latent class analysis in settings with more than three tests.