Lack of a perfect reference standard for pulmonary tuberculosis (PTB) diagnosis complicates assessment of accuracy of new diagnostic tests. Alternative strategies such as discrepant resolution and use of composite reference standards may lead to incorrect inferences on disease prevalence and diagnostic test sensitivity and specificity. Latent class analysis (LCA), a statistical method for analyzing diagnostic test results in the absence of a gold standard, allows correct estimation under strict assumptions. The model assumes that the diagnostic tests are independent conditional on the true disease status and that the diagnostic test sensitivity and specificity remain constant across subpopulations. These assumptions are violated when a factor such as severe comorbidity affects the prevalence and/or alters the diagnostic test performance. We aim to provide guidance on correct estimation of the prevalence and diagnostic test accuracy based on LCA when a known factor induces dependence among the diagnostic tests. If unaccounted for, this dependence may lead to misleading inferences.
Through likelihood evaluation and simulation we examined implications of likely model violations on estimation of prevalence, sensitivity and specificity among passive case-finding presumptive PTB patients with or without HIV. We generated independent results for five diagnostic tests conditional on PTB and HIV. We performed Bayesian LCA, separately for five and three diagnostic tests using four working models with or without constant PTB prevalence and diagnostic test accuracy across HIV subpopulations.
In evaluating three diagnostic tests, the models accounting for heterogeneity in diagnostic accuracy produced consistent estimates while the models ignoring it produced biased estimates. The model ignoring heterogeneity in PTB prevalence is less problematic. When evaluating five diagnostic tests, the models were robust to violation of the assumptions.
Well-chosen covariate-specific adaptations of the model can avoid bias implied by recognized heterogeneity in PTB patient populations generating otherwise dependent test results in LCA.