Implications of covariate induced test dependence on the diagnostic accuracy of latent class analysis in pulmonary tuberculosis

In application studies of latent class analysis (LCA) evaluating imperfect diagnostic tests, residual dependence among the diagnostic tests still remain even after conditioning on the true disease status due to measured variables known to affect prevalence and/or alter diagnostic test accuracy. Presence of severe comorbidities such as HIV in pulmonary tuberculosis (PTB) diagnosis alter the prevalence of PTB and affect the diagnostic performance of the available imperfect tests in use. This violates two key assumptions of LCA: (1) that the diagnostic tests are independent conditional on the true disease status (2) that the sensitivity and specificity remain constant across subpopulations. This leads to incorrect inferences.Through 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. Jointly conditioning on PTB and HIV, we generated independent results for five diagnostic tests and analyzed using Bayesian LCA with Probit regression, separately for sets of five and three diagnostic tests using four working models allowing: (1) constant PTB prevalence and diagnostic accuracy (2) varying PTB prevalence but constant diagnostic accuracy (3) constant PTB prevalence but varying diagnostic accuracy (4) varying PTB prevalence and diagnostic accuracy across HIV subpopulations. Vague Gaussian priors with mean 1 and unknown variance were assigned to the model parameters with unknown variance assigned Inverse Gamma prior. Models accounting for heterogeneity in diagnostic accuracy produced consistent estimates while the model ignoring it produces biased estimates. The model ignoring heterogeneity in PTB prevalence only is less problematic. With five diagnostic tests, the model assuming homogenous population is 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.