Understanding the effects of conditional dependence in research studies involving imperfect diagnostic tests.

When two imperfect diagnostic tests are carried out on the same subject, their results may be correlated even after conditioning on the true disease status. While past work has focused on the consequences of ignoring conditional dependence, the degree to which conditional dependence can be induced has not been systematically studied. We examine this issue in detail by introducing a hypothetical missing covariate that affects the sensitivities of two imperfect dichotomous tests. We consider four forms for this covariate, normal, uniform, dichotomous and trichotomous. In the case of a dichotomous covariate, we derive an expression showing that the conditional covariance is a function of the product of the changes in test sensitivities (or specificities) between the subgroups defined by the covariate. The maximum possible covariance is induced by a dichotomous covariate with a very strong effect on both tests. Through simulations, we evaluate the extent to which fitting a latent class model ignoring each type of covariate but including a general covariance term can adjust for the correlation induced by the covariate. We compare the results to when the conditional dependence is ignored. We find that the bias because of ignoring conditional dependence is generally small even for moderate covariate effects, and when bias is present, a model including a covariance term works well. We illustrate our methods by analyzing data from a childhood tuberculosis study.