Bayesian imputation of predictive values when covariate information is available and gold standard diagnosis is unavailable

We suggest a conceptually simple Bayesian approach to inferences about the conditional probability of a specimen being infection-free given the outcome of a diagnostic test and covariate information. The approach assumes that the infection state of a specimen is not observable but uses the outcomes of a second test in conjuction with those of the first, that is, dual testing data. Dual testing procedures are often employed in clinical laboratories to assure that positive samples are not contaminated or to increase the likelihood of correct diagnoses. Using the CD4 count and a proxy for risk behaviour as covariates, we apply the method to obtain inferences about the conditional probability of an individual being HIV-1 infection-free given the individual's covariates and a negative outcome with the standard enzyme-linked immunoadsorbent assay/Western blotting test for HIV-1 detection. Inferences combine data from two studies where specimens were tested with the standard and with the more sensitive polymerase chain reaction test.