Conflicting evidence in a Bayesian synthesis of surveillance data to estimate human immunodeficiency virus prevalence

Summary.  Inferential approaches based on the synthesis of diverse sources of evidence are increasingly employed in epidemiology as a means of exploiting all available information, perhaps from studies of differing designs. The application of the synthesis of evidence to real world problems generally leads to the formulation of probability models which are highly complex and for which there is a clear need for a well‐defined iterative process of model criticism. This process should include an appraisal of model fit and the detection of inconsistent or conflicting evidence. The latter is especially relevant as, typically, multiple sources of data provide information on the same parameter. Detected conflicts need then to be resolved. We present a case‐study of the detection and resolution of conflicting evidence, using as an illustration the estimation of the prevalence of human immunodeficiency virus (HIV) infection in England and Wales. We employ a Bayesian model to synthesize routine surveillance and survey data. The population aged 15–44 years is divided into mutually exclusive exposure groups. In each group g, we simultaneously estimate the proportion of the total population belonging to the group (ρ≫), the proportion of individuals infected with HIV (π≫) and the proportion of HIV positive individuals who are diagnosed (δ≫). The total number of HIV infections, both diagnosed and undiagnosed, is then estimated as a function of the parameters ρ≫, π≫ and δ≫. Model fit is assessed by examining the posterior mean deviance. Identification of the data items to which the model exhibits a lack of fit leads to the detection of conflicting evidence, one example of which is a conflict between census data and survey data over the size of the female Sub‐Saharan African born population. This conflict arises from a naive interpretation of the representativeness of the survey data and is resolved by using two approaches: exclusion of data and expansion of the model to accommodate the bias.