Estimates of human immunodeficiency virus prevalence and proportion diagnosed based on Bayesian multiparameter synthesis of surveillance data

Estimates of the number of prevalent human immunodeficiency virus infections are used in England and Wales to monitor development of the human immunodeficiency virus-acquired immune deficiency syndrome epidemic and for planning purposes. The population is split into risk groups, and estimates of risk group size and of risk group prevalence and diagnosis rates are combined to derive estimates of the number of undiagnosed infections and of the overall number of infected individuals. In traditional approaches, each risk group size, prevalence or diagnosis rate parameter must be informed by just one summary statistic. Yet a rich array of surveillance and other data is available, providing information on parameters and on functions of parameters, and raising the possibility of inconsistency between sources of evidence in some parts of the parameter space. We develop a Bayesian framework for synthesis of surveillance and other information, implemented through Markov chain Monte Carlo methods. The sources of data are found to be inconsistent under their accepted interpretation, but the inconsistencies can be resolved by introducing additional 'bias adjustment' parameters. The best-fitting model incorporates a hierarchical structure to spread information more evenly over the parameter space. We suggest that multiparameter evidence synthesis opens new avenues in epidemiology based on the coherent summary of available data, assessment of consistency and bias modelling.