Statistical inference in transmission models based on Bayesian synthesis of evidence from multiple sources

Policy makers need reliable models to understand the HIV epidemic, to predict the likely future burden of disease for planning, and to predict the likely effect of preventive interventions. Current methods are not adequate to this task. Some methods fail to make use of all the available data, use it in an inconsistent way, and are inherently unable to predict the long term effect of interventions. This is because the risk of acquiring HIV at any point in time depends on how many people already have it, giving rise to dynamic ?feedback? effects. Other methods, which allow for dynamic effects and can therefore predict long term effects of interventions, are not as ?evidence-based? as would be desirable, and it is difficult to tell how accurate their predictions are.

The project builds on successful work already completed by the applicants, who have recently developed methods for estimating the incidence and prevalence of HIV in the England & Wales. These methods are designed to (a) incorporate all the available information, so that predictions are less uncertain, (b) allow the consistency of the information to be established, (c) provide a systematic analysis of the uncertainty in predictions, based on the uncertainties in the data inputs. These methods have been used in the most recent Department of Health report on the state of the HIV epidemic in the UK.

The plan now is to extend and refine these methods, so that they can incorporate HIV transmission dynamics and thus allow policy makers to assess the effects of alternative interventions. This will also allow many more sources of data to be incorporated, reducing uncertainty in prediction still further.


Although the intention is to apply this to the analysis of the HIV epidemic in the UK, the methods to be developed will be applicable to the prevention and control of any human or animal infectious disease.

Reliable methods are need to predict the future course of the HIV epidemic and the effect of possible interventions. Current methods are not adequate. The earlier back-projection methods for incidence estimation has been compromised by anti-retroviral therapy. The ?Direct Method? for prevalence estimation has been shown to make inconsistent and incomplete use of the available data (Goubar, 2006). Models of incidence and prevalence alone cannot predict the long-term effect of lowering incidence because incidence and prevalence are related by feedback mechanisms. Dynamic transmission models address this issue. Here, incidence in any subgroup g depends on the prevalence of infection in each group j and the probability that members on each group j will infect susceptibles in group g. However, dynamic models are generally set out as complex systems of differential equations, and it is not possible to estimate the parameters formally from data. As a result, prediction uncertainty can only be analysed by scenario analysis.

Recently, the applicants developed an alternative approach to prevalence estimation (Goubar, 2006). This was a Bayesian multi-parameter evidence synthesis (MPES) of 6 distinct types of surveillance and survey data on HIV, to simultaneously estimate risk group size, group-specific HIV prevalence and proportion diagnosed, in each of 13 risk groups. MPES allows assessment of consistency in evidence, and propagates uncertainty in evidence correctly through to parameters and predictions. This method was used for the Department of Health?s official report on the status of the HIV epidemic in 2004. Recently we extended this model, so that instead of producing a series of annual prevalence estimates from a series of annual data ensembles, it produces estimates of rates of entry into each of the risk groups, group-specific HIV incidence and diagnosis rates.

We now propose to extend this further to incorporate the essential properties of dynamic transmission models. The main step is to re-parameterise the model, expressing incidence in each group g as a linear combination of proportion of number of infected in group j and probabilities in a contact-an-mixing matrix that individuals in group j will infect susceptibes in group g. This re-parameterisation means that information on sexual contact patterns and transmission probabilities can be combined with the core surveillance data in a single integrated analysis.

The combination of Bayesian propagation of uncertainty with dynamic modelling creates a powerful tool for evidence-based policy analysis, applicable to the dynamics and control of any human or animal infectious disease.