Bayesian analysis of two-component mixture distributions applied to estimating malaria attributable fractions

Malaria illness can be diagnosed by the presence of fever and parasitaemia. However, in highly endemic areas the diagnosis of clinical malaria can be difficult since children may tolerate parasites without fever and may have fever due to other causes. We propose a novel, simulation-based Bayesian approach for obtaining precise estimates of the probabilities of children with different levels of parasitaemia having fever due to malaria, by formulating the problem as a mixture of distributions. The methodology suggested is a general methodology for decomposing any two-component mixture distribution nonparametrically, when an independent training sample is available from one of the components. It is based on the assumption that one of the component distributions lies on the left of the other but there is some overlap between the distributions.