Estimating the prevalence of a disease, such as COVID-19, is necessary for evaluating and mitigating risks of its transmission. Estimates that consider how prevalence changes with time provide more information about these risks but are difficult to obtain due to the necessary survey intensity and commensurate testing costs. Motivated by a dataset on COVID-19, from the University of Notre Dame, we propose pooling and jointly testing multiple samples to reduce testing costs. A nonparametric, hierarchical Bayesian model is used to infer population prevalence from the pooled test results without needing to retest individuals from pools that test positive. This approach is shown to reduce uncertainty compared to individual testing at the same budget and to produce similar estimates compared to individual testing at a much higher budget through simulation studies and an analysis of COVID-19 infections at Notre Dame.

Estimating the prevalence of a disease is necessary for evaluating and mitigating risks of its transmission within or between populations. Estimates that consider how prevalence changes with time provide more information about these risks but are difficult to obtain due to the necessary sampling intensity and commensurate testing costs. We propose pooling and jointly testing multiple samples to reduce testing costs and use a novel nonparametric, hierarchical Bayesian model to infer population prevalence from the pooled test results. This approach is shown to reduce uncertainty compared to individual testing at the same budget and to produce similar estimates compared to individual testing at a much higher budget through two synthetic studies and two case studies of natural infection data.