Introduction
Accurate information on disease prevalence is needed to target limited health resources in order to maximize overall population health. Applying rigorous econometric methods to routinely collected data can produce accurate estimates of disease prevalence and under-detection rates at a fraction of the cost of alternatives such as prevalence surveys or universal diagnostic testing. Such estimates are valuable in developing countries to inform evidence-based health policy.

Methods
We develop a simple framework with minimal assumptions to capture key features of clinical decision making surrounding diagnostic testing in resource limited settings. When it is infeasible to test every at-risk patient, clinicians must triage available resources to test those deemed most likely to have the disease. We use standard econometric estimation methods and iterative numerical optimization techniques to estimate (a) disease prevalence and (b) the accuracy with which clinicians triage patients for testing. We implement an instrumental variables approach using national and local policy changes that exogenously shift the available resources for diagnostic testing as instruments. We apply this method to tuberculosis (TB), which recently surpassed HIV as the leading infectious disease cause of death in the world. We use a national database of TB test data from South Africa, which includes over 11 million patients, to examine diagnostic testing for multi-drug resistant TB (MDR-TB).

Results
The predictions from our model closely match observed patterns in the data. We find that at least one-quarter of MDR-TB cases were undiagnosed between 2004-2011. Our estimates show that the official World Health Organization estimate of 2.5% based on notification rates is too low, and MDR-TB prevalence in South Africa could be as high as 3.29 – 3.37%. Noise-to-signal ratios in MDR-TB detection estimated in our model enable the identification of areas where clinicians do a poor job of sorting patients by MDR-TB risk prior to testing.

Discussion
In the case of MDR-TB there is a need for greater investment in early detection and more effective treatment. Our method of identifying areas with high MDR-TB under-detection rates, which was heretofore unmeasured and contributes to high transmission rates, provides clinicians and policy makers with a formidable new tool for targeting efforts to control TB. This method should be deployed in countries such as India, China and Russia, which together account for over 50% of MDR-TB cases worldwide, as well as applied to other infectious and non-infectious diseases where prevalence data is lacking.