Pooled-testing methods can greatly reduce the number of tests needed to identify failures in a collection of samples. Existing methodology has focused primarily on binary tests, but there is a clear need for improved efficiency when using expensive quantitative tests, such as tests for HIV viral load in resource-limited settings. We propose a matrix-pooling method which, based on pooled-test results, uses the EM algorithm to identify individual samples most likely to be failures. Two hundred datasets for each of a wide range of failure prevalence were simulated to test the method. When the measurement of interest was normally distributed, at a failure prevalence level of 15.6% the EM method yielded a 47.3% reduction in the number of tests needed to identify failures (as compared to testing each specimen individually). These results are somewhat better than the reduction gained by using the Simple Search method (44.9%) previously published by May et al. (2010). However, the EM procedure was able to identify failures in just 2.6 testing rounds, on average, as compared to an average of 19.2 testing rounds required by Simple Search. In settings where the turn-around time for testing services is significant, the reduction in testing rounds provided by the EM method is substantial. Unfortunately the EM method does not perform as well when the measurements of interest are highly skewed, as is often the case with viral load concentrations.
Hanscom, Brett; May, Susanne; and Hughes, Jim, "Efficiently Identifying Failures using Quantitative Tests, Matrix-Pooling and the EM-Algorithm" (March 2014). UW Biostatistics Working Paper Series. Working Paper 402.