Motivated by the debate over how to deal with the huge backlog of untested sexual assault kits in the U.S.A., we construct and analyze a mathematical model that predicts the expected number of hits (i.e., a new DNA profile matches a DNA sample in the criminal database) as a function of both the proportion of the backlog that is tested and whether the victim-offender relationship is used to prioritize the kits that are tested. Refining the results in Ref. (Criminol Public Policy, 2016, 15, 555), we use data from Detroit, where government funding was used to process approximate to 15% of their backlog, to predict that prioritizing stranger kits over nonstranger kits leads to only a small improvement in performance (a 0.034 increase in the normalized area under the curve of the hits vs. proportion of backlog tested curve). Two rough but conservative cost-benefit analysesone for testing the entire backlog and a marginal one for testing kits from nonstranger assaultssuggest that testing all sexual assault kits in the backlog is quite cost-effective: for example, spending approximate to$1641 to test a kit averts sexual assaults costing approximate to$133,484 on average.
