Bayesian adaptive algorithms for locating HIV mobile testing services

Gregg S. Gonsalves, J. Tyler Copple, Tyler Johnson, A. David Paltiel, Joshua L. Warren

We have previously conducted computer-based tournaments to compare the yield of alternative approaches to deploying mobile HIV testing services in settings where the prevalence of undetected infection may be characterized by 'hotspots'. We report here on three refinements to our prior assessments and their implications for decision-making. Specifically, (1) enlarging the number of geographic zones; (2) including spatial correlation in the prevalence of undetected infection; and (3) evaluating a prospective search algorithm that accounts for such correlation. Building on our prior work, we used a simulation model to create a hypothetical city consisting of up to 100 contiguous geographic zones. Each zone was randomly assigned a prevalence of undetected HIV infection. We employed a user-defined weighting scheme to correlate infection levels between adjacent zones. Over 180 days, search algorithms selected a zone in which to conduct a fixed number of HIV tests. Algorithms were permitted to observe the results of their own prior testing activities and to use that information in choosing where to test in subsequent rounds. The algorithms were (1) Thompson sampling (TS), an adaptive Bayesian search strategy; (2) Besag York Mollié (BYM), a Bayesian hierarchical model; and (3) Clairvoyance, a benchmarking strategy with access to perfect information. Over 250 tournament runs, BYM detected 65.3% (compared to 55.1% for TS) of the cases identified by Clairvoyance. BYM outperformed TS in all sensitivity analyses, except when there was a small number of zones (i.e., 16 zones in a 4 × 4 grid), wherein there was no significant difference in the yield of the two strategies. Though settings of no, low, medium, and high spatial correlation in the data were examined, differences in these levels did not have a significant effect on the relative performance of BYM versus TS. BYM narrowly outperformed TS in our simulation, suggesting that small improvements in yield can be achieved by accounting for spatial correlation. However, the comparative simplicity with which TS can be implemented makes a field evaluation critical to understanding the practical value of either of these algorithms as an alternative to existing approaches for deploying HIV testing resources.