Bayesian decision theory for tree-based adaptive screening tests with an application to youth delinquency

Crime prevention strategies based on early intervention depend on accurate risk assessment instruments for identifying high risk youth. It is important in this context that the instruments be convenient to administer, which means, in particular, that they must be reasonably brief; adaptive screening tests are useful for this purpose. Although item response theory (IRT) bears a long and rich history in producing reliable adaptive tests, adaptive tests constructed using classification and regression trees are becoming a popular alternative to the traditional IRT approach for item selection. On the upside, unlike IRT, tree-based questionnaires require no real-time parameter estimation during administration. On the downside, while item response theory provides robust criteria for terminating the exam, the stopping criterion for a tree-based adaptive test (the maximum tree depth) is unclear. We present a Bayesian decision theory approach for characterizing the trade-offs of administering tree-based questionnaires of different lengths. This formalism involves specifying 1) a utility function measuring the goodness of the assessment; 2) a target population over which this utility should be maximized; 3) an action space comprised of different-length assessments, populated via a tree-fitting algorithm. Using this framework, we provide uncertainty estimates for the trade-offs of shortening the exam, allowing practitioners to determine an optimal exam length in a principled way. The method is demonstrated through an application to youth delinquency risk assessment in Honduras.