title: Towards theory integration: Threshold model as a link between signal detection theory, fast-and-frugal trees and evidence accumulation theory.
abstract: OBJECTIVE
  Theories of decision making are divided between those aiming to help decision makers in the real, 'large' world and those who study decisions in idealized 'small' world settings. For the most part, these large- and small-world decision theories remain disconnected.
  
  
  METHODS
  We linked the small-world decision theoretic concepts of signal detection theory (SDT) and evidence accumulation theory (EAT) to the threshold model and the large world of heuristic decision making that rely on fast-and-frugal decision trees (FFT).
  
  
  RESULTS
  We connected these large- and small-world theories by demonstrating that seemingly different decision-making concepts are actually equivalent. In doing so, we were able (1) to link the threshold model to EAT and FFT, thereby creating decision criteria that take into account both the classification accuracy of FFT and the consequences built in the threshold model; (2) to demonstrate how threshold criteria can be used as a strategy for optimal selection of cues when constructing FFT; and (3) to show that the compensatory strategy expressed in the threshold model can be linked to a non-compensatory FFT approach to decision making. We also showed how construction and performance of FFT depend on having reliable information - the results were highly sensitive to the estimates of benefits and harms of health interventions. We illustrate the practical usefulness of our analysis by describing an FFT we developed for prescribing statins for primary prevention of cardiovascular disease.
  
  
  CONCLUSIONS
  By linking SDT and EAT to the compensatory threshold model and to non-compensatory heuristic decision making (FFT), we showed how these two decision strategies are ultimately linked within a broader theoretical framework and thereby respond to calls for integrating decision theory paradigms.
authors.affiliation: Department of Mathematics, Indiana University, Gary, IN, USA.
authors.forename: Iztok
authors.initials: I
authors.lastname: Hozo
authors.affiliation: Departments of Hematology and Health Outcome Behavior, H. Lee Moffitt Cancer Center and Research Institute, Tampa, FL, USA.|Tampa General Hospital, Tampa, FL, USA.|Max Planck Institute for Human Development, Berlin, Germany.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Djulbegovic
authors.affiliation: Max Planck Institute for Human Development, Berlin, Germany.
authors.forename: Shenghua
authors.initials: S
authors.lastname: Luan
authors.affiliation: USF Health Program for Comparative Effectiveness Research, Division for Evidence-Based Medicine, Department of Internal Medicine, University of South Florida, Tampa, FL, USA.
authors.forename: Athanasios
authors.initials: A
authors.lastname: Tsalatsanis
authors.affiliation: Max Planck Institute for Human Development, Berlin, Germany.
authors.forename: Gerd
authors.initials: G
authors.lastname: Gigerenzer
mesh_terms: D000066491:Clinical Decision-Making / Q000379:methods*; D003657:Decision Making; D003661:Decision Support Techniques; D003663:Decision Trees; D006801:Humans; D008962:Models, Theoretical; D017603:Signal Detection, Psychological
keywords: clinical guidelines; evaluation; evidence-based medicine