Towards theory integration: Threshold model as a link between signal detection theory, fast-and-frugal trees and evidence accumulation theory.

RATIONALE, AIMS AND OBJECTIVES: 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.