Integrating and testing natural frequencies, naïve Bayes, and fast-and-frugal trees.

Abstract

This article relates natural frequency representations of cue-criterion relationships to fast-and-frugal heuristics for inferences based on multiple cues. In the conceptual part of this work, three approaches to classification are compared to one another: The first uses a natural Bayesian classification scheme, based on profile memorization and natural frequencies. The second is based on Naïve Bayes, a heuristic that assumes conditional independence between cues (given the criterion). The third approach is to construct fast-and-frugal classification trees, which can be conceived as pruned versions of diagnostic natural frequency trees. Fastand-frugal trees can be described as lexicographic classifiers but can also be related to another fundamental class of models, namely linear models. Linear classifiers with fixed thresholds and noncompensatory weights coincide with fast-and-frugal trees-not as processes but in their output. Various heuristic principles for tree construction are proposed. In the second, empirical part of this article, the classification performance of the three approaches when making inferences under uncertainty (i.e., out of sample) is evaluated in 11 medical data sets in terms of Receiver Operating Characteristics (ROC) diagrams and predictive accuracy. Results show that the two heuristic approaches, Naïve Bayes and fast-and-frugal trees, generally outperformed the model that is normative when fitting known data, namely classification based on natural frequencies (or, equivalently, profile memorization). The success of fast-and-frugal trees is grounded in their ecological rationality: their construction principles can exploit the structure of information in the data sets. Finally, implications, applications, limitations, and possible extensions of this work are discussed.

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Precision medicine for individual patients should use population group averages and larger, not smaller, groups

“…However, making treatment or other management choices based on a severely restricted sample can be highly misleading. This is a reason why predictive models often fail external validity assessments—in our desire to develop fine‐grained, precise risk estimates, the models typically overfit and generate wrong risk estimates when applied outside of the training data set …”

“…Hence, paradoxically the seemingly inferior treatment B based on the assessment from the small sample may be the best choice for the next (our) patient to be treated. Conversely, using methods to collapse risk categories in fewer clinically relevant categories may help improve risk assessment by including a larger number of patients who are similar enough to the patient we want to manage …”

“…This is a reason why predictive models often fail external validity assessments-in our desire to develop fine-grained, precise risk estimates, the models typically overfit and generate wrong risk estimates when applied outside of the training data set. 7 An increasingly common situation is that physicians and patients are tempted to search electronic medical records to find other patients who are matched to a very large number of characteristics. While an electronic health record database may include, for example, tens of thousands of patients with colorectal cancer, when a patient with colorectal cancer tries to match his own profile to other previous patients who not only had colorectal cancer, but also had the same values for 100 other characteristics, the eligible patients to compare against may be few, if any.…”

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