Natural frequency trees improve diagnostic efficiency in Bayesian reasoning

Abstract

When physicians are asked to determine the positive predictive value from the a priori probability of a disease and the sensitivity and false positive rate of a medical test (Bayesian reasoning), it often comes to misjudgments with serious consequences. In daily clinical practice, however, it is not only important that doctors receive a tool with which they can correctly judge—the speed of these judgments is also a crucial factor. In this study, we analyzed accuracy and efficiency in medical Bayesian inferences. In an empirical study we varied information format (probabilities vs. natural frequencies) and visualization (text only vs. tree only) for four contexts. 111 medical students participated in this study by working on four Bayesian tasks with common medical problems. The correctness of their answers was coded and the time spent on task was recorded. The median time for a correct Bayesian inference is fastest in the version with a frequency tree (2:55 min) compared to the version with a probability tree (5:47 min) or to the text only versions based on natural frequencies (4:13 min) or probabilities (9:59 min).The score diagnostic efficiency (calculated by: median time divided by percentage of correct inferences) is best in the version with a frequency tree (4:53 min). Frequency trees allow more accurate and faster judgments. Improving correctness and efficiency in Bayesian tasks might help to decrease overdiagnosis in daily clinical practice, which on the one hand cause cost and on the other hand might endanger patients’ safety.

Improving Diagnostic Efficiency with Frequency Double-Trees and Frequency Nets in Bayesian Reasoning

“…To assess diagnostic efficiency, we used a score according to Binder et al 16 This diagnostic efficiency score is the median time on task divided by the proportion of correct conclusions. Lower values of this score mean more correct and faster diagnoses.…”

“… 15 Determining how to improve the Bayesian reasoning process could be helpful for increasing the accuracy of medical decisions and thus minimizing important errors in patient communication and treatment. 16 …”

“… 7 , 18 Furthermore, it could be shown that frequency (double-)trees lead to more accurate solutions of Bayesian tasks (whereas probability [double-]trees help less). 16 , 17 A more advanced version of tree diagrams are double-tree diagrams and net diagrams, which are particularly suitable for the education of medical students and physicians (see Figure 1 ). 16 , 18 Double-tree diagrams and net diagrams already contain the correct solution of the task.…”

“… 16 , 17 A more advanced version of tree diagrams are double-tree diagrams and net diagrams, which are particularly suitable for the education of medical students and physicians (see Figure 1 ). 16 , 18 Double-tree diagrams and net diagrams already contain the correct solution of the task. Compared with tree diagrams, no further calculation is necessary.…”

“… 15 Diagnostic speed seems to be higher when indications are given as natural frequencies in tree diagrams. 16 , 35 The more mental steps that have to be taken, the longer it takes to reach a solution to Bayesian questions. 36 However, the diagnostic speed has not yet been investigated for double-trees and net diagrams, although this is interesting because the correct solution is already presented within the diagram.…”