ENTROPY-BASED EXPECTED UNCERTAINTY REDUCTION TO GUIDE THE CLINICAL EXAM

  

Purpose: The ability to anticipate the impact of potential clinical findings in discriminating among possible causes of a patient’s presenting complaint is an essential component of clinical judgment. We applied an information theory based measure (Benish, Meth Inf Med, 2003), based on both test sensitivity and disease probability, and compared it with familiar sensitivity-based measures (LR+, LR-, and the LR ratio).   

Method: The approach considers all diagnoses relevant for a clinical presentation, with sensitivities of all findings for all the diagnoses. Without “specificity,” it avoids the problem of “dynamic specificity.”      Entropy, or Sum p(Di)*log(1/p(Di)), expresses the uncertainty regarding the current probability distribution over diagnoses Di. We construct a tree whose first branch is a particular finding’s results (positive, negative) with probabilities composed of each p(Di) multiplied by the finding’s sensitivity for that diagnosis. After each branch there is an entropy tree, with the diagnoses’ probabilities contingent on the finding result, e.g., Sum p(Di | F+) * log (1/p(Di | F+)). This expected entropy uncertainty is compared to the pre-finding uncertainty, yielding an expected reduction in entropy uncertainty (ERIEU).    Comparisons are made between the ERIEU and the sensitivity based measures. Further, this approach was added to a balance beam aid for instruction in diagnosis (BBAID), to calculate ERIEU dynamically as other information is learned.    

Result: For a pair of diagnoses, there is a large family of entropy based measures, different for every pretest odds of the two diagnoses, compared to the 5 diagnosis-probability-independent sensitivity-based measures. As the number of diagnosis pairs N increases, the count of measures increases by a factor of N*(N-1)/2.  The BBAID calculates ERIEU dynamically, for all unknown findings, as the probability distribution changes (when additional findings are specified), and displays it for all unknown symptoms, for any selected diagnosis pair.    

Conclusion: The information-theory based measure, ERIEU, is distinct from the measures derivable from sensitivity alone. It changes dynamically as other information is acquired that changes the probability distribution among the diagnoses. Though this is too complicated to judge unaided or to calculate manually, we have added it to a diagnosis aid that represents the (naïve) Bayesian impact of information, for any pair of diagnoses. The display of ERIEU for each finding not yet asked for can guide physician’s selection of useful questions.