Page - 33 - in Applied Interdisciplinary Theory in Health Informatics - Knowledge Base for Practitioners

common information), then we have an objective basis for reducing the number of tests performed. Two additional concepts were used in Lee and Maslove [6]. The first of these was the conditional entropy of X given Y. This measures the average uncertainty about a random variable x that remains when y is known (x and y being the respective random variables for the ensembles X and Y). It is defined as: Eq 6. ܪሺܺȁܻሻൌσ ݌ ሺݔǡݕሻ݈݋ ݃ ଵ ௣ ሺ௫ȁ௬ሻ௫௬א஺ ೉ ஺ ೊ Referring back to the definition of an ensemble, AX is the alphabet of the ensemble X; that is, the set of legal values of the random variable x. Similarly, AY is the alphabet of the ensemble Y. A related concept is the mutual information between X and Y. This measures the amount of information that x conveys about y, and is defined as: Eq 7. ܫሺܺǢܻሻؠܪሺܺሻെܪሺܺȁܻሻ Note that we have followed the definitions as given in Mackay [7]. Lee and Maslove extracted laboratory test results from MIMIC II, a fully anonymised public database. They analysed a total of 29,149 ICU admissions, investigating the following laboratory tests: haematocrit; platelet count; white blood cell count (WBC); glucose; HCO3; potassium, sodium; chloride; BUN (Blood Urea Nitrogen); creatinine; and, lactate. Overall, their findings strongly supported the view that a significant amount of the bloodwork performed in ICUs is unnecessary. This had previously been discussed in [14], but Lee and Maslove were able to quantify the level of redundant information content. As a specific example, they found a high level of redundancy in information between the tests for BUN and creatinine; suggesting that if one is known, the other can be inferred with reasonable confidence. Furthermore, their analysis indicated that given the choice, it would be better to prefer BUN over creatinine. Of course, clinical judgement will always be needed but this information theoretic approach does provide an objective foundation to an informed choice. 6. Discussion We have shown in this chapter that information theory can have value in informing medical decision making. We have drawn on a number of studies in order to illustrate this. However, there is one area where we do beg to differ with most of those studies. Many of them bring in additional terminology to try and provide an intuitive semantics to some of the concepts in information theory; notions of “surprise”, “closeness to certainty”, perhaps a tendency to try and equate entropy to uncertainty. One can understand this. Within classical thermodynamics, entropy is perhaps one of the hardest concepts to gain a feeling for. However, we have been careful to refer only to measures of information and entropy. We have briefly alluded to an equivalence between Shannon entropy and entropy from statistical mechanics through associating the messages that can be potentially received from a patient with the internal microstates of that patient. P.Krause / InformationTheoryandMedicalDecisionMaking 33