Page - 31 - in Applied Interdisciplinary Theory in Health Informatics - Knowledge Base for Practitioners

We can see that the entropy varies between 0 and 1, with a maximum at 1 when ݌ ൌ ͲǤͷ (see figure 3). Figure 3. Variation of Entropy vs probability for a biased coin. Think of the coin flip as a test on the internal state of a patient. A “heads” says the patient may have the disease, a “tails” says the disease is not present. If the coin is unbiased then as a test it is not helping us; all internal states are equally possible. We need a test where the entropy is close to 0 or 1 in order for us to be able to gain anything informative about the internal state of the patient. Vollmer [13] explored the use of entropy to analyse the information content of a number of laboratory tests. He demonstrated how the concepts from information theory can be used as an aid to evaluating and understanding laboratory test results. We will use just one example to illustrate the point by using Figure 3 as a reference point. Stadelmann et al [10] reported that the probability of 10-year mortality for malignant melanoma could be estimated from tumour thickness t using the following formula: ݌ ൌͳെǤͻ͸ ͸ ൈ݁ିሺ଴ Ǥଶ଴ ଵ଺ ௧ሻ In Figure 4, we plot H vs tumour thickness t, using Equation 5. We can see that over quite a wide range of values, with median ൎ͵Ǥͷ݉݉, tumour thickness provides limited information about the outcome. 0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6 0.8 1 1.2 Probability P.Krause / InformationTheoryandMedicalDecisionMaking 31