Metrological references for health care based on entropy

Abstract

Consistent diagnosis in healthcare relies, in part, on quality assurance of categorical observations, such as responses to ability tests and patient surveys. Linking classifications on such nominal and ordinal scales to decision-making involves a combination of logit transformations and novel entropy-based estimates of measurement information throughout the measurement process. This paper presents how entropy can explain and predict entity attributes (such as task difficulty), instrument ability and resolution, and measurement system response. Cognitive ability studies in the EMPIR NeuroMET project are taken as an example, showing how better understanding of both entity and measurement system attributes leads to more fit-for-purpose and better targeted treatment.

The Role of Entropy in Construct Specification Equations (CSE) to Improve the Validity of Memory Tests

“…Our understanding means that memory task difficulty could be sufficiently explained and captured by mathematically formulating CSEs where entropy is shown to be the dominant explanatory variable. Strikingly, for the memory tests CBT and DST, as well as in our previous work on KCT [8,12,43], it is found that essentially the same CSE describes task difficulty within uncertainties for all these non-verbal sequence tests, with basically just one explanatory variable, namely Entropy. These results contrast with the conclusions of several previous studies, e.g., [10,41,42,45] where more than one explanatory variable was claimed to be significant, while at the same time not explicitly declaring measurement uncertainties nor using the Rasch model.…”

“…Continuing our presentation of entropy and memory task difficulty, the CBT and DST (and the Knox Cube Test (KCT), as shown in our earlier work [8,12,43], and other memory sequence tests) can be characterized in general in terms of a message in which a number, G , which can be summed to unity. The total number, P, of messages that can be obtained by distributing the symbols at random over the G cells (with never more than one symbol per cell) is P = G!…”

“…Continuing our presentation of entropy and memory task difficulty, the CBT and DST (and the Knox Cube Test (KCT), as shown in our earlier work [ 8 , 12 , 43 ], and other memory sequence tests) can be characterized in general in terms of a message in which a number, N j , ( j = 1,…, M ) of symbols of M different types (blocks or digits) can be distributed in a number, G , of categories (or cells) . The probability of encountering the j th symbol is , which can be summed to unity.…”

“…This can both contribute as a constant offset (intercept) in the overall entropy with the term , as well as to uncertainties in the Rasch model estimates of task difficulty and person ability θ, to account for potential variations in discrimination from person to person and/or item to item. The latter uncertainties can be estimated from the entropy relation , deduced following the usual practice of invoking a uniform distribution in a type B evaluation of measurement standard uncertainty, u , for an instrument (test person) with finite resolution ρ [ 8 ]. This uncertainty determines how steeply the ogive Rasch curve ( Figure 2 ) transitions from one score to another for the present case of dichotomous responses.…”

“…Recent examples of how this has been applied in memory tests is for the KCT are presented by Pendrill et al [ 8 ], Pendrill [ 12 ] and Melin et al [ 43 ]. These KCT results will be set in relation to the experimental demonstrations for the other memory tests CBT and DST in this paper in Section 3.3 .…”