A group-theoretical notation for disease states: an example using the psychiatric rating scale

As an example, we begin by modifying the original ‘Brief Psychiatric Rating Scale’ (BPRS), the most frequently used standards for evaluating the psychopathology of patients with schizophrenia. We consider a presumptively idealized (virtually standardized) BPRS (denoted BPRS-I) with assessments ranging from ‘0’ to ‘6’ to simplify our discussion. Next, we introduce the modulo group Z7 containing elements {0,1,2,…,6} defined by composition rule, ‘modulo 7 addition’, denoted by *. Each element corresponds to a score resulting from grading a symptom under the BPRS-I assessment. By grading all symptoms associated with the illness, a Cartesian product, denoted Aj, constitutes a summary of a patient assessment. By considering operations denoted A(j→k) that change state Aj into state Ak, a group M (that itself contains Aj and Ak as elements) is also considered. Furthermore, composition of these operations obey modulo 7 arithmetic (i.e., addition, multiplication, and division). We demonstrate the application with a simple example in the form of a series of states (A4？=？A1*A(1→2)*A(2→3)*A(3→4)) to illustrate this result.The psychiatric disease states are defined as 18-fold Cartesian products of Z7, i.e., Z7×18？=？Z7×…×Z7 (18 times). We can construct set G？≡？{a(m)i| m？=？1,2,3,…(the patient’s history of the i-th symptom)} and M？≡？{Am | Am ∈ Z7×18 (the set of all possible assessments of a patient)} simplistically, at least, in terms of modulo 7 addition that satisfies the group postulates.Despite the large limitations of our methodology, there are grounds not only within psychiatry but also within other medical fields to consider more generalized notions based on groups (if not rings and fields). These might enable through some graduated expression a systematization of medical states and of medical procedures in a manner more aligned with other branches of natural science.