Further suggestions on the group-theoretical approach using clinical values

In a previous report, we suggested a prototypal model to describe patient states in a graded vector-like format based on the modulo groups via the psychiatric rating scale. In this article, using other simple examples, we provide additional suggestions to clarify how other clinical data can be treated practically in line with our proposed model.

As illustrations of the wider applicability, we treat four cases commensurate with modulo arithmetic: 1) prescription doses of three medicines (lithium carbonate, mirtazapine, and nitrazepam), 2) changes in laboratory data (blood concentrations of lithium carbonate, white blood cells, percutaneous oxygen saturation and systolic blood pressure), 3) the tumor node metastasis (TNM) classification of malignant tumors applied for esophageal tumors, and 4) the coding schemes of the International Classification of Diseases (ICD) for selected diseases or laboratory data. For each case, we present simple examples in the form of product of states to illustrate these results.

1) Medications and their changes can be represented as elements of a modulo group; e.g., group S = {Sj | Sj ε Z(13)×Z(4)×Z(3)} can represent the set of all possible prescription combinations of three specified medicines. Likewise, 2) clinical values can also be expressed as a modulo group; e.g., group T = {Tj | Tj ε Z(600)×Z(50000)×Z(100)×Z(300)} representing the set of all possible data based on any number of clinical values and their differences. Also, 3) the TNM classification for malignant tumors can be treated within a single modulo group C = {Cj | Cj ε Z(8)×Z(4)×Z(2)×Z(2)}, the set of all composable disease states graded in terms of tumor expansion. Finally, 4) ICD coding schemes provide several examples treatable as a modulo group D = {Dj | Dj ε Z(7)×Z(7)× …×Z(7) (an n-fold product)}, constituting the set of all possible severities of diseases states and laboratory data within provided tuples.

Despite the limited scope of our methodology, there are grounds where other clinical quantities (prescription of medicine, laboratory data, TNM classification of malignant tumors, and ICD coding schemes) can be also treatable with the same group-theory approach as was suggested for psychiatric disease states in our previous report.