Further suggestions on the group-theoretical approach using clinical values

Abstract Background 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. Methods 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. Results 1) Medications and their changes can be represented as elements of a modulo group; e.g., group S = {Sj | Sj ∈ Z13×Z4×Z3} 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 ∈ Z600×Z50000×Z100×Z300} 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 ∈ Z8×Z4×Z2×Z2}, 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 ∈ Z7×Z7× …×Z7 (an n-fold product)}, constituting the set of all possible severities of diseases states and laboratory data within provided tuples. Conclusions 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.</p

Symmetrical treatment of "Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition", for major depressive disorders

BACKGROUND: We previously presented a group theoretical model that describes psychiatric patient states or clinical data in a graded vector-like format based on modulo groups. Meanwhile, the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5, the current version), is frequently used for diagnosis in daily psychiatric treatments and biological research. The diagnostic criteria of DSM-5 contain simple binominal items relating to the presence or absence of specific symptoms. In spite of its simple form, the practical structure of the DSM-5 system is not sufficiently systemized for data to be treated in a more rationally sophisticated way. To view the disease states in terms of symmetry in the manner of abstract algebra is considered important for the future systematization of clinical medicine. RESULTS: We provide a simple idea for the practical treatment of the psychiatric diagnosis/score of DSM-5 using depressive symptoms in line with our previously proposed method. An expression is given employing modulo-2 and −7 arithmetic (in particular, additive group theory) for Criterion A of a ‘major depressive episode’ that must be met for the diagnosis of ‘major depressive disorder’ in DSM-5. For this purpose, the novel concept of an imaginary value 0 that can be recognized as an explicit 0 or implicit 0 was introduced to compose the model. The zeros allow the incorporation or deletion of an item between any other symptoms if they are ordered appropriately. Optionally, a vector-like expression can be used to rate/select only specific items when modifying the criterion/scale. Simple examples are illustrated concretely. CONCLUSIONS: Further development of the proposed method for the criteria/scale of a disease is expected to raise the level of formalism of clinical medicine to that of other fields of natural science

Interpretation for scales of measurement linking with abstract algebra

The Stevens classification of levels of measurement involves four types of scale: “Nominal”, “Ordinal”, “Interval” and “Ratio”. This classification has been used widely in medical fields and has accomplished an important role in composition and interpretation of scale. With this classification, levels of measurements appear organized and validated. However, a group theory-like systematization beckons as an alternative because of its logical consistency and unexceptional applicability in the natural sciences but which may offer great advantages in clinical medicine. According to this viewpoint, the Stevens classification is reformulated within an abstract algebra-like scheme; ‘Abelian modulo additive group’ for “Ordinal scale” accompanied with ‘zero’, ‘Abelian additive group’ for “Interval scale”, and ‘field’ for “Ratio scale”. Furthermore, a vector-like display arranges a mixture of schemes describing the assessment of patient states. With this vector-like notation, data-mining and data-set combination is possible on a higher abstract structure level based upon a hierarchical-cluster form. Using simple examples, we show that operations acting on the corresponding mixed schemes of this display allow for a sophisticated means of classifying, updating, monitoring, and prognosis, where better data mining/data usage and efficacy is expected