Antonio Battista, Rosa Alessia Battista, Federica Battista, Luigi Cinquanta,
Gerardo Iovane, Michele Corbisieri & Angelo Suozzo

Abstract
The aim of the study is to model a new mathematical tool effective in the diagnosis of
colorectal cancer and useful as a mass screening test. This work enrolled 345 subjects from
January 2011 to January 2013, in 4 Italian Surgical Departments: 97 (27,4%) out of the total
were healthy controls (class 0) whereas 248 (72,6%) patients were affected by colorectal cancer.
The cancer patients were divided into four classes, according to TNM staging classification:
74 (20,9%) patients stage I (class 1); 61 (17,2) patients stage II (class 2); 76 (21,5%) patients
stage III (class 3); 37 (10,5%) stage IV (class 4).
Blood samples were collected after 24h from hospital admission and 17 biochemical
parameters (CEA, ceruloplasmin, haptoglobin, transferrin, TPA, CA 19.9, CA 72.4, PCR,
Ca 50, C4 Complement, CA 125, Alfa-1- antitrypsin, alpha-2-Macroglobulin, Ferritin, RBP,
Alpha-1-Acid Glycoprotein, Complement C3) were statistically analysed together with the
clinical and pathological disease staging (pre and postoperative evaluation, respectively).
Evaluation and comparison were made between two groups: healthy controls and the total
of affected patients.
Using the collected data, it was developed a mathematical model (artificial neural
network ANN) allowing the distribution of colorectal cancer and controls (apparently in
good health) patients in the two groups. This led to the definition of an index (B- index)
that, simply analysing the combined values of the 17 biochemical parameters, decides on
the either healthy or disease status of the patient. The use of the B-index, with a neural
network based on real values, allows colorectal cancer diagnosis with 80.078% accuracy,
probability of false positive (FP) = 0.333, probability of false negatives (FN) = 0.102, a 0.898
sensitivity and 0.667 specificity. However, by using B-index with a neural network based on
the implementation of extended reality values our analysis reaches an accuracy of 91.11%
in colorectal cancer diagnosis, with probability of false positive (FP) = 0.472, probability of
false negatives (FN) = 0.03%, a 0.9997 sensitivity and 0.7642 specificity. The results suggest a
promising role for B-index in colorectal cancer mass screening with an easily available, low
cost and non-invasive test.

https://kliniksanktmoritz.ch/wp-content/uploads/2022/04/2019-Battista-A.-et-al.-Journal-of-Interdisciplinary-Mathematics.pdf

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