Discriminant Analysis of Hematological Parameters in Breast Cancer Patients and Healthy Women: A Comparative Statistical Study

This research aims to analyze the differences in basic hematological parameters between healthy women and breast cancer patients. The goal is to understand the physiological effects of the disease on blood components and to evaluate the ability of these indicators to predict health status using one of the most important multivariate statistical methods: linear discriminant analysis. The sample consisted of 200 women (100 breast cancer patients and 100 healthy women). Data were collected from the records of the National Cancer Institute in Sabratha between August 2023 and January 2024. The data included six major hematological variables: red blood cells (RBCs), hemoglobin (Hb), hematocrit (HCT), mean corpuscular volume (MCV), white blood cells (WBCs), and platelets. The research employed an independent samples t-test to measure the differences between the two groups, in addition to applying discriminant analysis to identify the variables that contributed most to the segregation. The t-test results showed statistically significant differences in all hematological parameters. Breast cancer patients exhibited a marked decrease in platelets (HCT, Hb, and RBC) and a significant increase in white blood cells (WBC), reflecting physiological changes associated with the disease. Statistical hypothesis tests confirmed the validity of the data for discriminatory analysis, including the homogeneity of the variance-covariance matrices and the absence of multicollinearity among the variables. The discriminatory analysis demonstrated that the extracted function had high power to separate the two groups, with a canonical correlation of 0.899, a latent root value of 3.80, and a Wilkes lambda of 0.208, indicating high explanatory power. The structure matrix showed that HCT, Hb, and RBC were the most significant contributors to the discriminatory effect. The discriminatory function achieved an overall classification accuracy of 91%, demonstrating the effectiveness of the predictive model for classification based on hematological parameters.