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The diagnosis of breast cancer (BC) with a machine-learning model is a classification problem where the model involves training a model to identify the class of a given observation. However, real-world Wisconsin's BC diagnostic dataset, which is widely employed to implement a model for BC detection, consists imbalanced class. The benign class outnumbers the malignant class. The implementation of a model for BC detection with an imbalanced dataset leads to biased classification towards the majority class leading to lower accuracy and precision of malignant class. Thus, this research proposes a cost-sensitive logistic regression model for BC detection. During the training phase, benign and malignant class is weighted to influence the classification bias toward begin class. The study compared the model with standard logistic regression. The experimental result appears to prove that the proposed model outperforms as compared to standard logistic regression. The model has receiver characteristic curve area value AUC = 99.99. [ABSTRACT FROM AUTHOR]