Alzheimer's disease (AD) often manifests alongside sleep disorders, with disruptions in sleep patterns preceding the onset of Mild Cognitive Impairment (MCI) and early-stage AD. This research explores the potential of leveraging sleep-related electroencephalography (EEG) signals, obtained via polysomnography (PSG), for the early detection of AD. While Deep Neural Networks (DNNs) show promise in analyzing EEG signals for AD detection, ensuring the calibration of model predictions is essential for clinical relevance. This study investigates post-processing calibration methods for the XCM model across different sleep stages. Despite achieving accuracy metrics of around 94%, the results reveal misaligned confidences. Calibration of confidence models is enhanced through several post-processing approaches, with histogram binning emerging as the most effective method. These findings contribute to advancing AD detection using innovative Deep Learning approaches and emphasize the critical role of calibration studies in ensuring accurate and reliable predictions for clinical decision-making in diagnosis.