The traditional polysomnography (PSG) examination for Obstructive Sleep Apnea (OSA) diagnosis needs to measure several signals, such as EEG, ECG, EMG, EOG and the oxygen level in blood, of a patient who may have to wear many sensors during sleep. After the PSG examination, the Apnea-Hypopnea Index (AHI) is calculated based on the measured data to evaluate the severity of apnea and hypopnea for the patient. This process is obviously complicated and inconvenient. In this paper, we propose an AI-based framework, called RAre Pattern Identification and DEtection for Sleep-stage Transitions (RAPIDEST), to detect OSA based on the sequence of sleep stages from which a novel rarity score is defined to capture the unusualness of the sequence of sleep stages. More importantly, under this framework, we only need EEG signals, thus significantly simplifying the signal collection process and reducing the complexity of the severity determination of apnea and hypopnea. We have conducted extensive experiments to verify the relationship between the rarity score and AHI and demonstrate the effectiveness of our proposed approach.