Overnight polysomnography is the gold standard for the detection of obstructive sleep apnea-hypopnea syndrome (OSAS). However, it is expensive and needs attending personnel. The study of simplified sleep apnea monitoring is one of the recent trends for sleep medicine research. The proposed clinical prediction rules employ the vital and social statistics, symptoms, craniofacial traits, and obesity-related measures for initial screening of OSAS in an ambulatory setting. However, most of them are partially or completely clinical and not home-based. One disadvantage of this sort of screening methods is their inability to asses OSAS severity. Another approach of initial OSAS screening is a usage of just one or two physiological signals such as electrocardiography (ECG), pulse oximetry, snoring, nasal airflow, or even speech sound. In this study, we aimed to review the different strategies and to compare their performances, reported by means of their sensitivity–specificity and accuracy for OSAS incidence and severity. OSAS severity is determined by apnea-hypopnea index (AHI) value. Based on the data obtained from the related articles, the most accurate methods of AHI estimation exploit ECG and pulse oximetry signals.