The most appropriate physiological signals to develop simplified as well as accurate screening tests for obstructive sleep apnoea (OSA) remain unknown. This study aimed at assessing whether joint analysis of at-home oximetry and airflow recordings by means of machine-learning algorithms leads to a significant diagnostic performance increase compared to single-channel approaches. Consecutive patients showing moderate-to-high clinical suspicion of OSA were involved. The apnoea-hypopnoea index (AHI) from unsupervised polysomnography was the gold standard. Oximetry and airflow from at-home polysomnography were parameterised by means of 38 time, frequency, and non-linear variables. Complementarity between both signals was exhaustively inspected via automated feature selection. Regression support vector machines were used to estimate the AHI from single-channel and dual-channel approaches. A total of 239 patients successfully completed at-home polysomnography. The optimum joint model reached 0.93 (95%CI 0.90-0.95) intra-class correlation coefficient between estimated and actual AHI. Overall performance of the dual-channel approach (kappa: 0.71; 4-class accuracy: 81.3%) significantly outperformed individual oximetry (kappa: 0.61; 4-class accuracy: 75.0%) and airflow (kappa: 0.42; 4-class accuracy: 61.5%). According to our findings, oximetry alone was able to reach notably high accuracy, particularly to confirm severe cases of the disease. Nevertheless, oximetry and airflow showed high complementarity leading to a remarkable performance increase compared to single-channel approaches. Consequently, their joint analysis via machine learning enables accurate abbreviated screening of OSA at home.