Introduction: Patients with obstructive sleep apnea (OSA) suffer from several neurocognitive deficits. We investigated the cognitive and socio-cognitive profiles of patients with severe OSA, controlling for potentially relevant mediating variables (i.e. age, body-mass index, cognitive reserve and depression). Moreover, we studied the neuropsychological profile of a high-risk OSA phenotype characterized by severe OSA and severe nocturnal hypoxemia.Method: We assessed 29 previously untreated severe OSA patients with a mean age of 55.6 (± 9.9 years) and a mean apnea-hypopnea index (AHI) of 53.1 (± 17.4). A control group of 34 healthy participants was also enrolled. Participants completed an extensive neuropsychological battery that included social cognition, a relatively new investigation area among OSA patients.Data analysis: Data were analyzed with a Bayesian approach. Specifically, Bayesian ANCOVA was used to investigate whether the grouping variable could predict test performance. Age, body-mass index, cognitive reserve and state of depression were added as covariates to the null model to weight the effects of these potential confounding factors. Three groups were analyzed: healthy controls (H), OSA with severe apnea and severe nocturnal oxygen desaturation (D+), and OSA with severe apnea non-desaturators (D-). Performances on the various neuropsychological tests were treated as the dependent variables.Results: The results indicate that non-verbal reasoning, the theory of mind skills, and mental shifting ability were impaired in OSA patients. Patients with severe nocturnal hypoxemia underperformed compared to patients with the same severity of apnea but non-desaturators. Additionally, we observed a trend toward a worse performance among OSA desaturator patients in the following abilities: constructional ability, short term verbal memory, phonological fluency, and the ability to inhibit automatic and dominant responses.Conclusion: The data suggest a key role of hypoxemia in affecting cognitive functioning in OSA patients. Executive functions and the concomitant involvement of social cognition are particularly affected.