## 1 Introduction  
Intermittent O\({}_{2}\) desaturation in adult obstructive sleep apnea (OSA) patients has been proven to correlate with possible consequences such as hypertension [1; 2; 3; 4], cognitive deficits [5; 6], and cardiovascular disorders [7; 8; 9] (e.g., pulmonary hypertension [8], coronary artery disease [8; 9], cerebrovascular disease [8; 9], idiopathic cardiomyopathy [8], and congestive heart failure [8; 9]). However, O\({}_{2}\) desaturation with different severities may result from similar apnea-hypopnea indexes(AHIs) and vice versa [10; 11]. Studies have shown that deeper and longer O\({}_{2}\) desaturation events may contribute more to the daytime sleepiness [12; 13] and harmful health consequences than the shallower and shorter events [10]. More severe O\({}_{2}\) desaturations come from appenas, compared to hypopneas (e.g., see [11]). Intermittent O\({}_{2}\) desaturation results from sleep apneas and hypopneas, which constitute a variety of components in most of the AHI.  
A common ground of treating OSA patients could be improving O\({}_{2}\) saturation to reduce consequences. However, surgically treating very severe OSA patients (defined to AHI \(\geq\) 60 events/h here) can be difficult due to their narrow retroglossal space and confined framework, which is hard to enlarge via conventional uvuolapalotopharyngeal (UPPP) surgery [14]. In the literature, very severe OSA refers to having a high AHI or respiratory disturbance index (RDI) of 40 [15; 16], 50 [17; 18; 19; 20; 21], 60 [22; 23; 24; 25; 26], 70 [27], or 100 events per hour [28]. It is a distinct subgroup and differs from OSA with other severities. For example, patients with very severe OSA may have a low level (as 77 mmHg) of diurnal partial pressure of oxygen while they are not in sleep [29]. There may be residual on-Continuous-Positive-Airway-Pressure (CPAP) AHIs \(>\) 20 events per hour [30]. They have less positional OSA [31], a high prevalence of hypertension [29], higher insulin resistance [32], and about three times the chances of heart block compared to an unselected group of OSA patients [33]. The unfavorable anatomy is not necessarily related to obese or high body mass index (BMI) (e.g., see [23; 25]).  
The anatomical limitations and the characteristics of this group of very severe OSA make it hard (e.g., [PERSON]'s 17% (1/6) [34], [PERSON]'s 9% (1/11) [23], and [PERSON]'s 30% (3/10) [35]) to achieve the commonly used \"surgical success\" in sleep surgeries, i.e., AHI \(<\) 20/hour and AHI reduction \(>\) 50%, first proposed by [PERSON] et al. [36]. It is unclear whether increasing hypopnea in AHI, regardless of the qualification of surgical success, improves postoperative O\({}_{2}\) saturation and reduces the consequences. It is also unclear whether the one-stage multilevel surgery we proposed for severe OSA without operating on the bone [37] successfully improves the postoperative O\({}_{2}\) saturation with an unfavorable anatomical stage.  
If more severe O\({}_{2}\) desaturations come from appenas than hypopneas [11] and the surgery may shift apneas to hypopneas, it is reasonable to hypothesize that increasing hypopnea in AHI improves postoperative O\({}_{2}\) saturation in refractory very severe OSA patients. Here, we compared the pre- and post-operative postoperative polysomnographies (PSGs) and showed how increasing hypopnea in AHI reduces frequency of desaturation (by desaturation index (events/h)), reduces severity of desaturation (by mean SpO\({}_{2}\) desaturation (%)), and improves mean SpO\({}_{2}\) after the one-stage multilevel surgery in very severe OSA patients. We also showed how the improvement can be seen in classical non-surgical success patients.