Patients with obstructive sleep apnea (OSA) experience fragmented sleep and exhibit different sleep architectures. While polysomnographic metrics for quantifying sleep architecture are studied, there is little information about the impact of OSA on the ratio of different sleep-wake stages (wake, W; rapid eye movement, REM; non-REM stages 1 to 3, N1 to N3). This study, therefore, aims to investigate the relationship between apnea-hypopnea index (AHI, a measure of OSA severity) and all possible ratios of sleep-wake stages. Sleep architectures of 24 adult subjects with suspected OSA were constructed according to the American Academy of Sleep Medicine scoring manual, and subsequently analyzed through various correlation (Pearson, Spearman, and Kendall) and regression (linear, logarithmic, exponential, and power-law) approaches. Results show a statistically significant positive, linear and monotonic correlation between AHI and REM/N3, as well as between AHI and N1/W (p-values < 0.05). These findings imply that patients with increased severity of OSA may spend more time in REM than deep sleep, and in light sleep than wake (or less time in deep sleep than REM, and in wake than light sleep). A power-law regression model may possibly explain the relationships of AHI-REM/N3 and AHI-N1/W, and predict the value of AHI using REM/N3 or N1/W.