From the publication:
The research team performed a polysomnogram, or overnight sleep study, in 44 men ages 20 to 50 years who were overweight or obese. All subjects were otherwise healthy and were nonsmokers. Their selection for the study did not consider whether they had symptoms or a history of sleep apnea, according to Van Cauter. However, the sleep study showed that 29 (66 percent) of the men did have OSA [obstructive sleep apnea], which she said was moderately severe in most cases.
[…]
Later analyses demonstrated that higher total testosterone level strongly correlated with more shallow sleep. This association, Van Cauter said, was independent from the presence of other factors known to decrease sleep quality, such as age, race/ethnicity and OSA [obstructive sleep apnea] severity.