This paper reports the results of an experiment to evaluate the relationship between results obtained with a drowsiness estimation system we have developed using facial videos and those obtained with the Psychomotor Vigilance Task (PVT), which is a standard index of sleepiness used in sleep medicine. The correlation between PVT scores and the output of the drowsiness estimation system, which outputs drowsiness levels from assigned facial expressions, was calculated using data from 30 subjects. The Spearman's correlation coefficients between the drowsiness estimation results and the PVT mean response time, the slowest 10% response time, and the number of lapses were 0.36 (p <0.001), 0.43 (p <0.001), and 0.40 (p <0.001), respectively. Since this experiment showed a correlation between the drowsiness estimation results and those with PVT, it would seem possible to make specific interventions based on drowsiness estimation results learned from ground-truth drowsiness levels. Such estimation results could help prevent accidents resulting from drowsiness or insufficient vigilance while driving or working.