Yes, this should have been a pure dose-response study among people with any history of filled melatonin scripts.
The comparison between the US and UK probably leads to two issues - US users use way too much melatonin and swamp heart disease signal, while UK patients prescribed melatonin probably have significant sleep derangement (consider how much effort it takes to get prescribed something for sleep - you need to schedule an appointment, convince your doctor, go to the pharmacy, etc)
The comparison between the US and UK probably leads to two issues - US users use way too much melatonin and swamp heart disease signal, while UK patients prescribed melatonin probably have significant sleep derangement (consider how much effort it takes to get prescribed something for sleep - you need to schedule an appointment, convince your doctor, go to the pharmacy, etc)