It is interesting that the study authors highlight the higher energy expenditure as an advantage for weight loss, but do not seem to directly address that they did not observe this advantage during the 20 week study period.
[1] https://twitter.com/YoniFreedhoff/status/1062762047677571079
Studies have already shown that weight loss affects metabolic rates.
From the paper: "During the test phase, participants’ energy intake was adjusted periodically to maintain weight loss within 2 kg of the level achieved before randomization."
A key part of the study was that they fed the participants more or less each day to maintain weight.
In other words, there should not have been any weight change at all, as weight change would have confounded the results since weight loss is known to effect metabolism.
However, from a layman perspective, it seems like it would be nice to be able to collaborate the measure of increased metabolism not only through one method (doubly labeled water) but also through weight loss over time.
It's like having an inaccurate measuring stick and basing the results of a study solely on measurements made by that one stick, while at the same time making an effort to make sure that no other means of measuring exist.
The second phase of the study involved breaking the participants into three groups. They were fed the same number of calories. Each group had several biomarkers tracked. This included daily calories burned and ghrelin (a hormone) levels. I understand the critique targets the measurement of calories burned, via the doubly labeled water measurement of the metabolic date.
What I wonder is what the average weight change was for each of the three groups after 5 months. If the claim is that the high-fat diet group burned an average of 250 calories more, then that should be reflected in an additional weight loss of about 10 pounds (250 calories per day * 5 months * 30 days in a month / 3700 calories in 1 pound of fat). This would be because all the people across all groups were fed the same number of calories. If one group used 250 calories more per day, these extra calories had to come from somewhere. They would have to come from fat stores and muscle tissue inside of the body, resulting in a weight loss.
If the weight loss for that group correlates with the doubly labeled water measurement then it gives more credence to the study's results. If it does not correlate with weight loss, it is suspicious to claim that one group of people burned 250 more calories than the other over 5 months while eating the same number of calories but did not lose any weight.