The gut microbiota has been a popular area of research over the past few years and few aspects of this research have gained quite as much attention as the role of the gut microbiota in obesity.
One of the studies that started this was published in Nature in 2006. This study has been rather influential as Google Scholar states that, as of today, this study has now been cited 5,842 times.
https://www.ncbi.nlm.nih.gov/pubmed/17183312
The reason for its importance is that it was the first study to show that transplanting the microbiota from obese mice into lean mice made the mice fatter than mice getting transplants from lean mice.
Some previous studies had reported differences in the composition of the gut microbiota between obese and lean individuals, but this was the first study to provide evidence that this might be causal.
The key graph in the paper for this is Figure 3c (yellow highlights are mine).
In germ-free mice transplanted with gut microbiota from obese mice, body fat increased by 47% compared to 27% getting a microbiota from lean mice.
While this looks like a big difference, it is worth noting that this is not body fat percentage. This is the percentage increase in fat in relation to the initial body fat. This is difficult to interpret without knowing how much fat the mice started with.
The study does not state the starting body fat of the mice, but it does tell us in the results how much fat the mice gained in grams.
As we know the percentage increase in body fat and the total weight of that increase, we can calculate the amount of fat each group of mice had before the faecal transplant.
Mice getting a faecal transplant from obese mice gained 1.3 grams of fat, an increase of 47% relative to their starting fat.
Mice getting a faecal transplant from lean mice gained 0.86 grams of fat, an increase of 27% relative to their starting fat.
If we calculate their starting fat:
Lean transplant recipients: 1.3/0.47 = 2.76
Mice getting obese mice transplants had 2.76 grams of fat at the start.
Obese transplant recipients: 0.86/0.27 = 3.19
Mice getting lean mice transplants had 3.19 grams of fat at the start.
If we add those up…
2.76 + 1.3 = 4.05
3.19 + 0.86 = 4.07
The final body fat of both groups was almost the same at about 4.1 grams
If we graph the total weight of the body fat in the two groups of mice:
(This graph probably wouldn’t get you a paper in Nature).
As you can see, while the mice getting a faecal transplant from the obese mice gained a little more fat, they ended up with the same body fat at the end of the study as the mice getting faecal transplants from lean mice. As mice at this age would typically weigh about 25 grams, at 4 grams of body fat both groups of mice would be considered lean and therefore neither group of mice were obese after the transplantation.
This suggests that the results may not be quite as exciting as they first seemed.
Percentage increases in fat do have valid uses in science but they can also be used to make minimal differences look larger and to make them statistically significant.
It is always worth reading graphs carefully.
The call of the Honeyguide 
Umm, the starting amounts of fat differed by .4 grams and the final weights were nearly the same, right? Doesn’t that suggest that something is causing that difference? I think you’re emphasized by the wrong factor.
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You missed the point, Honey. The important data finding IS the percent change, as reported in the Jeff Gordon paper. The percent change is the only way of attempting to overcome a heterogeneous baseline value, in this case the Ob recipient group happened to be smaller. For example, in human research, where is there is a large amount of heterogeneity of baseline values, the percent change is the valid way of presenting the data. It doesn’t matter that the baseline weights were different, although the researchers should have made a better effort to match the weights of the two test groups. The results would, however, likely be the same if the avg. weights of the test groups were reversed.
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It would also be interesting to see two more groups: lean mice getting lean mouse transplant and obese group getting obese mice fecal transplant. Regardless, the groups would not have the same start weight because one group is obese and one group is lean… The point of the study is to see what happens to their current state – direction or magnitude of change. Percentage change is the only method to observe change when you start with different starting weight.
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Though the comments raise a valid point that percentage increase in mass is an important measure, they obscure the fact that the starting body fat amounts for the two groups were very different — so different that if you just looked at the fat amounts alone, that initial distinction pops out. The correct thing to do would have been to shuffle the mice so that the average initial body fat is the same for both groups, and then, with two equivalent groups see what the microbiota transfer does to percentage fat increase, using the percentage increase to iron out individual variation.
As is, one can’t tell if temporarily lean mice gain more fat, simply regressing to the mean, or whether the change is due to the microbiota. I don’t see how one can claim, as one commenter does, that “The results would, however, likely be the same if the avg. weights of the test groups were reversed.” Maybe yes, and I’d like to think so, but maybe no. How do we know?
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The issue addressed in the post isn’t really the elephant in the room, which is, the ob/ob treatment mice had a smaller initial mean weight. Unless the correlation between initial and final weights is 1.0, we expect the ob/ob treatment to have a larger mean change score or percentage change due to regression to the mean. Consequently, change scores or percent change (contra Veronica) are biased – the larger the initial difference in weight the larger the bias and the higher the probability of a type I error. The only way to estimate an unbiased effect is to use the initial weight in the linear model (“ANCOVA”) – so the correct models is
final = alpha + beta*initial + tau*T, or (ANCOVA-like linear model with post as the response)
final – initial = alpha + beta*initial + tau*T (ANCOVA-like linear model with change score as the response
(these give the same estimates of tau), where beta is the change from initial to final (equal to pre-post correlation if sigma_pre =sigma_post), T is treatment assignment dummy variable and tau is the treatment effect.
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Interesting analysis. To be sure I understand, you wrote:
“If we calculate their starting fat:
LEAN transplant recipients: 1.3/0.47 = 2.76
Mice getting obese mice transplants had 2.76 grams of fat at the start.”
OBESE transplant recipients: 0.86/0.27 = 3.19
Mice getting lean mice transplants had 3.19 grams of fat at the start.”
Should the 2nd line above be “OBESE transplant recipients: 1.3/0.47 = 2.76” and the 4th line
“LEAN transplant recipients: 0.86/0.27=3.19” ?
I don’t think this changes the calculations, however.
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Here is an update to my comment above. Thanks for the great initial analysis to get me thinking about this! https://rdoodles.netlify.com/2018/03/bias-in-pre-post-designs-an-example-from-the-turnbaugh-et-al-2006-mouse-fecal-transplant-study/
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Pingback: From fecal transplants, obesity and the importance of randomizaiton and normalization
Pingback: From fecal transplants, obesity and the importance of randomizatIon and normalization
Hi nice reading yoour blog
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