Saturday, July 12, 2008

What's the Expected Shape of a Weight Loss Curve?

We "discovered" low-carb diets about 6-7 months ago by reading Gary Taubes' recent book, Good Calories, Bad Calories (highly recommended, if admittedly somewhat controversial). Deciding that some of our own struggles with weight control even (or especially) in face of a 30-40-mile per week exercise program might be due to excessive carb consumption, we embarked on our own dietary revisions and experiments.

But regardless of the weight-loss method adopted, no one seems to show any accurate data on weight loss vs. time. You can find plenty of anecdotal data: "I lost 50 lbs. (10, 20, 100, whatever) in x weeks (months, days)." You can find before and after photos. You can find data correlated with lipid profiles, blood pressure, cardiac incidents, diabetes, even death. You can even find guidelines that suggest that you should plan to lose, say 1–2 lbs. per week, but is that right? Does it depend on how much you need to lose? Should the weight loss be linear over some period of time? Obviously, it can't be linear indefinitely, since your weight must necessarily level off at some point. The next simplest model might be an exponential approach to some target weight value. That model might arguably be correct if you make an incremental change to your diet/lifestyle that causes you to have a new natural weight setpoint. If that new setpoint is a bunch of pounds different from where you are now, what is the expected time constant for approaching the new set point? Or is that model too simple too? And for that matter, how much noise should you expect to see in the data? What "normal" day-to-day fluctuations should one expect to see? None of these questions seems to be answered in the literature, even though they are clearly easy to measure and clearly of great psychological importance to anyone trying to lose weight.

As scientists, we, of course, have been keeping records! The data are still somewhat limited and anecdotal. Observations so far:

(1) Low carb diets really work for us as means of reversing persistent long-term weight gain. We'll talk about our particular diets in another posting, but so far, we've seen losses of 10% body weight without much effort or hunger. It's a permanent diet change, but once you get used to it, it's painless, healthy and easy to continue.

(2) Over the time we have recorded so far (about 7 months), we still can't clearly distinguish between a linear fit and an exponential fit to the data. But all that really proves so far is that, if the exponential model is valid, we are seeing a time constant of somewhere in the range of 10-14 months. (We have each lost about 20 lbs so far and expect to be able to lose another 20 or so.)

(3) There are normal daily fluctuations of ± 1.5–2 lbs (remember that if you drink a pint, it's a pound added, and there are all sorts of things that can easily cause variations in fluid retention of a pound or two).

(4) There may be ~monthly cycles that may or may not match menstrual cycles that account for a couple of pounds of cyclic variations.

(5) There appear to be effects (usually temporary) associated with heavy exercise that go beyond simple fluid replacement issues. Again, these can account for temporary weight increases of a pound or two.

(6) There are also clearly seasonal and environmental effects due, at least in part, to the body's response to average temperature. This is another fluid retention effect, I think.

(7) There is often a perceived "plateau" effect where one seems to be stuck at certain levels for up to a few weeks at a time and then suddenly lose a few pounds. These are often reported anecdotally, especially when measurements are made infrequently (weekly or less often) but, in our case (daily measurements), we can't really prove that they're not just artifacts of the scatter in the data. We certainly see clusters of data points that are above and below the long-term trend lines, but we rarely see points that are appreciably outside a 1–2 lb. tolerance band about the longterm trend lines.

3 comments:

Stephan said...

This is great, thanks for keeping track of your progress and posting it! I think it's really interesting that you've seen fairly linear weight loss over 7 months. That's past the time when people in the NEJM study started gaining weight back, even in the "Atkins" cohort. I sometimes wonder whether that's due to compliance issues... or maybe it's because they added back carbs after the induction phase. What do you think?

Drs. Cynthia and David said...

Certainly our experience so far would indicate that any backpedaling is likely due to poor compliance and/or planned phasing out of dietary restrictions. We will be continuing to monitor for as long as the data are interesting—probably at least another 12 months or so. Studying our data carefully, we are starting to see some slowing of the rate of weight loss. There seems to be a typical more rapid loss in the first couple of weeks. Whether we then go into one or more linear loss regions with different slopes or can model everything with an exponential remains to be seen. We need another 2–3 months of data before we can draw any conclusions at all. Another factor is that having lost 10% of our body weight now, are we actually eating less to account for the decreased metabolic need? I don't think so—at least not noticeably, and that's got to have an impact on the slowing rates too. We'll write more about it later on.

Tony Kenck said...

I ran across an interesting article that indicates that a person can lose 31 calories per pound of body fat. So, if you start at 200 and 20% body fat, You could lose about 40 lbs *31 calories = 1240 calories per day of fat. As the fat goes down, the daily loss would also decrease.

I posted on it here. http://www.emotionsforengineers.com/2008/06/unified-feed-theory.html

Lyle McDonald did a recent set of posts on Leptin and how it can vary while losing fat as well. Here is the link. http://feeds.feedburner.com/~r/LyleMcdonaldSpeaks/~3/380707088/


I too found Taubes earlier this year, and I now understand that the picture he paints is really useful, but incomplete. There is a lot more than just insulin involved. However, like you, I have lost a lot of weight just by cutting back on carbs.

Keep going.

Cheers,
tony