Correlation

Correlation is a measure of the interrelatedness of two variables. If we observe that one variable always increases when a second variable increases, the two variables are said to be strongly positively correlated.

On the other hand, if one variable always decreases when a second variable increases, the two are said to be strongly negatively correlated. If we increase one variable and a second variable neither increases nor decreases, there is no correlation between the variables.

The cohort study is one of the methods scientists use to discern if there is a correlation between variables. A cohort is a defined group of people who are systematically observed over a particular period of time. Data is collected at specified intervals, and outcomes such as the presence or absence of a particular disease are also recorded. It is important the cohort be large, carefully measured, and not prone to attrition.

One of the largest cohort studies ever undertaken is the Nurses' Health Study. It began in 1976 with a group of female registered nurses aged 30 to 55, but the study has expanded to a second and now a third phase which have enrolled a total of over a quarter of a million participants.

Why nurses? As a group, they are used to responding to technical questionnaires, and they have demonstrated a professional motivation to continue participating in the study. Thanks to reports from their next-of-kin, their deaths are also followed up, including reviews of autopsy findings and other records.

More than one hundred refereed papers have resulted from the data collected. Among the titles are:

• Cigarette smoking and risk of stroke in middle-aged women


• Dietary fat intake and risk of coronary heart disease in women


• A prospective study of moderate alcohol drinking and risk of diabetes in women


• A prospective study of postmenopausal estrogen therapy and coronary heart disease

From these four papers, it is easy to see the some of the variables being compared and correlated in the Nurses' Health Study. Cigarette smoking and stroke; dietary fat intake and coronary heart disease; moderate alcohol drinking and diabetes; postmenopausal estrogen therapy and coronary heart disease. From reading the News section of the Nurses' Health Study, website, one might assume that these types of correlations have a cause-and-effect relationship.

This is not necessarily correct. Take another look at the fourth article in the bullet points, A prospective study of postmenopausal estrogen therapy and coronary heart disease, which was published in the New England Journal of Medicine 1985. This study and several like it identified a correlation between hormone replacement therapy and a decrease in the incidence of coronary heart disease in older women. Possible mechanisms were proposed, and it became a consensus opinion that, in the words of the paper's abstract, "postmenopausal use of estrogen reduces the risk of severe coronary heart disease."

This correlational wisdom lasted over a decade. Eventually scientists did a randomized controlled clinical trial of hormone replacement therapy in older women, the Heart Estrogen/Progestin Replacement Study or HERS. Published in 1998, the HERS study showed that women who already had heart disease would increase their risk of a heart attack if they received estrogen therapy. This was followed in 2002 by the Women's Health Initiative (WHI), another randomized controlled clinical trial, which concluded that hormone replacement therapy increased the risk of heart attack and stroke for postmenopausal women.

Since then, much speculation has ensued. It is possible that the women in the Nurse's Health Study who took estrogen were beneficiaries of the adherer effect. That is, because they initiated and adhered to what they thought was a preventive regimen of hormone replacement therapy, these nurses may have been more likely to engage in other preventive behaviors that do tend to produce longer and healthier lives.

Taking estrogen requires spending extra money for prescriptions and for medical followup. It is possible that the nurses who took estrogen belonged to higher socio-economic groups than those who did not. The correlation between estrogen use and better heart health may have been seen because both variables were positively related to income level.

A third explanation comes from a more careful analysis of the data from the Women's Health Initiative. It suggests that some of the discrepancies result from a time component in the effect of hormone replacement therapy on coronary heart disease in women. It appears that there is a small, nonsignificant decrease in coronary heart disease when women initiate hormone replacement therapy within ten years of the onset of menopause. If hormone replacement therapy is initiated more than ten years after menopause begins, the risk of coronary heart disease rises in proportion to the time elapsed. These effects were probably present in both the cohort studies and the randomized trials, but because the women were not originally stratified and compared according to the time that had elapsed after onset of menopause, the results of the studies were at odds.

The take-home lesson? In a correlation study there are always variables that aren't expected--in this case an adherence effect, a socio-economic effect, and an age stratification effect. Although the papers taken from a cohort study may be done carefully, and although the authors try to address every confounding variable they can think of, there is no way to be sure that a particular correlation equals causation. We can use a correlation study to create a likely hypothesis, but we must always test the hypothesis (preferably with many approaches in many carefully randomized controlled trials) before we can begin to accept its validity.

I've Lost the Weight. Now, How Do I Keep It Off?

When I recently completed my annual set of questionnaires from the National Weight Control Registry (NWCR), it dawned on me that many of my readers may not be aware of the NWCR. It's time to rectify that.

The National Weight Control Registry is a long-term longitudinal study of individuals 18 and older who have lost at least thirty pounds and have maintained that loss for a year or more. (If you meet those criteria and would like to enroll in the NWCR, you may do so here.) The database was started in 1994 and now contains the records of over 5000 individuals. Registry members have lost an average of 66 pounds (range: 30 to 300 pounds) and have kept at least 30 pounds off for an average duration of 5.5 years (range: 1 to 66 years). Eighty percent of registrants are women and twenty percent are men.

The NWCR does not offer diet advice and it does not perform randomized clinical trials. What it does do is collect a large amount of anecdotal information from a group of people who have been successful at long-term weight loss maintenance. The investigators request data annually from hundreds of volunteers using several long questionnaires. They then systematize and compare the data in various ways to suggest possible strategies that might be helpful to people who have lost weight and would like to maintain the loss.

Because the study group is self-selected and because they are not following any specified experimental protocol, the papers derived from this data cannot be used to support or disprove scientific hypotheses about maintenance of weight loss. However, while the public waits for large-scale randomized clinical trials of weight maintenance strategies, the observations made by the NWCR can give guidance to individuals who would like to maintain a significant weight loss. What works for one person may not work for another, but there is a chance that what has worked for many successful maintainers may also work for a particular aspiring maintainer.

That said, let's look at some of the observations made by the National Weight Control Registry. These have been published in articles in refereed journals that are listed here.

Of the NWCR members who have successfully maintained their weight loss,

• 78% eat breakfast every day. Only 4% report never eating breakfast.


• 75% weigh themselves at least once a week. More than 44% weigh themselves at least once a day.


• 62% watch less than 10 hours of TV per week.


• 90% exercise, on average, about 1 hour per day. The most common activity is walking, done by 76%.

Most NWCR members lose and maintain their weight loss using a low-calorie, low-fat approach to eating. However, there are a few low-carbers. In 2007, Phelan et al. published Three-Year Weight Change in Successful Weight Losers Who Lost Weight on a Low-Carbohydrate Diet in the journal Obesity. They compared 96 low-carbohydrate participants with 795 others, all of whom had enrolled in the NWCR between 1998 and 2001.

As one might expect, the low-carbers and the other Registry members (referred to here as the control group) approached maintenance in significantly different ways. By the end of Year 3, the low-carb group reported consuming more calories per day than the control group (1610 kcal vs. 1340 kcal), with a greater percentage of their food in the form of fat (59% vs. 33%). The low-carbers were less likely to endorse holding back food intake (15% vs. 62%) as a means of controlling weight, though they did specifically avoid eating carbohydrates (17% of calories vs. 47% of calories). Finally, the low-carbers indicated that they had expended significantly fewer calories in exercise per week than the control group did (1119 kcal vs. 2246 kcal).

The bottom line of the NWCR observations is shown in Figure 1 from the study, which is reproduced below. Note that weights are expressed in kilograms.


The low-carb participants lost slightly less than the other participants prior to study entry. Both groups regained some weight over the ensuing three years. (For those who are concerned about the intent-to-treat analysis, the authors report that the dropout rate was not significantly different between the two groups.) In the discussion, the authors conclude, "Comparing those individuals in the Registry who lost weight using a low-carbohydrate diet (n=96) vs. those who used other dietary strategies (n=795) we found no significant differences in magnitude of 3-year weight regain."

To reiterate, all of this data is anecdotal. It is compiled from a series of self reports, and as such is vulnerable to subjective errors. Nevertheless, a visit to the website of the National Weight Control Registry provides a great deal of interesting information, and suggests that successful long-term weight control may be possible on a low-carb diet.

The Scientific Method

Aristotle was a Greek philosopher who lived from 384 BC to 322 BC. His works contain the first known formal study of logic, which he applied in many areas of life, including the field of science. Aristotle made extensive observations of natural phenomena and then applied logic to these observations in an effort to systematize them. Sometimes these logical inferences were correct, for example his deduction that the Milky Way is not shaded by the earth from illumination by the sun because the sun is too large and the stars are too distant for this to occur. Sometimes Aristotle's reasoning led to incorrect conclusions, such as his belief that the sun, stars and planets circle the earth. And occasionally Aristotle's conclusions were incorrect because his observations were not as careful as they might have been--for instance, he believed that men have more teeth than women, and that heavier objects fall faster than lighter ones.

Aristotle believed that observations coupled with reasoning could decipher the laws of the universe. He discounted experiments as artificial contrivances with little relevance to the natural world. When isolated events contradicted the laws of the universe as he understood them, they were regarded as "monsters" that could be ignored. Because Aristotle was very highly thought of as a philosopher and logician, it was regarded as a form of heresy to contradict the laws of science Aristotle had deduced from his observations. For that reason, his incorrect scientific ideas carried a great deal of weight at least until the 1500's.

In the 1500's, men such as Francis Bacon and Galileo Galilei brought changes to the study of science. Bacon rejected the idea of science by logical reasoning and syllogism. He advocated the use of observation, hypothesis and experiment leading to a gradual and systematic formulation of general axioms which could be disproven if evidence came forth to contracdict them (the scientific method, illustrated above). Galileo, as every schoolchild knows, availed himself of technology that had not been available to Aristotle. His telescope revealed that satellites orbited the planet Jupiter and that the planet Venus had phases just like the moon. While logic dictated that the earth was the center of the universe, experimental observations made by an Italian physicist indicated that this could not be the case.

When science was dominated by the application of deductive reasoning, scientific progress was slow to nonexistent. Even highly educated people believed in such things as phlogiston and spontaneous generation. Thanks to the scientific method, experiments were performed by Antoine Lavoisier, one of the men who discovered oxygen, and we now realize that burning is not a process of releasing an invisible, weightless substance called phlogiston, but a process of oxidation. Thanks to the scientific method in the hands of Louis Pasteur, we know that flasks of broth do not become cloudy by creating bacteria on their own, but that microscopic organisms can reproduce and multiply in a broth that initially appears clear.

With all of this in mind, it is surprising that some 21st century health experts wish to return to the days of science by deductive reasoning. While certain phenomena may appear to be true by anecdote or under certain conditions, without a systematic comparison of different interventions, there is no way to know for sure if eating a particular type of diet is good for weight loss, weight maintenance or (more importantly) the avoidance of the diseases of Western civilization. As Gary Taubes says at the conclusion of Good Calories, Bad Calories, "What's needed now are randomized trials that test the carbohydrate hypothesis as well as the conventional wisdom. ...it's hard to imagine that this controversy will go away if we don't do them, that we won't be arguing about the detrimental role of fats and carbohydrates in the diet twenty years from now. ...it's hard to imagine that the cost of such trials, even a dozen or a hundred of them won't ultimately be trivial compared with the societal cost."

Some investigators are doing randomized clinical trials, such as the A TO Z Weight Loss Study to compare diets such as Atkins, Ornish, Zone and a standard low-fat/high-carbohydrate diet. More of these studies need to be done, so that we can understand the specific health effects of eating various types of diets in various types of people over extended periods of time. And even in the context of low-carbing, it would also be helpful to have studies that examine the effect of eating saturated fats vs. polyunsaturated fats; eating at least 12-15 carbs' worth of vegetables per day vs. eating very few plant foods; including dairy vs. avoiding dairy in our diets; and taking various supplements vs. using no supplements. Until we have the studies to confirm or disprove our presuppostions, we are on shaky ground, just like Aristotle. Most of the time he was correct. Some of the time he was not. Without the scientific method, it's hard to know which is which.