Be skeptical of small numbers

A nuclear bomb is far scarier than a fire cracker.  Both are dangerous, but a nuclear bomb is clearly more destructive.  Not exactly rocket science.  In science-speak, the magnitude of this destruction is called the effect size.  Researchers spend a lot of time determining if an effect is real and how big the effect actually is.  Unfortunately, this information tends to distill down to "there was an effect" or "there was no effect."  This post is inspired by a lunch conversation with the girlfriend's parents, as it seems that nearly every food is out to get us.  It is one thing to say that a food has an effect on our health, but it's just as important to ask how big the effect actually is.

Effect size is an easy concept to measure in the laboratory.  A treated neuron can depolarize 5 times per second while a control neuron can depolarize 2 times per minute - an increase of 3 times per minute.  Differences in blood concentrations of a hormone, weight gain in rodents, and increased muscle mass are all easily recognized as an effect size.  In nutritional epidemiology, and epidemiology in general, the effect size is the strength of the association between an exposure (a food) and an outcome (a disease or mortality).  This is often measured as a relative risk.

Before I can talk about relative risk, I should explain absolute risk.  Absolute risk is the probability that an individual will develop a health outcome during a stated period of time (Fig 1).  Absolute risk, often measured as an incidence rate, is only meaningful if we have the number of outcomes AND the size of the population at risk AND a period of time.  The statements "4 men had heart attacks" and "4 out of 10 men had heart attacks," do not contain enough information to draw meaningful conclusions.  Rather, we need to know that "4 out of 10 men had heart attacks over the 5 year study period."  If we have the valid rate information about one group of people, we can compare it to another group's.  Absolute risk is vital for the real world impact of some exposure, but we rely on relative risk to get a grasp on the effect size of an exposure.

Fig 1.  Absolute Risk

Relative risk is simply the ratio of the absolute risk in the exposed group compared to a non-exposed group (i.e. control group).  If there is no difference in incidence rates of disease, then the RR will be 1.  If the exposed group has a higher rate, then the RR will be greater than 1.  And if the exposed group has a lower rate, then the RR is less than 1.  They are often discussed as percents (e.g. an RR of 1.3 means a %30 increased risk in the experimental group compared to the control).  Scientific journals will report rate ratios, hazard ratios, observed-to-expected ratios, and odds ratios - all of which are permutations of relative risk that are particular to different study designs.  Now that we're up to speed on relative risk, let's talk about effect size.

Fig 2.  Relative Risk

Effect size can help determine if an association seen in a study is causal.  Provided that the study is reasonably well conducted, a large relative risk suggests a causal association between the exposure and the outcome.  But how large is large?  Smoking and lung cancer are a textbook example of this principle.  Lung cancer is exceedingly rare in populations that do not smoke, especially if there are no industrial hazards.  Based upon an average of relative risks derived from several cohort studies (remember the limitations), men and women who smoke more than 20 cigarettes per day are 16 times more likely to die of lung cancer than non-smokers.  That's a whopping 1,500% percent increase in the risk of dying from lung cancer!  More moderate smokers have a considerably lower risk than the heaviest smokers, but are still far more susceptible with a relative risk of 5.0 and 9.0 for women and men, respectively.  The shear size of the effect provides evidence that smoking can cause lung cancer.  So what about not-so-large effects?

Because nutritional epidemiology relies heavily on observation rather than randomized controlled trials, the strength of an association can be distorted by confounding variables.  In fact, chances are that every observed effect is confounded by myriad unmeasured variables; many are insignificant, but some are important.  A study from the Health Professionals Follow-Up cohort demonstrated that men who consumed the most sugar-sweetend beverages had a 25% increased risk of developing type 2 diabetes over the 20 year follow-up.  Men who drank the most artificially-sweetend beverages (e.g. diet soda) were 91% more likely to develop the disease compared to those who drank the least.  However, after adjusting for the known confounding variables, the sugar-sweetened beverages still increased the risk by 24%, whereas the risk seen in the diet-rinkers was completely abolished.  It is easy to see how a relatively large effect size suggests causality, but does not prove it.  But what if the effect persists after adjusting for confouners?

Source:  Wikipedia:  Processed meat

A relatively recent article in the American Journal of Clinical Nutrition reported that men who reported eating the most processed meat (2 ounces or greater per day) compared to those who ate the least (less than 0.7 ounces per day) had a 23% greater chance of having a stroke over the course of the 10 year study.  Fresh red meat had no effect.  23% sounds fairly alarming; should we go to our fridge and throw out all of our salami and deli meat?  Looking at it another way, the average man in this study had a 6% chance (2409 out of 40, 291 men) of having a stoke over an average follow-up of 10.1 years.  By eating the highest amount of processed meat, his chances now increase to 7.4% (6% x 1.23).  His absolute risk increased by 1.4%*.

This may seem like a lot to you.  But also bear in mind that obesity and heavy smoking increase the risk of stroke by 100% compared to lean persons and non-smokers, respectively.  Using the average Swedish man above, each factor would increase the risk of stroke  from 6% to 12%.  Trading processed meat for fresh meat surely doesn't cause any harm, and this potential risk may simply be worth avoiding.  But think about how we need to approach this as scientific evidence.  Given that this has all the standard caveats of a prospective cohort study; and that the food record was based on a single survey given at the beginning of the study; and that you can never meaasure all of your confounders (they forgot sugar); are studies like this actually capable of detecting a true 23% increase in the risk of a specific mortality from a single type of food?  And is it worth constantly changing our diets when we're presented with these kinds of results?

Next time you hear a claim about a foods effect on health, or read another headline, make sure you find out how strong the effect actually is.  More often than not, you will only have access to the relative effect.  So keep in mind that if a disease is exceptionally rare, it will take a very high relative risk to have any real impact.  The risk of non-Hodgkin's lymphoma is .003 per 1,000 people over 1 year, which is so unlikely that an increased risk of 15% probably doesn't reflect a true association, and even if it does, it is virtually irrelevant.  The relative risk allows us to better comprehend the effect, but the absolute risk is what matters to the individual.

The problem with nutrition is that when you change something in your diet, it has to be replaced by something else.  How can you know you are making a change for the better?  And enjoying your food is important as well.  There are few things better than salami with cheese and wine, and bacon is arguably the best food there is.  The goal is not to disparage every study, but for the sake of health and culture, be skeptical about small numbers.



*The baseline risk I am using for this example is a crude estimate.  By simply using the number of strokes dived by the number of study participants over 10.1 years, I am ignoring the fact that some men were followed for less while some where followed for more.  However, this crude estimate approximated stroke statistics in the U.S. that I came across.  So don't hate!