Confounding

What It Is

I think it’s easier to understand confounding by working through an example and then describing the general features of a confounder than to define it in an abstract way.  Following is an example, kept simple so that we can concentrate on the relationships between the confounder and the other variables.

Example.
You are a cardiologist. Recently, a higher than expected number of your patients with atrial fibrillation (AF) have improved from persistent to paroxysmal, and in some cases, reversal of AF. You haven’t changed your management of AF. During routine office visits many of these patients volunteer that they have been seeing an acupuncturist at a nearby clinic to get “complementary and integrative” AF treatment.

There is no theoretical basis for thinking that acupuncture can improve AF, but you don’t want to dismiss this information out of hand. You decide to systematically question your patients with AF about their use of acupuncture as well as other health-related changes they may have made after their diagnosis. You also include changes in weight and blood pressure as part of your data collection. After querying about 100 of your patients (you of course obtained IRB approval first), you have the following data:

For this example we will calculate the risk ratio (relative risk) to see if acupuncture seems to confer a higher likelihood of improving your AF status.

Proportion (risk) with AF improvement among acupuncture users: 18/33 = 0.5455
Proportion (risk) with AF improvement among patients not using acupuncture: 22/67 = 0.3284
Risk Ratio comparing acupuncture to no acupuncture: 0.5455/0.3284 = 1.66
So the likelihood of improving your AF when you use acupuncture compared to not using it is increased by about 66%.

You weren’t expecting that. You keep digging in the data to see what else might be going on with the patients. You then discover the following:

Proportion (risk) with weight loss ≥10% among acupuncture users = 21/33 = 0.6364
Proportion (risk) with weight loss ≥10% among patients not using acupuncture = 9/67 = 0.1343
Risk Ratio comparing acupuncture to no acupuncture: 0.6364/0.1343 = 4.74

That’s a pretty strong relationship between acupuncture use and weight loss. An improvement in AF after a weight loss ≥10% is well documented in the peer-reviewed literature and has a plausible mechanism through mitigating the effects of obesity-related pericardial and epicardial fat and increased blood pressure. So is the AF improvement with acupuncture actually due to the fact that these same patients are more likely to have had a clinically significant weight loss?

If that’s the case the numerical relationship (association or risk ratio) between acupuncture and AF improvement would be due to confounding. Confounding means the association between an exposure (or treatment) and an outcome is biased, or distorted, because of the exposure’s (treatment’s) association with another factor that is extraneous to the exposure-outcome pair being examined.

If an extraneous factor is causing confounding three conditions must be true:

1. The extraneous factor must have a causal relationship with the outcome (“it is a risk factor for disease”).
2. The extraneous factor must be associated (correlated) with the exposure (treatment).
3. The extraneous factor cannot be part of the hypothetical causal pathway between the exposure (treatment) and the outcome. That is, the extraneous factor is part of a separate causal pathway for the outcome.

How could we determine whether a weight loss of ≥10% is confounding the (supposed) relationship between acupuncture and improvement in AF? Even though it seems likely, it might not be the case. Epidemiologists use stratified analysis, i.e., for this example looking at the risk ratio for the effect of acupuncture on AF improvement within fairly homogeneous categories of weight loss. (Statisticians use software to run regression models which is a lot faster…) If the risk ratios for acupuncture within those weight loss categories gravitates towards 1.0 (the risk ratio of “no relationship”) then confounding through weight loss probably accounts for the statistical association between acupuncture and improvement in AF.

You run the data and find the following for patients who lost ≥10% of their body weight:

Proportion with AF improvement among acupuncture users: 14/21 = 0.667
Proportion with AF improvement among patients not using acupuncture: 6/9 = 0.667
Risk Ratio comparing acupuncture to no acupuncture: 0.667/0.667 = 1.00

Then you run the data for patients who lost <10% or didn’t lost any weight:

Proportion with AF improvement among acupuncture users: 4/12 = 0.333
Proportion with AF improvement among patients not using acupuncture: 17/58 = 0.2931
Risk Ratio comparing acupuncture to no acupuncture: 0.333/0.2931 = 1.14

The risk ratio within each weight loss group is closer to 1.0 than when you analyze all the patients without stratifying (risk ratio not stratifying = 1.66). This suggests that most, if not all, of the association we see between acupuncture and improvement in AF is due to the higher proportion of acupuncture users also losing ≥10% of their body weight.

What happened? When you look at the first table in this example, there are 18 patients using acupuncture who had an improvement in AF. Comparing this to where those patients ended up by weight loss group, we see that 14 of the 18 (77.8%) belonged to the group with ≥10% weight loss and only 4 (22.2%) to the other group.

In this example, the confounder (weight loss ≥10%) created a correlation between acupuncture and AF improvement where none existed. However, confounding can also hide an association between an exposure (treatment) and an outcome by skewing the risk ratio towards 1.0 and even reverse the direction of an association (e.g., skewing a risk ratio to be <1.0 when it is really >1.0, or vice versa).

What It’s Not

Assessing the data for confounding depends on having an idea of your proposed causal pathway, because “controlling for confounding” in multiple regression or through stratification when your potential confounder is actually part of the same causal pathway as your exposure or treatment of interest is called “overadjustment.” In these situations you are not controlling for a confounder, you are controlling for an intermediate outcome. For example, suppose our cardiologist was looking at weight loss and thought change in blood pressure could be a “confounder.” Weight loss can result in decreased blood pressure, and decreased blood pressure has plausible mechanisms for halting progression of (or preventing) AF. It doesn’t make sense to say, “weight loss is irrelevant in this situation.” The causal pathway was weight loss –> decreased blood pressure –> AF prevention/stabilization. Of course, both weight loss and decreased blood pressure might operate under additional mechanisms outside of your causal pathway.

Why It’s Important

Randomizing people to an exposure or treatment can minimize the bias from confounding, but we don’t always have that choice. It may not be feasible (e.g., randomizing people to live for long periods of time at specific latitudes to study the effects of sunlight exposure) or ethical (e.g., randomizing people either to raise their children or give them up for adoption). In these situations we have to think carefully about how confounding might bias our statistical results.

Caveat

Remember that the example of acupuncture, weight loss and atrial fibrillation is very simplified. In a real study we would define what is meant by “AF improvement” and how long that improvement needed to last. Is a ≥10% weight loss the best cutoff to choose? What was the timing of the acupuncture visits, the weight loss and the AF improvement? Etc. etc.

Finally, remember that confounding is not interaction. Interaction means the effect of one factor depends on the status of another factor, and not that the other factor is distorting its relationship with the outcome.