Confounding is about the characteristics of the study subjects; patients with certain characteristics tend to have certain exposures. The aim of an observational study is to examine the effect of the exposure, but sometimes the apparent effect of the exposure is actually the effect of another characteristic which is associated with the exposure and with the outcome. This other characteristic is a confounder, provided that it is not an intermediate step between the exposure and the outcome.8
Therefore, a high cholesterol value should not be treated as a confounder in a study of the risk of coronary heart disease (outcome) in patients with severe obesity (exposed group) and patients with normal weight (reference group); although a high cholesterol value is associated with both obesity and coronary heart disease, it is an intermediate step because it may be caused by obesity.
There are two principal ways to reduce confounding in observational studies: (1) prevention in the design phase by restriction or matching; and (2) adjustment in the statistical analyses by either stratification or multivariable techniques. These methods require that the confounding variables are known and measured. In an RCT, on the other hand, the randomisation process allows the investigator to assume that not only known, but also unknown, potential confounders are distributed evenly among the exposed and the unexposed. Therefore, they are not associated with the exposure, hence they cannot be confounders.
Confounding can be reduced by restricting the study population to those with a specific value of the confounding variable.12
This method, also known as specification,10
makes examinations of the association between the confounder and the outcome invalid, and the findings cannot be generalised to those who were left out by the restriction.
- Example—Ayanian and colleagues examined the effect of specialty of ambulatory care physicians on mortality after myocardial infarction in elderly patients. They found that patients who saw a cardiologist had lower mortality than patients who saw an internist or a family practitioner. They excluded patients who died within three months, patients with metastatic cancer or a do-not-resuscitate order, patients who enrolled in a health maintenance organisation, patients residing in nursing homes, patients who lacked Medicare part B coverage, and patients with no ambulatory visits. These restrictions could serve to reduce confounding from the degree of morbidity, as the moribund and the, presumably, perfectly well patients, with no need for ambulatory visits, were excluded.15
Matching constrains subjects in different exposure groups to have the same value of potential confounders, often age and sex.10
However, with increasing numbers of matching variables, the identification of matched subjects becomes progressively demanding, and matching does not reduce confounding by factors other than the matching variables. Matching is most commonly used in case–control studies, but it can be used in cohort studies as well.
- Example—In a study of predictors of peripheral arterial disease, Ridker and colleagues nested a case–control design in the Physicians’ Health Study cohort, consisting exclusively of men. They identified 140 cohort members who developed peripheral arterial disease (cases). Controls were selected with the incidence density sampling technique and matched on age and smoking status to reduce confounding by these variables. The matching variables, the 11 candidate predictors, and remaining confounders (hypertension, body mass index, family history of premature atherosclerosis, diabetes, and exercise frequency) were then included in a multivariate model. The authors concluded that the total cholesterol/high density lipoprotein cholesterol (TC/HDL-C) ratio and C reactive protein (CRP) were the strongest lipid and non-lipid predictors of peripheral arterial disease.16
Stratification means that the study population is divided into a number of strata (subsets), so that subjects within a stratum share a characteristic, and each stratum is analysed separately. If the study population is to be divided into more than a few strata, it has to be large to begin with to yield conclusive results. Stratified analyses are the best way to evaluate effect modification (see below), but they are also a way of examining, or adjusting for, confounding. Confounding can be adjusted for if the strata are recombined with the Mantel-Haenszel method or a similar method.8
- Example—Ridker and colleagues studied whether CRP would improve prediction of risk of myocardial infarction. They used data from the Physicians’ Health Study and included 245 cases with myocardial infarction and 372 controls. Baseline exposure data were obtained from blood samples drawn at the time of inclusion in the Physicians’ Health Study. Patients were stratified according to baseline cholesterol value, and separate logistic regression analyses were presented for each stratum. Baseline concentrations of CRP were associated with increased risk of myocardial infarction in all strata.17
Multivariate analyses are methods that simultaneously adjust (control) for several variables to estimate the independent effect of each one. Usually, one of the variables in the model describes whether a patient is exposed, another describes whether the outcome is observed, and the remaining variables describe the values of potential confounders. A multivariate model will then estimate the effect of the exposure on the outcome, given that exposed patients and reference patients are similar with respect to the confounders in the model. The most commonly used multivariate methods are the Cox proportional hazards model, the logistic regression model, and the linear regression model.
Although multivariate models have proven to be useful and have gained an enormous popularity, they may also be treacherous since there is no limit to the amount of data that can be included in the analyses and condensed into very few numbers. As a consequence, a multivariate model can be like a black box, and if nothing but the adjusted estimates is presented, readers have no chance of understanding why the estimates turned out as they did. It is therefore essential that the construction of multivariate models is carefully documented and presented, and that the models are biologically plausible.
- Example—Based on data from the Nurses’ Health Study, Solomon and colleagues found that those with rheumatoid arthritis had a higher risk of myocardial infarction and stroke than those without rheumatoid arthritis. This was based on two pooled logistic regression models. The first included only rheumatoid arthritis (exposure), myocardial infarction or stroke (outcomes), and age (potential confounder). The second model included more potential confounders: hypertension, diabetes, high cholesterol, parental history of myocardial infarction before age 60 years, body mass index, cigarette use, physical activity, alcohol use, aspirin use, menopausal status, hormone replacement therapy use, oral glucocorticoid use, non-steroidal anti-inflammatory drug use, folate intake, omega-3 fatty acid intake, and vitamin E supplement intake. The authors showed that many of the potential confounders were associated with rheumatoid arthritis, and they stated that potential confounders were known or suspected risk factors for cardiovascular disease. Nonetheless, the two models yielded similar results, suggesting that there was no confounding by the additional potential confounders. This was not discussed.18