Instructor Resource Chapter 14 Copyright © Scott B. Patten, Permission granted for classroom use with Epidemiology for Canadian Students: Principles, Methods & Critical Appraisal (Edmonton: Brush Education Inc.

Chapter 14. Confounding and effect modification in analytical studies

Objectives Define extraneous variables, confounding, and effect modification. Describe key procedures to control confounding: standardization, restriction, randomization, matching, stratification, and regression models. Identify strengths and weaknesses of key procedures to control confounding. Define effect modification. Define external validity (generalizability).

What are extraneous variables? Extraneous variables are variables that occur outside of the exposure-disease relationship. Extraneous variables can be: confounding variables effect modifying variables

What is confounding? Confounding occurs when the effects of extraneous variables become intermixed with the effects of exposures. This leads to confounded estimates of exposure- disease associations. Confounding is a serious threat to the fundamental assumption of epidemiology: that diseases distribute in relation to their determinants. Confounding draws this relationship into question.

A definition of confounding Confounding is an intermixing of the effect of an exposure with that of an independent risk factor for the outcome (disease), leading to an estimated association that no longer reflects the causal impact of the exposure of interest.

The confounding triangle

Confounding (continued) Confounding is not like other forms of bias, even though investigators sometimes use the term confounding bias. Bias is a systematic error in estimation of a population parameter such as, for example, an odds ratio. In a study free of defects in participation and measurement, the odds ratio estimated from a study will have an expected value equal to the underlying parameter in the population, even if it doesn’t represent a single causal effect.

Ways to control confounding standardization restriction randomization matching stratification regression models

Standardization This procedure was introduced in chapter 9 with the example of mortality in Ontario and Nunavut. The goal in that example was to compare mortality in 2 different places, and there was a concern about the comparison being confounded by age and sex. Standardization is usually used to adjust rates or frequencies, and is most often used with mortality data. There are 2 types: direct and indirect standardization.

Restriction The classical procedure for preventing confounding at the design stage is restriction. This simply means not allowing people that are exposed to a potential confounder to participate in the study. Since the restricted sample does not include people exposed to the confounder the effect of the confounder cannot distort the study’s estimates.

Randomization In randomization, an investigator randomly assigns an exposure to the study participants and then looks for an effect. This is NOT to be confused with random selection of a study sample. When the exposure is randomly assigned, the law of large numbers ensures an equal distribution of the confounder in exposed and nonexposed groups—hence, no exposure-confounder association (the dotted line on the confounding triangle). There can therefore be no confounding.

Matching Matching involves making sure that groups being compared are exact matches in terms of the distribution of confounding variables. Matching is a type of partial restriction: it does not prevent all subjects exposed to a confounder from participating in a study, but it places some restrictions on who can participate. Like restriction and randomization, matching targets the left-hand side of the confounding triangle—eliminating the exposure-confounder association.

Approaches to matching: case-control studies Pair matching: In a case-control study, this means selecting each member of the control group to have the same value of the confounding variable as a matched member of the case group. Frequency matching: in a case-control study, this means ensuring that the frequency of the confounder is the same in case and control groups.

Approaches to matching: cohort studies Pair matching: In a cohort study, this means selecting each member of the nonexposed cohort to have the same value of the confounding variable as a matched member of the exposed cohort. Frequency matching: In a cohort study, this means ensuring that the frequency of the confounder is the same in exposed and nonexposed cohorts.

Controlling confounding (continued) Restriction, randomization, and matching are techniques that control confounding at the design stage. Matching is a partial exception since matching often needs to be accounted for in data analysis, so matching controls confounding at both design and analysis stages. The remaining approaches address confounding at the analysis stage of a study.

Stratification Stratified analysis divides the contingency tables arising from a study into groups (strata). The groups are defined by levels of the confounding variable. Since confounding is caused by intermixing, unmixing through stratification will lead to a change in the estimated effect if the unstratified (crude) estimate was distorted by confounding.

Stratified analysis (continued) Stratified analysis leads to a set of adjusted estimates, called stratum-specific estimates. Stratum-specific estimates are adjusted for confounding. There is, of course, a drawback to this approach. Since stratum-specific estimates derive from a subset of the sample rather than the whole sample, they are subject to random error to a greater extent. In other words, they tend to be imprecise. There are procedures to regain precision of adjusted estimates in stratified analysis. These involve calculating pooled estimates from the (adjusted) stratum-specific estimates.

Regression models Regression models produce adjusted estimates (i.e., adjusted for the effects of a confounder, which is included as a variable in the model). In general, they involve developing a best-fitting linear equation (of the type introduced in chapter 10), or a transformed version of such a linear equation. Time-to-event or survival analysis methods are also used for this purpose.

Strengths and weaknesses of restriction Restriction is easily understandable—a strength. The most important weakness is the degree of distortion restriction imposes on population relationships. The frequencies, risks, or rates observed may no longer reflect those of the target population. Restriction can also make it more difficult to find study subjects, since they must be determined to be free of the restricted characteristic. Finally, restriction has a negative effect on the generalizability of estimates.

Strengths and weaknesses of randomization Randomization is widely viewed as the best procedure to control confounding due to its unique ability to address both measured and unmeasured confounding variables. However, it can only be employed in special situations: where equipoise exists. Most randomized controlled trials employ restriction in addition to randomization, and have long lists of inclusion and exclusion criteria to safeguard their internal validity. As in all cases of restriction, this can affect the generalizability of estimates

Strengths and weaknesses of matching Matching can sometimes be easy and inexpensive, and in special situations can increase precision. However, it distorts population relationships. In many situations, matching is expensive and inefficient, because finding appropriate matches can be difficult. In situations where several potential confounders are being matched simultaneously, it can have severe impacts on recruitment into a study.

Strengths and weaknesses of stratification Stratification can be more transparent than regression modelling: it can directly show the stratified tables. A disadvantage is that precision is lost within strata, making it hard to see when confounding has occurred. The problem of small stratified tables (or “sparse data”) is even worse when there are multiple confounders. It is usually not possible to simultaneously stratify on several confounders.

Regression models These can be less transparent than stratified analysis since the models often produce coefficients rather than understandable estimates of effect. The main advantage is that they are more effective at adjusting for multiple confounders. Also, when there are confounding variables that do not naturally fall into groups (e.g., age), these can be adjusted for without creating artificial groups (e.g., arbitrary age ranges).

Regression models (continued) There are several families of models. Some are log transformed and produce coefficients that are log ratios (log odds ratios, etc.) Some are not log transformed and these tend to produce coefficients that represent differences.

Generalizability Another term for generalizability is external validity. Generalizability refers to whether an estimate that is internally valid (unbiased) can be applied to another population. An invalid estimate can never be generalized to another population. A valid estimate may or may not be generalizable. Assessment of generalizability is a matter of sophisticated judgement.

Effect modification Effect modification happens when an extraneous variable modifies the effect of the exposure of interest. Unlike confounding, effect modification is not an artifact that can (or should) be adjusted away or controlled. Instead, effect modification is a real aspect of the exposure-disease relationship under investigation. When effect modification has occurred, there are multiple effects of exposure, and different measures of effect need to be reported separately—e.g. stratified estimates should be reported.

Stratified analysis (continued) Stratification is a very useful tool for distinguishing effect modification from confounding. After stratification for a confounder, you expect to see 2 stratum-specific (adjusted) estimates that are similar to each another, but different from the unadjusted (unstratified, or crude) measure of effect. If there is effect modification, the 2 stratum-specific estimates will be different from each another.

Stratified analysis (continued) This distinction between similar and dissimilar stratum-specific estimates is key to the analysis of epidemiological data—so key that it has its own terminology. When 2 stratum-specific estimates are similar to each another, they are said to be homogeneous or to display homogeneity. When they are different, they are said to be heterogeneous.

Statistical tests for homogeneity Statistical tools can help determine whether 2 stratum-specific estimates are homogeneous. In stratified analysis, a test called the Mantel- Haenszel test for homogeneity is commonly employed. In modelling, tests for statistical interaction between exposure and potentially modifying variables are often used. These are called tests of interaction. The identification of effect modification is a key task in epidemiological analysis. While good procedures exist to test for it, judgement is also needed.

End