Effect modification is not a problem that investigators need to protect against, instead, it is a natural phenomenon that the investigators wish to describe and understand. Different groups may have different risk estimates when effect modification is present.

Effect modification occurs when the effect of a factor is different for different groups. We see evidence of this when the crude estimate of the association (odds ratio, rate ratio, risk ratio) is very close to a weighted average of group-specific estimates of the association. Effect modification is similar to statistical interaction, but in epidemiology, effect modification is related to the biology of disease, not just a data observation.

In the hypertension example, we saw both stratum-specific estimates of the odds ratio went to one side of the crude odds ratio. With effect modification, we expect the crude odds ratio to be between the estimates of the odds ratio for the stratum-specific estimates.

* * Why study effect modification? Why do we care?

- to define high-risk subgroups for preventive actions,
- to increase the precision of effect estimation by taking into account groups that may be affected differently,
- to increase the ability to compare across studies that have different proportions of effect-modifying groups, and
- to aid in developing a causal hypothesis for the disease

If you do not identify and handle properly an effect modifier, you will get an incorrect crude estimate. The (incorrect) crude estimator (e.g., RR, OR) is a weighted average of the (correct) stratum-specific estimators. If you do not sort out the stratum-specific results, you miss an opportunity to understand the biological or psychosocial nature of the relationship between risk factors and outcomes.

## Planning for effect modification investigation

To consider effect modification in the design and conduct of a study:

- Collect information on potential effect modifiers.
- Power the study to test potential effect modifiers - if a priori you think that the effect may differ depending on the stratum, power the study to detect a difference.
- Don't match on a potentially important effect modifier - if you do, you can't examine its effect.
- To consider effect modification in the analysis of data:
- Again, consider what potential effect modifiers might be.
- Stratify the data by potential effect modifiers and calculate stratum-specific estimates of the effect of the risk on the outcome; determine if effect modification is present. If so, present stratum-specific estimates.

##
Example
Section* *

Continuing the use of our example for confounding, part of our research hypothesis may be that the relationship between diabetes and CHD is different for males and females. Stratifying results by sex shows:

Category | CHD | No CHD | Total |
---|---|---|---|

Diabetes | 13 (12.3%) | 93 | 106 |

No Diabetes | 25 (2.1%) | 1191 | 1216 |

Total | 38 (2.9%) | 1284 | 1322 |

PR = 5.97

OR = 6.66

Category | CHD | No CHD | Total |
---|---|---|---|

Diabetes | 13 (11.8%) | 97 | 110 |

No Diabetes | 65 (5.8%) | 1050 | 1115 |

Total | 78 (6.3%) | 1147 | 1225 |

PR = 2.03

OR = 2.16

The prevalence ratio for females is 5.97, while it is only 2.03 for males. The overall estimate is closer to a weighted average of the two stratum-specific estimates and thus sex does not seem to be a confounder. Sex does modify the effect of diabetes on coronary heart disease.

Both groups have an increased risk of CHD for those with diabetes, but for females, those with diabetes are almost 6 times as likely to develop CHD. This is in comparison to males, where those with diabetes are only about 2 times as likely to develop CHD. Notice that the overall rates of CHD differ by sex as well. Overall males have higher incidence of CHD (6.3%), but the differential risk for those with and without diabetes is not as large as in the females. For females, the overall incidence of CHD is lower, at 2.9%, but the differential risk for those with and without diabetes is larger.

##
Summary of confounding v effect modification
Section* *

To review, confounders mask a true effect, and effect modifiers mean that there is a different effect of the exposure on the outcome for different groups.

In summary, the process is as follows:

- Estimate a crude (unadjusted) estimate between exposure and outcome.
- Stratify the analysis by any potential major confounders to produce stratum-specific estimates.
- Compare the crude estimator with stratum-specific estimates and examine the kind of relationships exhibited.

##
With a Confounder:
Section* *

- The crude estimator (e.g. RR, OR) is outside the range of the two stratum-specific estimators ( in the hypertension example - the crude odds ratio was higher than both of the stratum specific ratios).
- If the adjusted estimator is importantly (not necessarily statistically) different (often 10%) from the crude estimator, the “adjusted variable” is a confounder. In other words, if including the potential confounder changes the estimate of the risk by 10% or more, we consider it important and leave it in the model.
- Do not report the crude overall estimate (RR, OR). Instead an adjusted estimator should be reported. This can be done using the Mantel-Haenszel method or statistical modeling.

##
With Effect modifiers:
Section* *

- The crude estimator (e.g. RR, OR) is closer to a weighted average of the stratum-specific estimators.
- The two stratum-specific estimators differ from each other.
- Report separate stratified models or report an interaction term.