In a previous article on confounding, we used a hypothetical prospective cohort study to demonstrate how sex might confound the effect of condylar fracture on the development of mandibular asymmetry. The data from that study are shown in Table I . The data were stratified by sex, and the relative risk for all participants was initially calculated by simply combining the data from the girls and boys, producing an unadjusted relative risk of 16.23. This unadjusted relative risk for all participants was confounded by sex, which was evident because the relative risk for all participants did not fall in the range established by the stratum-specific relative risks for girls and boys. That is, 16.23 was not somewhere between 19.61 and 19.61 for girls and boys, respectively. By statistically adjusting for the confounding influence of sex, the adjusted relative risk for all participants was 19.61, the only possible average of the 2 stratum-specific relative risks.
| Asymmetry | No asymmetry | Total | Risk | RR | |
|---|---|---|---|---|---|
| Girls | |||||
| Condylar fracture | 10 | 40 | 50 | 0.2000 | 19.61 |
| No condylar fracture | 50 | 4850 | 4900 | 0.0102 | |
| Boys | |||||
| Condylar fracture | 15 | 135 | 150 | 0.1000 | 19.61 |
| No condylar fracture | 25 | 4875 | 4900 | 0.0051 | |
| All participants | |||||
| Condylar fracture | 25 | 175 | 200 | 0.1250 | 16.23 |
| No condylar fracture | 75 | 9725 | 9800 | 0.0077 |
This hypothetical study was obviously contrived to make it easier to understand confounding. In a real study, it would be highly unlikely that the relative risks for girls and boys would be exactly the same. A real study would most likely have produced relative risks for girls and boys that were different to a greater or lesser degree. If the stratum-specific results in a study are different, the questions are: how different are they, and is this difference important?
These questions bring us to the topic of this article: effect modification (sometimes called interaction). As with the previous article on confounding, let’s begin with a hypothetical study to illustrate effect modification and then discuss it in more detail. We get a call from another investigator who is interested in our study, which was conducted on children who were 7 years old at the beginning of the study. He wants to see whether the strong relationship we found between condylar fracture and the development of mandibular asymmetry exists in older children. This investigator is from a country that has good dental records on all children, so he is considering doing a retrospective cohort study of children 8 to 11 years old. After further discussion, he decides to restrict the study to girls to avoid the issue of confounding by sex. However, the investigator is concerned that age might be a confounding factor, so he decides to collect data from girls in 2 age groups, 8 to 9 and 10 to 11 years old. After review and approval by an institutional review board, the investigator selects a random sample of 20,000 girls who were either 8, 9, 10, or 11 years old, 3 years ago, and who had no reference to mandibular asymmetry in their dental records at that time. He then queried the database again to determine how many of these girls developed mandibular asymmetry in the subsequent 3 years, leading to the present. The data for this hypothetical study are presented in Table II .
