Observational studies in orthodontics, such as cohort or case-control studies that examine the influence of risk factors on the occurrence of malocclusions, are especially prone to confounding, as are similar studies that examine the influence of treatments on the outcome of malocclusions. The demographic variables of age, race, and sex can be potentially confounding factors in observational studies in orthodontics, as can other variables. To better understand confounding, we will start by considering a hypothetical clinical orthodontic study. This study will investigate whether condylar fracture is a risk factor for mandibular asymmetry in growing children. We decide to conduct a large cohort study. We identify a cohort of 10,000 children, aged 7 years, and none has mandibular asymmetry. Then, among these children, we identify those with a history of condylar fracture (200 of 10,000) and those without condylar fracture (9800 of 10,000): ie, those exposed and not exposed to a previous condylar fracture ( Table I ).

We suspect that there might be a difference in the occurrence of asymmetry according to sex, so we collect data separately for girls and boys over a 3-year observation period ( Table II ). The first column with data shows the number of children who developed asymmetry sometime during the 3-year observation period. We can now calculate the cumulative incidence (risk) over the 3 years for the occurrence of mandibular asymmetry among those exposed and not exposed to condylar fracture for both girls and boys. Using these risks, we can calculate the relative risk (RR; also called a risk ratio) for each stratum of sex: ie, for girls and boys. For example, for girls, the risk of asymmetry over 3 years among those with condylar fracture is 10/50 = 0.2000, and the risk among girls with no condylar fracture is 50/4900 = 0.0102. The RR for girls is 0.2000/0.0102 = 19.61. Since the stratum-specific RR values for girls and boys are the same ( Table II ), we decide to simply combine the data and calculate and report the total RR for all participants. When we calculate the RR for all participants, we are somewhat surprised. The RR for all participants, although still high, is less than we expected. We anticipated that this RR would be the same as observed for girls and boys separately (RR = 19.61). But the RR for all participants is 16.23. What happened?

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