Indirect adjustment of relative risks of an exposure with multiple categories for an unmeasured confounder

With observational epidemiologic studies, there is often concern that an unmeasured variable might confound an observed association. Investigators can assess the impact from such unmeasured variables on an observed relative risk (RR) by utilizing externally sourced information and applying an indirect adjustment procedure, for example, the "Axelson adjustment." Although simple and easy to use, this approach applies to exposure and confounder variables that are binary. Other approaches eschew specific values and provide only bounds on the potential bias.

For both multiplicative and additive RR models, we present formulae for indirect adjustment of observed RRs for unmeasured potential confounding variables when there are multiple categories. In addition, we suggest an alternative strategy to identify the characteristics that the confounder must have to explain fully the observed association.

We provide examples involving studies of pediatric computer tomography scanning and leukemia and nuclear radiation workers and smoking to demonstrate that with externally sourced information, an investigator can assess whether confounding from unmeasured factors is likely to occur.