The Case-Only Odds Ratio as a Causal Parameter

Abstract

In the simplest case-only design, cases of a disease are cross-classified into a 2 × 2 table describing a genotype attribute and exposure to some environmental agent. In some instances, the genetic attribute has described inherited genes; in other instances, it has described mutations, for instance, damage to proto-oncogenes or tumor suppressor genes leading to cancer. Here, the population case-only odds ratio is written as a causal parameter in terms of potential outcomes with and without exposure to the agent. It is shown that the case-only odds ratio makes sense as a causal parameter with inherited genes, but its magnitude does not have a causal interpretation with mutations, although deviations from 1 do provide information. The difference is that the environmental agent certainly did not cause an individual to inherit particular genes, but it may have caused the mutation.