Omission of main effects from regression models with a ratio variable as the focal exposure can result in bias and inflated type I error rates

Objectives Ratio variables (eg, body mass index (BMI), cholesterol ratios, and metabolite ratios) are widely used as exposure variables in epidemiologic studies on cause-and-effect. While statisticians have emphasized the importance of including main effects of the variables that make up a ratio variable in regression models, main effects are still often omitted in practice. The objective of this study is to demonstrate the impact of omitting main effects from regression models with a ratio variable as the focal exposure on bias in the effect estimates and type I error rates. Study Design and Setting We demonstrated the impact of omitting main effects in three steps. First, we showed the connection between regression models with ratio variables and regression models with product terms, which are well-understood by epidemiologists. Second, we estimated models with and without main effects of a ratio variable using a real-life data example. Third, we performed a simulation study to demonstrate the impact of omitting main effects on bias and type I error rates. Results We showed the impact of omitting main effects in regression models with ratio terms. In the real-life example, the ratio term was only statistically significantly associated with the outcome when omitting main effects. The simulation study results indicated that the omission of main effects often leads to biased effect estimates and inflated type I error rates. Conclusion Regression models with a ratio term as an exposure variable need to include main effects to avoid bias in the effect estimates and inflated type I error rates.