The Table 2 Fallacy: Presenting and Interpreting Confounder and Modifier Coefficients

TLDR

It is common to present multiple adjusted effect estimates from a single model in a table, such as odds ratios for exposures and confounders, but heterogeneity across covariate levels complicates interpretation. The authors use causal diagrams to illustrate the problems and propose suggestions to limit misunderstandings when multiple effect estimates are presented, such as distinguishing total from direct effects and employing multiple models for covariate total-effect estimates. They suggest limiting misunderstandings by distinguishing total from direct effect measures in a single model and using multiple models to produce covariate total-effect estimates. Presenting exposure and confounder effect estimates from a single model can lead to mistaken interpretations, confusion between direct and total effects for covariates, and confounding of covariate estimates even when the main exposure estimate is unbiased.

Abstract

It is common to present multiple adjusted effect estimates from a single model in a single table. For example, a table might show odds ratios for one or more exposures and also for several confounders from a single logistic regression. This can lead to mistaken interpretations of these estimates. We use causal diagrams to display the sources of the problems. Presentation of exposure and confounder effect estimates from a single model may lead to several interpretative difficulties, inviting confusion of direct-effect estimates with total-effect estimates for covariates in the model. These effect estimates may also be confounded even though the effect estimate for the main exposure is not confounded. Interpretation of these effect estimates is further complicated by heterogeneity (variation, modification) of the exposure effect measure across covariate levels. We offer suggestions to limit potential misunderstandings when multiple effect estimates are presented, including precise distinction between total and direct effect measures from a single model, and use of multiple models tailored to yield total-effect estimates for covariates.