Background Each year, numerous studies relate an outcome (e.g. offspring birthweight) to several exposures (e.g. maternal characteristics) using standard multiple linear/logistic regression. The results are often reported as coefficients/odds ratios for all exposures simultaneously, described as “mutually adjusted”. As discussed recently by Westreich and Greenland, depending on the nature of the theoretical model underpinning the data, this approach confuses the effects of exposures, confounders and mediators. The results presented in such a table are often uninterpretable. Interpretation of the different exposures is often only achievable through multiple models, informed by a priori knowledge of the data structure. We use the example of the associations between multiple maternal characteristics and birthweight, and show how directed acyclic graphs (DAGs) can help to clarify which analyses should be reported.

Methods The Avon Longitudinal Study of Parents and Children (ALSPAC) is a prospective population-based birth cohort study that recruited 14,541 pregnant women resident in Avon, UK with expected dates of delivery 1st April 1991 to 31st December 1992 (http://www.alspac.bris.ac.uk/). Here, we focus on the 10,104 singletons with complete data on offspring birthweight and sex, and the following maternal characteristics: age at delivery; parity; social class; height; ethnicity; smoking during early pregnancy; education level.

Results In considering each putative exposure, several plausible DAGs were drawn, resulting in different sets of confounders to be included in some instances. The effect estimates for each exposure, adjusted only for appropriate confounders, are compared to those from the single, “mutually adjusted” model. For example, when considering maternal education as an exposure, the only factors which could be considered as genuine confounders on the grounds of temporality were ethnicity and (possibly) height. In the mutually-adjusted analysis (i.e. adjusted for all other maternal characteristics) there was no evidence of an association between maternal education and birthweight (coefficient for degree compared to ‘O’ Level 0.02 kg ([95% CI 0.01, 0.05], p=0.062). When appropriately adjusted for only the genuine confounding factors of ethnicity and height, there was weak evidence of an association between maternal education and birthweight (coefficient for degree compared to ‘O’ Level 0.04 kg ([0.00, 0.07], p=0.04).

Conclusion The common practice to analyse several exposures simultaneously can lead to errors in interpretation, as they cannot all be confounders for each other. More careful consideration of the use of multiple regression is required, with distinction between genuine confounders and mediators becoming more widely understood.