# Interpret multiple logistic regression

I have two groups of patients who were part of an intervention many years ago, and some covariates about their characteristics e.g., age, BMI, and years since the intervention. I have conducted a logistic regression in order to see the association of the intervention (yes/no) with a clinical outcome (yes/no), controlling for these known individual factors such that

$$Outcome = \beta_0 + \beta_1 Intervention + \beta_2 Age + \beta_3 BMI + \beta_3 YearsSinceInt$$

I have obtained some coefficients from my logistic regression but now when it comes to interpret the results I am being asked by a physician to interpret each coefficient in order to see the effect of each variable on having the binary outcome. I am a bit afraid of running into the Table 2 Fallacy so I argue that we should only interpret the Intervention variable. Nonetheless, it is a cross-sectional study so I am a bit torn whether we can actually give interpretation to each coefficient and only talk about association and never about causal effects.

What do you suggest? Can I give interpretation to each coefficient or I should only interpret the Intervention coefficient? Is there a way to see the effect of each variable on the outcome without running the risk of falling into Table 2 Fallacy and over-interpretating control variables?

• FYI, this is multiple-regression, NOT multivariate-regression
– mkt
Commented Jul 27, 2022 at 10:10
• The real problem is not how you should show the data but how the readers will interpret them. Most of the mdeical literature, such as trials published on NEJM or The Lancet, now use this type of representation (and, thus, readers are aware of what table 2 represents... Or at least they should). You could try to use more models, including also variables not significant in the univariable regression as predictors, to show the relative effects in each model, demonstrating how these variables change. Commented Jul 27, 2022 at 10:16

The interpretation of fitted regression coefficients $$\beta_i$$ as causal effect requires some additional insight into your scenario. E.g., if you know for sure that your variable Intervention is not causally affecting any of the other regressors Age, BMI, or YearsSinceInt, then you can interpret $$\beta_1$$ as the total causal effect of Intervention on the (log-odds of) Outcome. Otherwise, it is only the direct causal effect.