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I have read answers to the similar questions here and read other resources but I could not find a solid answer to this point. Sorry for my simple terminology.

While analyzing the data from an obervational study that investigates the effect of an independent variable (categorical) on an outcome (categorical), I look at:

  1. factors that are different in cases that have independent variable present and not. I start with a table that compares cases for this variable.

  2. factors that are different in regard to outcome.

For example, my outcome is "mortality" and my independent variable of interest is "diabetes". I also have data on 10 other variables from the study patients.

From the 1st analysis above, I get information on how patients with and without diabetes differ: Variables A,B,C,D are different in patients with and without diabetes.

From the 2nd analysis on mortality, I find Diabetes and variables, A,C,E,G to differ.

Now to remove the effect of confounders and to measure the association of diabetes with mortality, I build a regression model. In this model, should I:

  • include diabetes, variables A, B, C, D, E, G because they have an effect on mortality or having diabetes?

  • include diabetes, A, and C only because A, C are the only common confounders?

  • include diabetes, and A,B,C,D because these are the only variables that effect having diabetes?

Thanks for any help.

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1 Answer 1

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For this problem you need to use techniques from causal inference to determine what are the causes of your outcome Mortality.

The question here is "Does diabetes have an effect on mortality which isn't captured by my other variables?" and if so, "How big is that effect?".

You need to use partial correlation to single out the causal graph of effects. The information you lay out is not sufficient to really say what is causing what.

At a minimum you need to remove variables whose partial correlation with Mortality goes to zero once Diabetes is accounted for.

For example, in your second analysis A and C differ. But do they differ because they cause mortality or because they are correlated with Diabetes which may actually be causing Mortality.

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  • $\begingroup$ It seems like you are doing bivariate tests and then multivariate tests. But a variable in a multiple regression may well have totally different results than its bivariate relationship. A second key point is that which variables you leave in and out of the model, and thus the slope you calculate really needs to be based on your theory. How do you know from regression what is and what is not a confounder? $\endgroup$
    – user54285
    Sep 28, 2021 at 2:27

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