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I've conducted a logistic regression in which a binary outcome was the dependent and some continuous factors were entered as independent variables.

First: Can this model determine that the independent factor will proceed the dependent factor or do we just have associations (since I conducted a case-control study by which I can't determine the causality)?

Second: if the odd ratio is 1.22 of the continuous variable (Biomarker) and the outcome is the binary outcome (vitamin deficiency or obese patient). How can I interpret this results?

Finally, when I entered other risk factors to the model do I interpret the result as dependent and independent risk factor?

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If you have not taken other steps to ensure that the two factors don't occur in a fixed temporal order, than no, logistic regression will not ensure that that's true.

Your interpretation would be something along the lines of: "A one-unit increase in BIOMARKER increased the odds of vitamin deficiency by 1.22".

Finally, when I entered other risk factors to the model do I interpret the result as dependent and independent risk factor?

It's a little unclear what you're asking here. The estimates determined in any logistical regression model are conditional on any other variables you've included in the model.

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    $\begingroup$ I'd just add that the interpretation assumes deficiency was coded as 1 and no deficiency was coded as 0. $\endgroup$ – Penguin_Knight Jan 29 '16 at 20:19
  • $\begingroup$ But if I interpret the results this way, is it meant that the biomarker is the risk factor for having the vitamin D deficiency, isn't it? In other words, it gives an indication about the direction of the association. Can I say that the biomarker X increased in patients with the outcome (i.e. Vitamin deficiency) by 1.22 as compared with individuals without vitamin defceincy?? $\endgroup$ – Reem M.Al Haj Jan 29 '16 at 20:19
  • $\begingroup$ @ReemM.AlHaj If you're interested in then other direction of relationship, why are you using logistic regression? $\endgroup$ – Fomite Jan 29 '16 at 20:35
  • $\begingroup$ @Fomite it's not about direction, but actually, I want to test the independent association between these variables. I have two biomarkers one of them failed to reach the significance level in partial correlation, but when I divided the vitamin deficiency into deficient or not there was a significant difference between the two groups so I conducted logistic regression with 3 different models. indeed, this is my first time with statistics. $\endgroup$ – Reem M.Al Haj Jan 29 '16 at 20:43
  • $\begingroup$ @ReemM.AlHaj Logistic regression is inherently about modeling the response of a binary variable to one or more other variables. While that doesn't necessarily suggest that one causes the other, it's hard to back that exposure out the other direction. I'd suggest, depending on your data, something as simple as an ANOVA if you want to know the level of biomarker as it varies between groups. $\endgroup$ – Fomite Jan 29 '16 at 20:50

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