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I'm looking at the risk of seizure in patients with metastasizing brain cancer and so far have several variables that I want to check to my dependent variable of seizure yes/no.

These are variables such as age, sex, tumor size and much more.

Now if I understand it correctly, first I run a univariate regression and the result will tell me whether there is a statistical significant relationship between one variable and my dependent variable.

However, I see in similar studies that they also do multivariate regression, but do not specify how, exactly.

Can someone help me understand why I would do a multivariate regression in such a project?

Thank you.

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    $\begingroup$ Just a note on terminology: multivariate regressions mean you have multiple dependent variables. These can get complicated. Multiple regressions mean you have multiple IVs. It's quite straight forward as the answer below shows. Also, the advantage of using multiple IV's in the same model lets you get estimates for each IV controlling for the other ones, which is very beneficial. $\endgroup$
    – Huy Pham
    Dec 2, 2018 at 17:16

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For the sake of simplicity, let's say your independent variables consist of age, sex and tumour size only.

When you fit a univariate binary logistic regression model relating your dependent variable (seizure, yes or no) to the independent variable age, the model is ultimately enabling you to answer this question:

How does age affect the probability of seizure in the target patient population (i.e., for all patients in the population, regardless of their sex and tumour size)?

When you fit a univariate binary logistic regression model relating your dependent variable (seizure, yes or no) to the independent variable sex, the model is ultimately enabling you to answer this question:

How does sex affect the probability of seizure in the target patient population (i.e., for all patients in the population, regardless of their age and tumour size)?

When you fit a univariate binary logistic regression model relating your dependent variable (seizure, yes or no) to the independent variable tumour size, the model is ultimately enabling you to answer this question:

How does tumour size affect the probability of seizure in the target patient population (i.e., for all patients in the population, regardless of their age and sex)?

When you fit a multiple binary logistic regression model relating your dependent variable (seizure, yes or no) to the independent variables age, sex and tumour size, the model is ultimately enabling you to answer more pointed questions (assuming you only include main effects for these independent variables in your model):

  1. How does age affect the probability of seizure for patients in the target patient population having the same sex and the same tumour size?

  2. How does sex affect the probability of seizure for patients in the target population having the same age and the same tumour size?

  3. How does tumour size affect the probability of seizure for patients in the target population having the same age and the same sex?

Of course, if you include interactions between any of the independent variables in your multiple binary logistic regression model, that expands the list of questions you can ask.

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    $\begingroup$ Thank you. That explains a lot. So when inputting the multivariate analysis in my statistical software (STATA), if I want to answer the question: "How does age affect the probability of seizure for patients in the target patient population having the same sex and the same tumour size)?" Do I select seizure, sex and tumor size as the dependent variables, and age as the independent variable? $\endgroup$
    – Paze
    Dec 2, 2018 at 16:41
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    $\begingroup$ You're welcome! No, you only select seizure as the dependent variable and then include age, sex and tumour size together as the independent variable. The 3 questions I listed in my answers, 1., 2. and 3., can all be answered based on this one model! That's the beauty of multiple binary logistic regression! $\endgroup$
    – Isabella Ghement
    Dec 2, 2018 at 16:44
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    $\begingroup$ Paze, Isabella provided you with some nice guidance, but there are many other factors you'll want to consider to ensure you understand what you are doing. Get a copy of "Applied Logistic Regression" by Hosmer, Lemenshow, and Sturdivant. You'll want to make sure your continuous variables are linear in the log of odds, you'll want to understand why a variable can be statistically significant in a simple regression but insignificant in multiple regression. The book does a great job of taking you from square 1 to proficiency in logistic regression. Statistics is very much garbage in garbage out. $\endgroup$
    – ColorStatistics
    Dec 2, 2018 at 18:04
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    $\begingroup$ And thank you very much Isabella for your invaluable help! $\endgroup$
    – Paze
    Dec 2, 2018 at 18:37
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    $\begingroup$ Grea advice, @ColorStatistics! The only thing I don't agree with is "Statistics is very much garbage in garbage out". I would qualify that statement as follows: "When applied thoughtlessly, statistics can very much be garbage in, garbage out." 😝 $\endgroup$
    – Isabella Ghement
    Dec 2, 2018 at 18:54

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