Multiple Logistic Regression Question

Question

I am conducting a project where I have to conduct regression on a data set with rather large amount of variables and am in need of some help.

To give some context, we are looking at whether certain prognostic variables make individuals more likely to undergo surgical or non-surgical treatment. There are a variety of variables, which are grouped into different prognostic categories (each category has 3 to 20 different variables). Categories include past medical history, which may include the presence of hypertension, obese, etc. These prognostic variables are usually binary, but can also be categorical with >2 categories or continuous.

From my understanding, I would conduct some sort of multinomial logistic regression, where the outcome is surgical or non-surgical treatment (categorical). However, I am uncertain whether I should include all variables in this model or conduct several logistic regressions for the prognostic categories. I also am wondering what other considerations I should have when conducting this analysis.

I would like to use either R or SPSS to conduct this analysis.

Thank you!

Answer 1

I'd recommend that you have a read of the third edition of Hosmer, Lemeshow, and Sturdivant's "Applied Logistic Regression." Specifically, Chapter 4, section 4.2 provides a step by step approach to what they call the "Purposeful Section of Covariates" approach to logistic regression modelling. It essentially involves several steps:

1. Univariate analysis of each independent variables
2. Fitting a multivariable logistic model to all variables that passed the first round of univariate screning and reducing the model to include only those variables that produced statistically meaningful results
3. Comparing the coefficients from the reduced model in step 2 with the full model in that step to verify that you haven't excluded certain variables that might have a dramatic effect on the other variables (and hence should be left in the model).
4. Obtaining a preliminary main effects model (described in detail in the book)
5. Assumption checking and verification of the main effects model
6. Checking for interactions in the main effects model and developing a preliminary final model
7. Performing adequacy checks of the final model.

You can read Chapter Four (or at least parts of it online).

Of course there are other approaches to building statistical models (including automated approaches -- but I'm not a fan of these) and each approach depends on exactly what you are trying to accomplish.

So, I'd recommend that you start out by reading this material and some of the works referenced in the book. It should help you get a sense for popular model building and variable selection strategies.