# Comparing categorical outcome variables in repeated measures design

I am working on an observational prospective longitudinal study with a repeated measures design. The same categorical outcome is measured for five times, for all the participants, over a time period. So there are five outcome (dependent) variables and a few predictor variables. First of all, I would like to compare the proportion of a value in the first outcome variable, compared to its proportion in every of the other four outcome variables, and find out if it's significantly smaller as assumed.

I have a few questions:

1) Can I use a statistical analysis on two outcome variables, without including predictor variables?

2) What statistical analysis should I use?

3) For some of the participants there are missing values in one or more of the five outcome variables. How should I deal with it in my analysis?

Thanks!

## 1 Answer

It sounds like you'd want to use a generalized estimating equations (GEE) or mixed model for this analysis where the participant is a random effect. You'd use a contrasts to determine if the first measurements is different from the average of the other four. You could even try a Markov Chain Monte Carlo approach too.

To deal with missing data, I'd recommend using multiple imputation.

• But GEE does rather was generally with missing data, assuming you have a relatively large number of participants. – StatsStudent Jun 2 '15 at 21:01
• Thanks for the answer! More specifically, I am looking for risk factors for the outcome, expressed by Odds Ratios. But In some other post I have read, that GEE estimates of associations are notoriously inefficient. Is GEE an appropriate method in my case? – Alex Jun 15 '15 at 23:07
• Before evaluating all of the predictors, I just want to find the OR for the outcome in every of the 2nd to 5th time points, compared to the first time point (as a predictor), and not the average of the other four. How can I do that? It seems that in GEE the exposure should always be at the same person-time point as the outcome. It also seems that GEE doesn't evaluate time points separately. – Alex Jun 15 '15 at 23:07
• GEE should be fine for what you describe above. You'll handle the tests using a contrast. A good introductory text to help guide your analysis can be foundin Chapter 25 of Applied Regression Analysis and Other Multivariable Methods by Kleinbaum, et al. amazon.com/Applied-Regression-Analysis-Multivariable-Methods/dp/…. In this chapter this are some good examples that show constrasts to estimates different times points like you are trying to do using GEE (aka the marginal model). – StatsStudent Jun 17 '15 at 5:49