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?