I have a dataset that consists of several continuous variables that are measured at months 1, 2, 3, 4 and 5. I have a total of 50 subjects. So, for each subject, I have several variables measured across 5 months. I have missing values in several places in there. Other subjects came only for the first 1, 2, 3 measurements, others came at the first and last measurements and skipped the ones in the middle etc.

What I want to discover is how 3 of those variables affect all other variables with time across all subjects. If I only had measurements for a single month, I would just only use a correlation test and that would be enough. And if I only had a single subject, I would also use a correlation test. But now that I have measurements for 50 subjects across five different months, what test do I use?

I hope I made myself clear, english not being my native language.