Time series with biological replicates

Question

[Sarah]

Hi,

We analysed the bacterial composition of 10 stool samples (10 different patients; proportion values for the bacterial species) across 3 time points. I would now like to know if there is a trend for any of the detected bacteria to decrease/increase over time.

What statistical test can I use for it? I spent quite some time searching for an appropriate test. The typical tests that are used in ecology research don't allow multiples measurements for the same time point.

Thanks a lot for your help, very much appreciated!

Best wishes, Sarah

[rpolicastro]

Since you have count data, I think a good place to start would be a negative binomial regression. Since you want to know whether there are different trends for different bacteria over time, you would ultimately want an interaction term in your model, such as count ~ time:bacteria. Depending on how many observations you have per factor level, you could control for differences in patients with a model such as count ~ patient + time:bacteria.

Edit: If you want to stick with proportions (which I suggest against if you have the actual count values), you can use a beta regression instead of negative binomial.

[reza.jabal]

I second @rpolicastro answer regarding negative binomial. Also suggest generalized mixed models for the differences in patients. You can model the heterogeneity as a random effect in your model.