Analyzing how the microbiota of different sample types from the same donors together can predict microbiota

I have a project where I have collected samples from three different compartments (urine, bladder, and vaginal swabs) from the same study participants, consisting of either healthy controls or patients. All samples were sequenced together.

I can look at how the microbiota of the individual sample types relate to the diagnosis quite well. But I wanted to look into whether using the three sample types together (with participant ID as a random effect variable) could improve the ability of the microbiota to predict diagnosis. However, I am unsure which test to perform to analyze this.

Does anyone have experience with this type of analysis?

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