How are PDO and PDX used in computational and predicative models for tumour biology? There are wet methods: Patient-derived models: Patient Derived Xenograft (PDX) and Patient Derived Organoids (PDO) to reflect tumor biology. 

Are there any databases or computational tools that use the outcomes from PDO/PDX experiments to create a predictive computational model for cancer or other diseases?
Potential pitfall!

I'm not sure about predictive models, but you need to be aware of a potential pitfall in blindly aligning PDX or PDO based sequencing data without first removing contaminating host organism reads, as otherwise these will lead to a lot of false positive variants caused by miss alignment.  In my experience even a small mount of host material can lead to a ten fold increase in called variants due to miss aligned host reads looking like true variants.  I'd recommend using Xenome, source.  

Note Xenome was designed for DNA sequencing it's not splice-aware, so for RNA-Seq there is no optimal solution other than removing reads which align to the host organisms genome.  Although the issue here is that in conjunction with a splice-aware read aligner synteny between the host and grafted genomes might create some interesting problems.  However for RNA-Seq provided FACS or similar confirms low-levels of host contamination I expect levels of expression will not be badly affected.  Although this really needs investigating.

Finally and rather annoyingly Xenome produces none-standard FASTQ so you'll need to fix it's output with:

awk '{if (NR % 4 == 1) print \"@\"$0; else if (NR % 4 == 3) print \"+\"$0; else print $0 }' as reported here on seqanswers.