Ways to measure effectiveness of a gene therapy trial?
If all you cared about was genomic integration, then your best bet would be some kind of sequencing. If you sequence the modified region and the flanking regions you could be sure that the new sequence was present in the genome.

It would probably be more interesting to look at how the new genes affect the cell. For example you could look at differences between protein expression in modified and unmodified cells. For that you could use RNAseq.