Human beings share about 99% of their genes with chimpanzees and only slightly fewer with other monkeys. As a result, the reactions of these creatures are a very good guide to possible reactions of human patients. Even lower down the scale, other animals share the same basic physiology with humans. Furthermore, it would be immoral to risk the life of a human being when a medicine or procedure could instead be tested on a non-human animal.
In fact, most animal experiments are done on animals that are nothing like hum