Animal testing seems to be part of the pre-clinical stage, right before phase 1, when human volunteers are tested. There is this web site: FDA faqs

quote from that site: "During preclinical drug development, a sponsor evaluates the drug's toxic and pharmacologic effects through in vitro and in vivo laboratory animal testing. Genotoxicity screening is performed, as well as investigations on drug absorption and metabolism, the toxicity of the drug's metabolites, and the speed with which the drug and its metabolites are excreted from the body. At the preclinical stage, the FDA will generally ask, at a minimum, that sponsors: (1) develop a pharmacological profile of the drug; (2) determine the acute toxicity of the drug in at least two species of animals, and (3) conduct short-term toxicity studies ranging from 2 weeks to 3 months, depending on the proposed duration of use of the substance in the proposed clinical studies. "

I used to be a chemist and have worked for a company that was developing new drugs and they did use dogs and monkeys, from what I was told. I was only a temp there for less than a month. I tried to ask questions to learn all I could about the whole process but I never saw any animals or where they were kept. All I do know is the building was new, every room immaculate, and the one person I met who had contact with the animals cared about them.

As for the scientific process it does require multiple testings of many samples in order to have a certain amount of statistical accuracy. I have no idea how that works when dealing with animals. The impression I have been given is that dog and monkey testing is done only when they truly believe the drugs are ready for humans - and there is evidence to back that belief.