The reason to test on animals at all is to make sure that the drug has the intended effects and to watch for possible unintended side effects.
First, the drug is tested just on cells maintained in a petri dish. But the problem with that is that it isn’t an entire system. You can, for example, test how a certain substance reacts with certain mammalian cells in a petri dish, but that doesn’t tell you how it would impact the rest of the system. So, it might work fine with the cells in the petri dish, but once it encounters nerve cells for example, it might damage them. You need to see the results in something that is actually living.
Animal testing is EXTREMELY expensive (cheap, though, relative to testing on higher order mammals and people, though). For my work alone (which is one testing, in one lab, in one building, of a really big university) I have 500 mouse cages, with a couple of mice per cage. It costs $1.50 per day per cage. That’s nearly 275K a year on the mice alone. So, I assure you, if there were an equally effective way to test these drugs, researchers would be JUMPING on it. We work very hard for every grant dollar we get, and if I could save a million over a 4 year period, I would absolutely do it. And don’t get me wrong - I’m all for finding alternatives, if only to get the annoying PETA people away from my building.

Seriously, I just want to throw my shoe at their heads!! The problem is that replicating a living creature is nearly impossible (ah, the wonder of God’s creations! Seriously, we’re VERY complicated, don’t let anyone tell you different.

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I don’t want to sugarcoat or mislead by saying they live in a mouse hotel. I’m half kidding about that. The conditions they live in are pretty swank to be sure, but of course, that time does come to an end for them, and the testing can be downright cruel. I don’t want to get too graphic here, but what I’m working on is for Charcot-Marie-Tooth, which is a nerve disorder. Once its time to test the drugs on the mice, the results aren’t very pretty. But I have to remember that those results could INSTEAD be happening in a person, and that would be even worse.
Most of the time, it does go straight from mouse testing to human testing. Testing on larger animals is pretty infrequent.
Sometimes larger animals ARE used though. For example, if you need to look at the effects a drug has on the heart, a mouse heart is incredibly tiny, so pigs are more often used instead since you can actually LOOK at their heart. Again, it’s 275K a year for mice. I have no idea how much it is for larger animals, but I can’t imagine that would be cheap.
Anti-depressants you asked about specifically…well, it’s sad but here goes. To see if the anti-depressant works, one of the tests they do is a shock test. If the mouse doesn’t care that it’s getting shocked then the drug didn’t work. If it tries to get away or fight, then the drug is working. And that’s the sort of the results researchers are hoping to see. There are other tests, too, which also aren’t pretty, but again, it’s either test them on the animals first or go straight to humans.
One drug I worked on turned out to give the mice heart attacks.

That’s why you do these tests, to get all the bugs out.
The other HUGE benefit to mouse studies specifically (versus larger animals and people) is that these lines have been bred brother to sister for so long that essentially these mice are clones of one another. You simply can’t get a homogeneous population in humans or higher order mammals. It’s important to test a drug on what are essentially clones because then you can isolate that the results you are seeing are the results of the drugs themselves rather than any differences in the mice. Furthermore, mice breed quickly. One of the effects you are looking for too on some of these drugs is how it affects offspring. And mice have offspring FAST. Remember, in the wild, a mouse only lives about 4 months. You’re talking 50 days til they can get pregnant, and a gestation of 20 days with 10-12 pups. I can get to the fourth generation with mice in no time, and, again, if you want drugs to get to market quickly, you need to test on something that breeds quickly.
Oh, and the entire mouse genome has been mapped and there are strains of mice that have been developed specifically with a gene missing to test the impact of that specific gene, which is pretty helpful, and again, not something you can do with people.
And yes, once the animal testing is done, small scale tests are done on willing members of the population (such as yourself and other willing participants, which here, are generally broke university students), but again, you would NOT want to get a drug before it was even tested on mice. I’ve seen drugs have the unintended consequences of sudden heart attacks, blindness, and death. And, I’ve seen alot of drugs that just went kaput and didn’t do anything at all, not even what we were hoping they would do.