The previously linked article does a pretty good job of describing the difficulties in such as lawsuit, but I will add a few other things.
First, the person who sues has the burden of proving the statement is false. Sometimes this is easy, "Dr X did not attend medical school." Other times it is next to impossible. Lets say that a patient - fake or not - posts "I went to see Dr X and complained of chest pain and he did not order an EKG." Can you prove that every patient you have seen since medical school who complained of chest pain you ordered an EKG for? Not "I always do that", but actual proof, that is medical records. (Remember you have the burden of proving that the statement is false.)
Second, to reiterate from the article, opinion can never be the basis of a defamation claim. Lets say that the review said "I had an appointment and the Dr only spent seconds with me." An impression of time is an opinion, and can never be the basis for defamation. One could also argue that the statement is not false, because 30 minutes is still 1800 seconds.
Third, there is the implicit threat. Not only do you have to prove that the statement was not an opinion, and was false, you also have to provide discovery so that the defendant can rebut your argument. Lets say that the statement was "Dr X fraudulently billed insurance for a procedure he did not do during the office visit." Lets assume you can link this to a specific patient and can provide medical records to support that you in fact did do a specific procedure. Can your prove that the medical records were truthful? The defendant will almost certainly demand you provide medical records, billing records, and put you and your staff under oath for a deposition. (Whether they get those things is a different question, but they probably will, with the later more likely than the former.) Congratulations, you won your defamation case and got $10K in damages (which after lawyer fees means you end up losing $50K), but now the DOJ is suing you for billing violations found during the legal action, and if you are very unlucky you are facing criminal prosecution. Lawyers will deny it, but deposition and subpoena are used as weapons, and you have a lot to lose, even if you did your best to avoid mistakes. I guarantee you they will find some.
Finally, the other reality in litigation. If you go after a patient, you might get an apology but you will certainly not end up with any money after attorney fees. But if you try to go after someone like healthcare.com, they have the deep pockets and attorneys to bankrupt you with legal fees. There is a reason why defamation cases are either won in horrific "open and shut" cases where fault has already been admitted (Duke/Virginia "rape" cases) or are prosecuted by people who already have incredibly deep pockets (e.g., "Hulk Hogan) to start with.
(The other thing is that you say the statements caused you to lose a contract. Unless the hospital said "We were going to offer you a contact, but solely because of what we saw on an online review we decided not to", your suit will almost certainly fail on that alone. If the defendant can show there was any other reason why the hospital - I assume - might have not offered a contract you will lose.)
There is one other concern that depends on the specific state: Lets say whatever company offers to settle for $10 and you reject that. If you do go to trial, and lose, then you are liable for all of their attorney fees. Even if you were to win, and the jury awarded you $5, you would still be liable for all of their attorney fees. (You rejected a settlement offer and received a less-favorable judgement.)
If you are in a state with an anti-SLAPP statute, it makes it even tougher to sue, and you will be liable for the defendant's attorney fees if you do not actually win. Basically anything remotely related to healthcare is considered "speech about a matter of public concern."
I am not a lawyer, there are things that a lawyer will probably say are not technically true. So give this the weight it is (not) due, but what I am writing is close to reality. Bottom like: it might be theoretically possible, but you would likely have better odds buying a Powerball ticket tonight. There is a reason the "First Amendment" is First.
