Every state has its own statute of limitations for injuries caused by drugs. I'll post my SOL scorecard in the next few days. The shortest statutes are one year - Kentucky, Louisiana and Tennessee. The longest is six years.
Most states recognize what is called a "discovery rule." That means the clock on the statute of limitations starts to run when the plaintiff knew or should have known that their injuries were caused by the fault of another.
Please keep in mind there are all kinds of limitations to the discovery rule and every state and everyone's case is different, so no one should assume based on the discovery rule that they have "plenty of time" to bring suit.
Generally, someone who used Zantac and was diagnosed with cancer before September 2019 probably "should have known" that they might have a case against the makers of Zantac in September 2019 when the FDA press release about the possible connection came out. As a practical matter then, even someone who was diagnosed with cancer caused by Zantac in 2010 can still sue in most states without worrying about the statute of limitations.
Someone who used Singulair and was diagnosed with neuropsychological injury before March 4, 2020 probably "should have known" that they had a case against the makers of Singulair in March 2020. That is when the FDA required Merck to include a black box warning on Singulair, warning consumers of the connection between Singulair and those specific injuries.
Remember, the statute of limitations starts when the injured party "knew of should have known" about the connection between the injury and the product. Many people discovered that Singulair was the cause of their injuries before March 2020 and even tried to warn others about the dangers of Singulair. For those people, the clock on the statute of limitations may have started ticking whenever they actually discovered the connection.