Merck & Co. has vowed to defend itself against each of more than 3,800 pending state and federal lawsuits alleging it knew its popular painkiller, Vioxx, could be dangerous long before the company voluntarily pulled it from the market last year.

The New Jersey drug maker’s first chance to do so begins with jury selection Monday in a small-town Texas courtroom 30 miles south of Houston.

“We intend to defend these cases individually over many years,” Merck’s general counsel, Kenneth C. Frazier, said in a statement. The company’s most recent lawsuit count reached 3,857.

“Merck acted responsibly, from researching Vioxx prior to approval in clinical trials involving almost 10,000 patients to monitoring the medicine while it was on the market to voluntarily withdrawing the medicine when it did,” Mr. Frazier said.

Thousands of plaintiffs seeking potentially billions of dollars in damages allege otherwise. They include Carol Ernst, whose husband, Robert, died in his sleep in May 2001 after taking Vioxx for about eight months to ease pain in his hands.

Mrs. Ernst’s lawyer, Mark Lanier, aims to skewer Merck’s marketing efforts and top leadership while seeking to convince a dozen jurors that the company knew Vioxx increased the risk of heart attack or stroke years before it pulled the drug.

“I think it’s a good case. It’s an interesting case. And the world’s eyes will be watching,” Mr. Lanier said.

Last week Merck asked State District Judge Ben Hardin to postpone the case for two months because pretrial publicity—primarily stemming from Texas Attorney General Greg Abbott’s June 30 lawsuit alleging Merck falsely touted the safety of Vioxx—could have tainted the jury pool.

Judge Hardin said the first step in jury selection would forge ahead Monday with 100 potential jurors filling out questionnaires. The judge said he would examine their answers to gauge any bias before ruling on the request for a delay.

About 20 million people took the anti-inflammatory drug prescribed for arthritis and acute pain since it came on the market with great fanfare in 1999. In 2000, a study found that some Vioxx users suffered twice as many heart attacks and other cardiovascular problems as users of the older painkiller naproxen, sold under the brand name Aleve.

In 2002, the U.S. Food and Drug Administration added warnings to Vioxx’s label. Follow-up research showed Vioxx doubled the risk of heart attack or stroke if taken for 18 months or longer, which prompted Merck to pull the drug.

The Ernst case is unusual in that Robert Ernst died of an arrhythmia—or irregular heartbeat—rather than a heart attack. Merck’s legal team plans to zero in on how no studies link Vioxx to arrhythmia.

Undaunted, Mr. Lanier’s team says sudden death doesn’t leave enough time for the heart muscle to show whether Vioxx caused any damage.

Mr. Lanier said that generally the first few cases tried in so-called “toxic torts” don’t favor plaintiffs because “it just takes a while to learn how to try it and figure out all the ins and outs.”

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