NEW ORLEANS—A study of arthritis drugs found that, contrary to common belief, Pfizer Inc.’s painkiller Celebrex posed no higher risk to a patient’s heart than ibuprofen or naproxen, two widely used rivals.

Patients assigned to take Celebrex suffered numerically fewer heart-related deaths, heart attacks and strokes than those assigned to either of the other drugs, according to two different analyses of the 24,000-patient study.

But...