Two common painkillers, ibuprofen and diclofenac, can slightly increase the risk of heart problems if taken in high doses for a long time, data suggests.
People with severe arthritis often take the drugs, which also calm inflammation, to go about daily life.
The researchers said some patients would deem the risk acceptable, but they should be given the choice.
A study, published in the Lancet, showed the drugs posed even greater risks for smokers and the overweight.
The risks have been reported before, but a team of researchers at the University of Oxford analysed the issue in unprecedented detail in order to help patients make an informed choice.
The group investigated more than 353,000 patient records from 639 separate clinical trials to assess the impact of non-steroidal anti-inflammatory drugs.
They looked at high-dose prescriptions levels, rather than over-the-counter pain relief, of 150mg diclofenac or 2,400mg ibuprofen each day.
They showed that for every 1,000 people taking the drugs there would be three additional heart attacks, four more cases of heart failure and one death as well cases of stomach bleeding - every year as a result of taking the drugs.
So the number of heart attacks would increase from eight per 1,000 people per year normally, to 11 per 1,000 people per year with the drugs.
"Three per thousand per year sounds like it is quite a low risk, but the judgement has to be made by patients," said lead researcher Prof Colin Baigent.
He added: "So if you're a patient and you go and sit in front of your doctor and discuss it, you are the one who should be making the judgement about whether three per thousand per year is worth it to allow you, potentially, to go about your daily life."
He said this should not concern people taking a short course of these drugs, for example for headaches.
However, he did warn that those already at risk of heart problems would be at even greater risk as a result of the high-dose drugs.
High blood pressure, cholesterol and smoking all increase the risk of heart problems.
Prof Baigent said: "The higher your risk of heart disease, the higher your risk of a complication. Roughly speaking, if you've got double the risk of heart disease, then the risk of having a heart attack is roughly doubled."
He said patients should consider ways to reduce their risk, which could include statins for some patients.
A similar drug called rofecoxib (known as Vioxx), was voluntarily taken off the market by its manufacturer in 2004 after similar concerns were raised.
There are more than 17 million prescriptions of non-steroidal anti-inflammatory drugs in the UK each year. Two thirds are either ibuprofen or diclofenac.
A third drug, naproxen, had lower risks of heart complications in the study and some doctors are prescribing this to higher-risk patients.
The drug does a similar job to aspirin by stopping the blood from clotting although this also increases the odds of a stomach bleed.
Prof Alan Silman, medical director of Arthritis Research UK, said the drugs were a "lifeline" for millions of people with arthritis and were "extremely effective in relieving pain".
He added: "However, because of their potential side-effects, in particular the increased risk of cardiovascular complications which has been known for a number of years, there is an urgent need to find alternatives that are as effective, but safer."
Prof Donald Singer, member of the British Pharmacological Society and from the University of Warwick, said: "The findings underscore a key point for patients and prescribers - powerful drugs may have serious harmful effects.
"It is therefore important for prescribers to take into account these risks and ensure patients are fully informed about the medicines they are taking."