For people who have problems with their heart and blood vessels, a Mediterranean or low-fat diet can reduce the chance of dying early and of having a non-fatal heart attack, a detailed new study shows.

Published in the journal BMJ, the research analyzed data combined from 40 previous studies that enrolled a total of 35,548 people. The people in the studies either had cardiovascular disease or had at least two risk factors for it, such as high blood pressure, diabetes, obesity, or high cholesterol. The analysis compared how well various diets protected people at risk of heart problems, compared to just giving people a brochure about healthy eating.

The researchers said, “there were no convincing differences between Mediterranean and low fat” diets in terms of whether one reduced the risk of death or chance of heart attack more than the other. People at higher risk were most likely to see the greatest benefits of the diets.

The researchers defined a low-fat diet as limiting fat intake to 20% to 30% of daily calories and saturated fat intake remaining below 10% of daily calories. The Mediterranean diet was defined as eating a lot of fish, fruit, vegetables, and monounsaturated fats like olive oil. People on those two diets fared better than those on five other eating plans, such as diets that limited fat even more, also limited sodium intake, added plant-based requirements, or used a complex formula for many calculable aspects of food like carbohydrates, protein, and fiber. The names of the other diets studied were very low fat, modified fat, combined low fat and low sodium, Ornish, and Pritikin.

Those other five diets “generally had little or no benefit compared with” being given a healthy eating brochure, the researchers wrote. The researchers said their findings are important because they only looked at data from randomized controlled trials, which are the gold standard in research design because the people in those studies don’t get to pick if they are in a treatment group or in the control group. Randomized controlled trials are particularly sensitive to finding out whether a treatment is effective and ensuring that outcomes are not being influenced by some other factor.