One of the most basic assumptions underlying the Affordable Care Act is the compelling idea that people with health insurance will be healthier. It follows, right? People who learn they have diabetes will be prescribed drugs to  manage their disease. People who find out they have high cholesterol or blood pressure early will get the medical advice and treatments to prevent heart disease.

A study published Tuesday in Health Affairs reports new evidence of health insurance's salutary effects on chronic disease, quantifying those effects down to changes in blood sugar control, blood pressure and a slight drop in cholesterol. Expanding coverage to half the number of non-elderly uninsured people, the authors estimate, will mean 1.5 million additional people will be diagnosed with chronic diseases and 659,000 will gain control of their illness.

The analysis adds to a growing, if somewhat uneven, body of evidence probing health insurance's effects on health. A study of the aftermath of insurance expansion due to health care reform in Massachusetts found that among people between 20 and 64 years of age, there was a significant drop in mortality: 8 fewer deaths per 100,000 adults. Another Massachusetts study found that after health care reform, residents got more preventive care and reported better health.

But in Oregon, researchers tracked people who were randomly assigned, by lottery, to be eligible for coverage through Medicaid or not. They found that Medicaid coverage had a major impact on mental health and on financial security, but no significant effect on cholesterol or high blood pressure.

Research examining the expansion of Medicaid to pregnant women in the 1980s and 90s found that insurance coverage was associated with less infant and child mortality.

That all suggests health insurance matters for health -- to a degree that can vary depending on how the question is studied.

"I suppose one of the major motivations for us in doing this study is there’s been so much debate about the Affordable Care Act and relatively little discussion of health, whereas there’s been quite a bit of discussion about financial outcomes," said Joshua Salomon, a professor of global health at the Harvard T.H.Chan School of Public Health, and the leader of the new study. "That always struck us as peculiar."

Salomon and colleagues analyzed data from a national survey administered between 1999 and 2012, in which participants also had their health measured through various tests. They compared health measures of those who had insurance with those who lacked it. They found that insured people were more likely to have chronic conditions diagnosed. People who had a diagnosis and insurance were more likely to have their disease under control.

These approaches all have limitations, and the new study is no different: what health insurance does for health turns out to be a simple question that's hard to study since so many factors besides insurance coverage contribute to health. The new study comes with a raft of qualifiers, the researchers acknowledged. The large national survey it draws on can't rule out possible underlying differences between people who have health insurance and those who don't. That means the study may overestimate the health benefits of having coverage, said Sharon Long, a senior fellow at the health policy center of the Urban Institute.

Still, researchers generally agree that having access to health insurance has benefits.

"Being on Medicaid is better than being uninsured," said Katherine Baicker, a professor of health economics at the Harvard Chan School of Public Health. "What seems much less clear to me is how that option compares to other options. None of these studies say which is better: expanding Medicaid, or vouchers for private insurance."

The real question now may not be how big the effect of insurance is on health, but how to structure insurance so that it gives people the best chance of staying  healthy. There is also growing interest in comparing insurance coverage to other ways that money could be spent to improve health, for example by reducing poverty, which is associated with poor health outcomes, spending on food stamps, or structuring insurance plans differently.

"We know we improve health care coverage, but .... what are some of the other strategies to improve health?" Long said. "There's a lot of work beginning to look at what if we address air population, water pollution, what do we see? Might there be other strategies" than simply expanding coverage?