As we recently wrote, it’s better for patients to have Medicaid than to be uninsured, contrary to critics of the program. But is having Medicaid, as those critics also say, much worse than having private insurance?

This idea has become a talking point for conservatives who back big changes to Medicaid, as the Senate health bill proposes. The poor would benefit simply by being ushered off Medicaid and onto private insurance, they write.

But it’s far from proven that Medicaid is worse than private insurance. A lot depends on what kind of insurance is compared with Medicaid, and how they are compared.

Many studies that measure Medicaid against private insurance suffer from the same flaws that compare Medicaid with being uninsured. They’re terribly confounded, and can show only associations, not causation. People with private insurance are healthier and wealthier than those on Medicaid, and in ways not fully controlled for in statistical analyses. These factors almost certainly predispose someone on Medicaid to have worse outcomes than someone with private insurance.

Perhaps the most convincing way to compare Medicaid and private insurance would be with a randomized controlled trial that pits them head to head. No such trials exist. Recall that the Oregon Medicaid study randomly offered, via a lottery, the opportunity for low-income adults to enroll in Medicaid. It did not have another study arm that offered private insurance.

But we do have a decades-old trial that looked at varying levels of cost-sharing: the RAND Health Insurance Experiment. This is relevant because one substantial difference between Medicaid and most private coverage is the level of cost-sharing. Medicaid is nearly free. Most private coverage comes with deductibles and co-payments.

The RAND study randomly assigned 2,750 families to one of four health plans. One had no cost-sharing whatsoever — kind of like Medicaid. The other three had cost-sharing (money people had to pay out-of-pocket for care) at levels of 25, 50 or 95 percent — capped at $1,000 at the time, which is about an inflation-adjusted $6,000 today. This level of personal liability acts like a deductible, making the plan with a 95 percent level of cost-sharing comparable to a “Bronze” plan on the Affordable Care Act’s exchanges today.

The RAND study found that the more cost-sharing was imposed on people, the less health care they used — and therefore the less was spent on their care. The study also found that, over all, people’s health didn’t suffer from lower health care use and spending.

Lower spending and no decline in health — these are the results that everyone cites to justify increased cost-sharing, and to justify shifting people from Medicaid to private plans with high deductibles.

But the results of the RAND study, like so much in health care, are complicated. A deeper dive into the data shows that people decreased their consumption of necessary health care in equal measure to unnecessary health care. As a rule, people are terrible discriminators of what care is needed and what’s not. Since most people under the age of 65 are healthy, even in the RAND study, that doesn’t matter much.

But even if most people are healthy, some are not (and particularly those on Medicaid). In the RAND study, poorer and sicker people — exactly the kind more likely to be on Medicaid — were slightly more likely to die with cost-sharing.

Free care also resulted in improvements in vision and blood pressure for those with low income. As an influential 1983 New England Journal of Medicine paper put it: “Free care does make a difference.”

One limitation of the RAND study is its age. It took place between 1971 and 1982. There have been no studies of cost-sharing to rival it since. Still, the best recent evidence we have is that giving free care to poorer and sicker people improves health and saves lives. It is reasonable to conclude that switching them to a plan with high cost-sharing (even a private plan) would do the opposite.

Some of the more recent studies were nicely summarized in a paper by Katherine Swartz for the Robert Wood Johnson Foundation’s Synthesis project. She found that increased cost-sharing for low-income populations was associated with a shift toward more costly services, like increased emergency room visits because people skipped taking their drugs. She also found that increased cost-sharing affects poor people differently than everyone else, confirming RAND’s findings. A more recent study found that enrollment in plans with high deductibles led to reductions in necessary care, which would have consequences for the poor and sick.

Austin wrote previously herehow increased cost-sharing may lead people to take fewer drugs for their high cholesterol, hypertension and diabetes. In his first Upshot column, Aaron wrote that parents delay taking their children for asthma treatment when cost-sharing rises.

Even small premiums can lead to problems. A $10 increase in monthly Medicaid premiums was followed by a 6.7 percent reduction in Medicaid and coverage of CHIP (Children’s Health Insurance Program) for people just above the poverty line.

Unquestionably, private coverage can work very well for many people. Take us, for instance. The insurance that we each have from our employers is probably better for us than Medicaid would be. Though these plans come with cost-sharing, we have incomes that can handle it. Our plans cover things that Medicaid often does not, like dental checkups.

Our plans have great networks, and they reimburse well for the care we receive. Just like Medicaid enrollees, we also receive support from the federal government, which waives tax collections on dollars contributed to premiums. That tax break is higher than the cost of Medicaid in many cases.

We’re also relatively healthy and would probably be fine on any plan (unless and until our health deteriorates).

But because our plans require considerable cost-sharing, even Medicaid enrollees would struggle on them. More important, neither House nor Senate repeal and replace bills offer poor Medicaid enrollees plans as generous as ours.

The Senate’s health care plan, for example, would offer much less generous plans. A 64-year-old woman with an income of $11,400 would face a deductible of at least $6,000. For her, such a plan is not better than Medicaid; it is most likely much worse if she is also sick. Because of the deductible, the care she’d need would be financially out of reach.

A recent paper in Health Affairs documented that outcomes in Arkansas, which allowed poor people to buy private plans on the exchanges, were similar to those in Kentucky, which expanded access to poor people through Medicaid. But those private plans came with significant cost-sharing subsidies, which would be stripped away by the Senate’s bill. Even so, the evidence did not suggest that the private coverage of Arkansas was better than the public coverage of Kentucky.

There are certainly private plans for poor and sick Americans that are better than Medicaid. But plans with very high cost-sharing — which are the ones being offered in Congress as A.C.A. replacements — are not among them.