A new study by the Centers for Disease Control and Prevention suggests that vaccination provides stronger and more reliable protection against the coronavirus than a past infection does, the agency said on Friday.

Unvaccinated people who had previously recovered from a coronavirus infection were five times as likely to get Covid as people who had received both shots of the Pfizer-BioNTech or Moderna vaccines, the C.D.C. said.

The study’s authors cautioned, however, that certain gaps in patient data and biases in their study participants could have influenced the results.

“We now have additional evidence that reaffirms the importance of Covid-19 vaccines, even if you have had prior infection,” said Dr. Rochelle P. Walensky, the C.D.C. director, in a statement accompanying the release of the report.

The question of whether people who have had Covid really need a shot has gained traction among some Americans as vaccine mandates take hold across the country. Scientists have urged Covid survivors not to skip the vaccine, noting that the strength and durability of so-called natural immunity depends heavily on people’s age and health, and the severity of an initial infection.

The C.D.C. study used a roundabout experimental design. The researchers examined roughly 7,000 people hospitalized this year with Covid-like illness across nine states. They then looked at how many of those hospitalized patients were indeed infected with the coronavirus. The odds of testing positive for the virus were considerably higher among unvaccinated, previously infected patients than they were among vaccinated people.

The study comes with several caveats, however. The researchers cautioned that the findings may not translate to non-hospitalized people with different levels of access to medical care, and that some patients in the vaccinated group may unknowingly have also had previous infections.

The researchers also noted that separate research in Israel had failed to show that vaccinated people were better protected than those who had only been infected. In general, scientists said, studies on the topic had drawn contradictory conclusions.

Still, some patterns have emerged. Two doses of an mRNA vaccine produce more antibodies, and more reliably so, than a coronavirus infection does. But the antibodies from prior infection are more diverse, potentially helping people fend off variants.

Whatever the effect, doctors have warned that acquiring natural immunity is perilous and uncertain. Not everyone survives Covid in the first place, and those that do may not be able to count on a vigorous immune response.