In 2008, when Senator John McCain was the oldest person to seek a first term in the White House, his campaign set out to reassure the public about his health. It let reporters examine 1,173 pages of handwritten notes, lab results and insurance documents, including details of the senator’s biopsies, his prostate exams and even the “very light tan freckling” on his buttocks.

He was 71 years old.

Today, President Biden is 81 and his rival, Donald J. Trump, is 77, and many voters believe both men are too old for another term. Their doctors proclaim them fit to serve, but neither has agreed to throw open his medical charts to prove it.

Mr. Biden released a six-page summary of medical test results in February, but his doctor has refused to be interviewed by reporters, breaking from past practice. Mr. Trump has revealed less than Mr. Biden; his last public note from his doctor, in November, was three paragraphs long. Neither man has sat for a comprehensive assessment of his mental fitness, a battery of tests often administered to people their age.

The longstanding truth about the American political system is that presidents and presidential candidates choose what to test, what to ignore, how much medical information to release to the public and, in the end, what voters will know about their health and well-being.

But the election between the two oldest people to ever seek the presidency is challenging that notion. Not only are Mr. Biden and Mr. Trump failing to do anything extra to reassure Americans that they can lead well into their ninth decade of life, they are doing less than their predecessors in some important ways.

The New York Times sent five-page letters to the Trump campaign and the White House with detailed questions about the health of the candidates. The Trump campaign did not respond to the letter, which included questions on mental fitness, cardiac health and whether he has taken Ozempic to lose weight.

The White House directed questions about Mr. Biden’s health to his doctor’s summary of the president’s physical in February, which concluded that Mr. Biden was fit for duty. “Joe Biden is proud to have been transparent with his health records as vice president, as a presidential candidate and as president,” said Andrew Bates, a White House spokesman. “He believes all leaders owe that level of honesty to the American people.”

The Times’s questions about mental fitness, however, were not addressed in the summary.

“I don’t want to be ageist, and I would never make an armchair diagnosis, but I do think we need full-blown neuropsychological exams,” said Dr. Rudolph E. Tanzi, a professor of neurology at Harvard Medical School and the director of the McCance Center for Brain Health at Massachusetts General Hospital.

He was referring to a series of 33 tests known as the Neuropsychological Assessment Battery, which can detect dementia and other brain dysfunction.

“You’ve got to take an exam to drive,” Dr. Tanzi said. “These guys are taking the exam to be in the White House, where you have buttons you can push that might end the world.”

In interviews with a dozen of the country’s leading experts on aging, all described inexorable patterns that almost always accelerate after age 80. The body becomes more frail, more prone to damage and less likely to recover quickly. The risk of cognitive disease grows. Three percent of people between 65 and 69 have been diagnosed with dementia; by age 90, it is 35 percent.

Questions about the age and health of the two candidates are coursing through the political debate. So far, the answers have not been forthcoming.

That means Americans are left to judge their fitness for office in what experts on aging say is the worst possible way: from afar, largely based on snippets of their public appearances — the good and the bad.

The president has a common retort for anyone who expresses concern about his age and mental fitness: “Watch me.”

His aides have said he works out regularly, lifting weights some mornings and riding on a Peloton. Last month, he delivered a forceful, energetic State of the Union address. And for the past few weeks, he has crisscrossed the country to give speeches and collect campaign cash at a pace that might exhaust any candidate, of any age.

But other appearances are enormously damaging. At an exclusive New York fund-raiser last summer, he recounted the racial violence in Charlottesville, Va., that inspired him to run for president in 2020. Minutes later, he told the same story again, practically word for word, drawing concerned glances from the crowd.

“I know I look like I’m 30,” Mr. Biden later joked to tepid laughter in the room. “I’ve been around doing this a long time.”

In February, the special counsel investigating Mr. Biden’s handling of classified documents described him as an elderly man with “diminished faculties.” The report, by the prosecutor Robert K. Hur, enraged Mr. Biden and his allies, who said it painted a wildly inaccurate picture.

A New York Times review of the transcript of the interview, which stretched over two days in October as Mr. Biden was responding to the Hamas attack on Israel, found that he was clear and cogent through most of the questioning, fumbling only on occasion with dates and the sequence of events.

All of the doctors interviewed for this story said it is difficult, if not impossible, to diagnose someone based on isolated moments or observations. They said stress, a lack of sleep or multitasking — rather than any mental decline — could lead to flubs.

“Those things are real, OK? But they’re not telling you if he can make a decision or not,” said Dr. Nir Barzilai, the director of the Institute for Aging Research at the Albert Einstein College of Medicine.

During Mr. Biden’s physical, his physician and a team of specialists chose not to conduct the Neuropsychological Assessment Battery, or a similar comprehensive assessment of his mental fitness.

The doctor decided there was no need for such a test because Mr. Biden regularly demonstrated what the medical team considered high-level executive functioning, according to people familiar with the decision.

One person on Mr. Biden’s team put it this way: After the president navigates hours of complicated foreign policy meetings during grueling trips overseas, it would be pointless to have him sit for a test asking which picture is a lion and which is a rhinoceros.

Dr. Sayed Azizi, the clinical chief of behavioral neurology and memory disorders at Yale University, said exams that go well beyond those kinds of simple questions are common in some fields after a certain age.

“Oftentimes, even in medicine, physicians who are over age 70 or so, they have to yearly go to the doctor and either take those tests or not, or somebody has to certify them that they’re OK to practice medicine,” he said. “Most hospitals have that.”

The White House contends that the details released by Dr. Kevin O’Connor, Mr. Biden’s physician, are sufficient and several past presidential doctors have chosen not to address reporters in the White House briefing room. Dr. O’Connor said an “extremely detailed” exam yielded no findings that would be consistent with neurological disorders such as a stroke, multiple sclerosis or Parkinson’s disease.

He said Mr. Biden’s noticeably stiffer walk was the result of arthritis of the spine, pain in his hip and peripheral neuropathy, a condition defined by a loss of sensation in his feet.

Dr. O’Connor’s summary also included the results of common blood tests, medications being taken and a discussion of the president’s struggle with sleep apnea. But Dr. O’Connor has not provided any supporting documents.

The biggest omission, according to medical experts, was the lack of cognitive testing. Dr. Tanzi said such tests should be administered to any presidential candidate 50 years or older, by doctors who do not have any political or personal allegiance to them.

“It has to be an independent assessment,” he said. “That’s absolutely essential.”

The unknowns about Mr. Trump

Even by the standards of previous candidates — and in contrast to Mr. Biden — the information Mr. Trump has provided about his own health has been exceptionally opaque.

In his letter in November, Dr. Bruce A. Aronwald said Mr. Trump’s “cognitive exams were exceptional.”

But he offered no backup for any of his claims. He did not say what kinds of tests the former president had been given. He did not provide the results of any bloodwork. He did not say what medicine Mr. Trump is taking. He did not explain what cognitive exams the former president took, when he took them or what the specific results were.

Without more information or testing, medical experts say it is impossible to judge Mr. Trump’s health with any precision, beyond the fact that he is subject to the same kinds of rapid declines that often afflict people his age.

“It can go down very quickly,” said Dr. Azizi, who studies the way the brain ages, losing about a gram of weight every year from the age of 16. He said that as the brain gets older, a person’s longstanding tendencies and habits are often amplified.

Mr. Trump, who is running for president while defending himself against dozens of felony counts, regularly talks about his stamina and vitality. He holds lengthy and bombastic rallies, often staying onstage for more than an hour.

But he has also had a series of gaffes.

During a campaign speech in New Hampshire in January, he confused Nikki Haley, his Republican opponent, for former Speaker Nancy Pelosi. He has claimed he defeated former President Barack Obama in 2016, when he actually ran against Hillary Clinton.

Recently, during a news conference, he seemed to confuse Gov. Kathy Hochul of New York with the state’s former governor Andrew Cuomo, who has not held that office since 2021.

Fred Trump, the former president’s father, developed Alzheimer’s in his mid-80s. Those who study the disease say Mr. Trump’s risk of developing Alzheimer’s, already higher because of his age, increases by about 30 percent because of his father’s diagnosis.

In 2018, the former president’s doctor revealed that Mr. Trump insisted on taking a dementia screening test known as the Montreal Cognitive Assessment and answered all 30 questions correctly. Dr. Ronny Jackson, then the White House physician, concluded that “the president is mentally very, very sharp; very intact.”

Mr. Trump went on TV to boast about his results, listing the words that he had been asked to remember in the right order: “Person. Woman. Man. Camera. TV.”

Medical experts quickly noted that the test does not measure intellect and that just about everyone without Alzheimer’s or another kind of dementia should get a perfect score.

Because of the absence of information Mr. Trump’s campaign has released, it is also difficult to know whether the former president’s risk of other health issues has increased in recent years.

When Mr. Trump was president, his weight, history of high cholesterol and lack of exercise put him at higher risk of developing cardiac disease that could lead to a heart attack or stroke, according to a letter released by his doctor in 2018.

In 2018, Mr. Trump’s doctor said he was 239 pounds, just one pound shy of the medical definition of obesity for his height and age. Last year, when he was booked at the Fulton County jail in Georgia, he listed his weight at 215 pounds — a figure that many critics called into question.

Much of the public information about his health has been riddled with exaggerations. After Mr. Trump announced his candidacy in 2015, his doctor, Harold Bornstein, a gastroenterologist from New York, wrote that “if elected, Mr. Trump, I can state unequivocally, will be the healthiest individual ever elected to the presidency.”

The doctor later admitted that Mr. Trump dictated the line, adding “I just made it up as I went along.”

‘You want to be reassured’

In a New York Times/Siena College poll of six battleground states last fall, 70 percent of voters said Mr. Biden was too old to be president. Less than half of voters expressed similar misgivings about Mr. Trump, though his critics say his disregard for facts and word-salad speeches prove that he is unfit to hold office again.

Doctors have expressed deep skepticism about relying only on information provided by candidates’ personal physicians for information about their health.

“There is a public need to know about the physical and mental fitness of anybody who’s going to go into the highest office in the country,” said Dr. Joe Verghese, a professor of neurology and medicine and the director of the Resnick Gerontology Center at the Albert Einstein College of Medicine.

“You want to be reassured that steps have been taken to ensure that the person you’re electing into office will have the physical and mental capability,” he said.

There are no legal requirements to release health information, and candidates often invoke the same desire for personal privacy at the heart of protections against the release of medical records for all Americans.

Mr. McCain’s political advisers in 2008 considered his disclosures vital to dealing with voter concerns about his age and the potential for illness in office.

Barack Obama, who was 47 when he defeated Mr. McCain, released a one-page letter from his doctor during the 2008 campaign, but later offered supporting lab tests and electrocardiograms.

In 1988, both Michael S. Dukakis, the Democratic candidate, and George Bush, the Republican, gave interviews about their health and allowed reporters to talk directly to their doctors. After Mr. Bush took office, his physician continued to give interviews, and a panel of doctors held a news conference to talk about his health challenges and treatments.

Bill Clinton resisted releasing his records in 1992 and again during his re-election in 1996, even after his opponent, Bob Dole, released detailed health information and allowed his personal physician to be questioned by reporters. George W. Bush and his doctor gave interviews about his health during the 2000 campaign, and the younger Mr. Bush’s doctor answered reporters’ questions in 2002 after the president choked on a pretzel.

Neither Mr. Biden nor Mr. Trump has acknowledged making any accommodations because of his age.

For both men, doctors say, caution is medically warranted: Old people are more frail than younger ones. Last week, former Senator Joseph I. Lieberman of Connecticut died from complications of a fall at 82.

“Falls are one of the biggest killers of older Americans,” said Dr. Zaldy Tan, a professor of neurology and director of the memory and aging program at Cedars-Sinai Health System.

Campaigning for the presidency — and actually holding the job — is enormously taxing. During her own campaign for the White House, Vice President Kamala Harris compared it to the rigors of being a lawyer during an extended trial.

“It requires adrenaline and stamina; it requires being in shape mentally and emotionally,” she said. “It’s a marathon.”