The Martha’s Vineyard Hospital has tested more than 350 people for the coronavirus since the outbreak began over a month ago. Sixteen of the tests have come back positive.

But not everyone who contacts the hospital to report symptoms is tested, making the actual rate of infection Islandwide difficult to determine with any real precision.

With testing for Covid-19 emerging as a national issue, hospital president and chief executive officer Denise Schepici, and head of hospital operations and nursing chief Claire Seguin spoke with the Gazette last week about the intricate process for testing on the Island. In an interview, both said they believe there is adequate capacity for testing on the Vineyard — but they also confirmed the hospital has turned away some symptomatic patients, telling them to quarantine instead.

They defended the hospital’s strict testing policies and criteria and said they didn’t see a need for broader mass testing on the Island.

Recent population estimates developed by the Gazette based on Steamship Authority data and other available information puts the current Island population at around 20,000. Using that number, the Vineyard has tested approximately 1.5 per cent of its population. Statewide, the number is approximately 2.6 per cent.

Ms. Schepici and Ms. Seguin said the hospital’s testing criteria are set by Partner’s Healthcare, the hospital’s parent network, and leave a large amount of discretion for who gets tested to individual physicians screening patients. The criteria are aligned with guidelines from the CDC, which change often, they said.

For a variety of reasons, including the fear that a negative test will give people a false sense of security, the hospital turns away some symptomatic patients determined to be low risk, and instead simply tells them to isolate for 14 days.

“Doctors will say, you have symptoms of a respiratory viral illness — those are the exact words — and the advice right now is that you go home and self-quarantine for two weeks,” Ms. Seguin said. “I will say, we have had that.”

She declined to specify the number of symptomatic patients who had been turned away from testing, but said the number was small.

“I don’t think it’s been a lot,” Ms. Seguin said.

Ms. Schepici said it would be difficult to estimate the number of positive cases on-Island that have presented with symptoms but haven’t been confirmed by a test.

“What makes that a hard metric to wrap your arms around is that a lot of these people don’t have Covid,” Ms. Schepici said. “They have a sore throat, and a cough, and muscle aches . . . But we’re going to say in an abundance of caution, you’re going to self-quarantine at home. That’s why it’s a hard metric to get your arms around.”

Symptomatic patients who do not receive a positive test are not entered into the state’s epidemiological database, MAVEN — meaning they are not monitored by local boards of health and they do not trigger any contact-tracing process. They are also not included in the total positive case count provided by the state, hospital or local boards of health.

“At this time, we have to prioritize,” Ms. Seguin said. “There isn’t this unlimited amount of tests that we have out there.”

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The hospital officials described the steps involved in viral serology testing at the hospital. In almost all instances, the process begins with a phone call to either a primary care physician or the hospital’s screening hotline, if a person does not have a doctor. During the phone call, a doctor asks prospective patients a series of questions in order to assess their risk. Two basic elements play into the risk assessment: symptoms, and other risk factors. And while the symptoms doctors at MVH assess have remained the same since testing began, the other risk factors change daily.

“The basic criteria for how the patient presents — cough, fever, sore throat — none of that changes,” Ms. Seguin explained. “But as for who gets tested, who actually gets tested — that’s the thing that changes.”

As it stands now, anyone who is over the age of 70 and experiencing severe chronic lung disease, severe heart disease, immunosuppression or is on immunocompromising medication or dialysis, will automatically receive a test if they are exhibiting symptoms. Anyone who lives in a long-term care facility or group home, like Windemere, or is homeless, or is more than 36 weeks pregnant, also will automatically receive a test if symptoms are present. Medical workers and inpatients who show symptoms automatically receive tests as well.

For anyone else with symptoms, it is up to the primary care physician or doctor to authorize the test. That’s where the discretion comes in.

“Criteria is a guide, but it is not meant to replace a physician’s judgment,” Ms. Schepici said. “If you called, and you had a symptom of Covid, and your doctor feels that you are high risk, and thinks, oh, if you live with eight other people in your house, and you should really know, then they’re going to go ahead and approve that test.”

It also can work the other way.

“Sometimes there are folks with symptoms, and we’re just going to instruct them to self quarantine,” Ms. Seguin said. “They are pretty low risk from the categories, and if their doctor thinks it is appropriate, they will do that.”

Anyone authorized to get a test is instructed to schedule an appointment for the hospital’s drive-up testing tent, which is booked in advance like a doctor’s appointment. The patient will receive a nasal swab from a fully-donned nurse, which is then packaged and sent via courier to Boston in a viral medium. The turnaround time on tests is now 24 hours.

The hospital also has a 45-minute testing kit, but due to limited supplies reserves those tests for in-patients and health care workers.

Once the test is registered in the state system, a primary care physician or hospital staffer will notify the patient of the result. In an almost parallel process, the hospital’s internal prevention infectionist will inform the health agent from the town if the result is positive.

Ms. Schepici and Ms. Seguin said the lower testing rate on the Vineyard compared with the state at large is likely because of the low prevalence of the virus on the Island, as opposed to, for example, the city of Chelsea. They added that it was important to preserve much-needed testing equipment for harder-hit communities.

Both said they were satisfied with the current rate at which testing is being conducted on the Island, and said the main goal with testing is to focus on high-risk patients, using those numbers to plan for capacity at the hospital.

“If you think about the way we use criteria, it is a way for us to prioritize those patients who are likely to get really, really sick from this,” Ms. Seguin said. “As far as patient safety and good, sound, clinical care, I’m happy with the process that we have for now.”

Ms. Schepici said part of the reason for the limited testing and strict criteria was that the hospital could not handle a rush of patients demanding requests.

“We’re just going to be bombarded,” she said. “And it’s just not fair to our health care workers. It’s not fair to our supply system. It’s not fair to everybody else who is trying to follow the rules.”

Ms. Schepici also said mass testing would be unnecessary and counterproductive at this point, fearing that thousands of negative tests could prompt people to take greater risks than if they are simply told to quarantine.

“The point is this: if we test that person, and the person is negative, right, that gives that person the false sense of security that they don’t have the virus,” the hospital president said. “We can’t open it up to mass testing for that very reason.”

She continued:

“That’s why we’re not doing that testing. That’s why we’re saying, self-quarantine. If it is medically necessary, and the physician thinks it meets the criteria, they’re going to have you come in. But if it’s not . . . the pill we’re giving, is quarantine. It’s the quarantine pill. That’s what it is.”