It's been a while since any member of the Basile family missed school or work for a visit to the doctor.

"We had perfect attendance two years in a row," said mother Meredith Basile. "No lates. No sick days."

Instead of waiting in a doctor's office, she and husband Joe found family physician Dr. Brian Thornburg, who treats them and their two children at their home in Naples, Florida.

ABC News

Related: Save money and time by bringing doctor to you with telemedicine.

Thornburg is one of an estimated 10,000 concierge doctors in the US.

For a fee, these doctors offer personalized care and around-the-clock access, often treating their patients at home for everything from a routine checkup to the occasional stitch or two.

On top of their regular health insurance, patients pay Thornburg a $100 monthly fee for whatever home care they might need.

Although critics say the service is only for the rich and famous, ABC News' consumer health advocate Michelle Katz disagrees. She said there could be hidden savings in concierge medicine.

"They (parents) don't have to take off work. They don't have to find babysitters," Katz said. "They can be in the comfort of their own home."

Katz estimated how the Basiles saved about $2,000 a year with concierge medicine by following two money-saving tips:

1. Combining checkups. In the Basiles' case, they pay $100 a month to Thornburg for all of their regular care. Four separate checkups at a doctor's office would have cost this family $750 even with their insurance.

2. Reducing ER visits. US families visit emergency rooms on average twice a year at a cost of $1,200 a visit. By saving the Basile family trips to the ER, Thornburg helped them cut their overall healthcare costs.

When their son, Luca, split open his chin on the kitchen counter, Thornburg came to their home and stitched up the wound.