Josh and Ruth Wagner were thrilled with the delivery of their healthy son in late December.

It was icing on the birthday cake that the pregnancy didn’t stretch into January, when deductibles reset on the Wagners’ health insurance.

“It would have cost us several thousand dollars more,” said Josh Wagner, 35, of Richfield.

The math behind such statements can be complicated, and vary with the health care needs of different families.

But the bottom line is: As more people have high deductibles with their health insurance, the timing of medical procedures can make a bigger difference in how much they pay out-of-pocket for their health care.

For years, doctors have described a phenomenon that could be described as a “deductible rush,” as patients who have already satisfied their deductible for the year rush during the fourth quarter to have procedures done that can be scheduled in advance. That way, the health plan picks up the tab.

In a medical journal last year, a University of Minnesota researcher and colleagues described how the issue can play out at birth centers.

“Financially, you’re going to catch a break if your pregnancy and delivery happens before December 31 — all in the same year,” said Katy Kozhimannil, who studies the impact of health policy on reproductive-age women and their families at the University of Minnesota.

Noting the old joke among parents about how a baby born in December, rather than January, can be claimed as a dependent during tax season, Kozhimannil added: “This is not the only potential financial benefit to having your baby at the end of the year.”

Health plan rules can vary, but a deductible in general is the sum of money that an enrollee must pay before full coverage kicks in. Whereas premiums are required for all enrollees, deductible payments are tied to use of health care services by an individual or family.

Figuring out what goes toward the deductible can be complicated. Under the federal Affordable Care Act, for example, certain types of preventive care must now be fully covered in most plans, even before the deductible is met.

Most services, however, must be paid out-of-pocket during the deductible period, so employers like the idea that enrollees in high-deductible plans have an incentive to be judicious in their use of health care.

Typically, boosting deductibles has been a primary strategy for limiting growth in premiums. This year on the state’s MNsure health insurance exchange, for example, premiums are up significantly, and more people as a result are buying “bronze” plans with deductibles that can run about $6,000 per person.

Kozhimannil and her colleagues noted the popularity of these bronze plans when writing about the impact of high deductibles on spending related to childbirth.

In an article subtitled “Childbirth in the Bronze Age,” the researchers said the average out-of-pocket cost for vaginal deliveries was $2,244 in 2010, with women in high-deductible plans paying almost twice as much as those in traditional insurance policies.

Deductibles have gotten bigger since then, and more prevalent. Given the trends, more women will have pregnancy-related out-of-pocket costs that are both high and hard to predict, the researchers wrote, adding that some could delay having children as a result.

They also noted the timing quirk for December babies.

“Pregnant women who have exceeded their annual deductible amount and deliver infants before their deductible resets for the year could save thousands of dollars,” they wrote last year in the Journal of the American Medical Association. “Death and taxes might be life’s only certainties, but birth and deductibles are poised to become their equivalent in the private U.S. health system.”

Deductibles clearly give families a reason to figure out costs in advance, and shop for the best value, Kozhimannil said in an interview. The problem is, shopping around is easier said than done.

Getting price quotes from health care providers can be difficult. Routine prenatal visits are generally covered at 100 percent, and exempt from deductible requirements, Kozhimannil said, but some women will need lab tests and additional screenings that could require significant out-of-pocket costs, nonetheless.

At the Minnesota Birth Center’s locations in Minneapolis and St. Paul, staff members work with patients upfront to walk through expected out-of-pocket spending, said Tricia Balazovic, the center’s administrative director.

The chance that costs to a family could be higher if a baby is born in January vs. December is a reason, she said, for families to think about the timing for other health care services they might need.

When the baby arrives in January and covers the deductible for the new year, Balazovic has seen some families decide it’s a good time for dad to get a vasectomy. Conversely, when the baby likely will come before year’s end, parents might make that trip to the dermatologist they’ve been delaying, or not worry so much about care costs during the year for other kids in the family.

“There are strategies for dealing with it,” she said.

While the deductible rush inspires patients to speed up the timing of some health care services such as MRIs or certain orthopedic procedures, that’s not really an option with childbirth, said Alina Salganicoff, vice president for women’s health policy at the California-based Kaiser Family Foundation.

The most costly scenario for a family with a high-deductible plan, she said, is when a woman needs a pregnancy-related hospitalization during one calendar year, and then delivers the baby in the following year. While such a sequence could induce sticker shock at the medical bills, parents should get used to it.

“Once you have a kid,” Salganicoff joked, “that’s when the real expenses begin.”