With Republicans in their strongest legislative position since the 1920s, 2015 will likely be a year of significant initiatives on post-Obamacare health reform. As we move into the New Year, let’s make a resolution to keep one reform principle in mind: The United States needs to move beyond the “Heliocentric Doctrine” of health insurance, whereby patients and insurers switch dance partners every January 1.

Consider two identical twins, recently diagnosed with the same catastrophic illness last June. They both have the same have health insurance. Whether it is through their employer, or an Obamacare exchange, or Medicare does not really matter.

They have been diagnosed with the same cancer. It is genetically determined: There is nothing that either of them could have done to avoid it. It will require many months of treatment by drugs and surgery, and the treatment will evolve as oncologists observe how the twins’ cancers respond to different therapies.

Generally speaking, both twins have been healthy up to now. All of a sudden, in the second half of 2014, they entered that small minority of patients who, in any period of time, account for a large share of health spending.

Because of the high cost of treatment, their insurer has likely put cancer drugs on the most expensive tier of their prescription formularies (the list of drugs that the plan will cover). This means that the twins might each face a 30 percent coinsurance rate for very expensive medicines. If they are enrolled in individual Obamacare exchange plans or non-grandfathered employer-based pans, they will pay directly out-of-pocket up to $6,350 ($6,600 in 2015). If they are on Medicare, let’s assume that they have a Medicare Advantage policy or one of two Medicare supplemental policies (also known as Medigap) that also limit out-of-pocket costs.

Here is the twist: Despite receiving exactly the same treatment, and covered by exactly the same plan, one of the twins might face little, if any, direct out-of-pockets costs, while the other might have to make complicated treatment decisions based on prices of different drugs and procedures.

How can this be? In this case, the one twin had no medical costs in the first half of the year. The other went on a ski vacation in February, had an accident on the slopes, and spent a day or two in the hospital having his broken bones mended. It was not a big deal in the scheme of his life—certainly not on the scale of cancer—but it caused him to incur medical and hospital bills up to his out-of-pocket limit for 2014.

So, once diagnosed with cancer, the skiing twin will face completely different financial decisions than the non-skiing twin. Indeed, he may even be relieved that the winter accident—now trivial in hindsight—has eliminated some of the financial trade-offs of his cancer treatment.

Anyone with experience of cancer in his family will protest that this illustration is overly simple. Nevertheless, it describes the absurdity of America’s unexamined Heliocentric Doctrine of health insurance. Our health insurance is designed around the amount of time it takes the Earth to revolve around the sun—one year.

These days almost all of us face significant deductibles, co-payments, co-insurance, and maximum out-of-pocket costs. Although Americans are finding them harder to meet, these obligations exert discipline on health spending, and are surely one factor responsible for the decrease in the rate of growth in health spending over the past few years.

However, when it comes to paying medical bills directly out-of-pocket, the meter goes back to zero on January 1. Whether you are healthy, recently diagnosed with a serious illness, in the depths of expensive treatment, or recovering does not matter. What matters is that a new year has begun on the date fixed by the Roman Republic in 153 B.C. for the start of the newly elected Consuls’ terms.

This nonsensical Heliocentric Doctrine is enshrined in employer-based plans, Obamacare exchange plans, and Medicare plans. Neither patients nor health insurers take a long-term view of what the appropriate balance is between patients’ direct out-of-pocket payments versus claims paid by insurers.

In other countries where private health insurance dominates, with Switzerland being the prime example, no one tolerates this absurdity. Instead, patients and insurers have contracts that last multiple years, and each are rewarded for good behavior during the long term. This type of health insurance is especially effective for very sick people with lots of illnesses, who would no longer have to worry about losing their doctors because of having to choose a new plan every year.

As the American people decide how to move beyond the failure of Obamacare, 2015 will see many plans and proposals put forward. Let’s resolve that the health reform that succeeds Obamacare will move beyond the Heliocentric Doctrine, and that New Year’s Day no longer be a day of worrying what your new health insurance will cover.