I was reading a medical home advocacy group’s upbeat approach to a recent JAMA study that had found scant benefit in the concept when, suddenly, we tumbled into Alice in Wonderland territory.

The press release from the leadership of the Patient-Centered Primary Care Collaborative (PCPCC) started out reasonably enough. The three-year study of medical practices had concluded that the patient-centered medical home (PCMH) contributed little to better quality of care, lower cost and reduced utilization. This was an “important contribution,” said the PCPCC, because it showed “refinement” of the concept that was still necessary.

That was just the set up, though, to this challenge from Marci Nielsen, chief executive officer of the group.

“It is fair,” said Nielsen, “to question whether these pilot practices (studied) had yet transformed to be true medical homes.”

Where might one find these true medical homes? The answer turns out to be as elusive as a white rabbit. Formal recognition as a medical home via accreditation “can help serve as an important roadmap for practices to transform.” However, accreditation as a PCMH “is not necessarily synonymous with being one.” Conversely, you can be a “true PCMH” without having received any recognition at all!

But maybe the true medical home does not yet exist, since, “the evidence base” for the model “is still being developed.”

In Through the Looking Glass, Humpty Dumpty scornfully informs Alice: “When I use a word, it means just what I choose it to mean — neither more nor less.” And so we learn that a true medical home means just what the PCPCC says it does.

It’s confusing. If the truly transformational medical home lies in the future, why does the PCPCC chide the JAMA researchers in this “otherwise well-conducted study” for failing to “reference the recent PCPCC annual report which analyzed 13 peer-reviewed and 7 industry studies and found cost savings and utilization reductions in over 60 percent of the evaluations”?

In my continuing pursuit of fairness, I picked an article on that list that was recently published in a prestigious academic medical journal, a near-peer of JAMA. The PCPCC summary of the 2013 study by Fifield et al. in the Journal of General Internal Medicine awards it three colorful icons (a green dollar sign, a red ambulance and an orange stethoscope) symbolizing cost reductions, reductions in emergency department and/or hospital use and increased preventive services.

However, here’s how the authors of the actual study summarized the results of a randomized trial involving adult primary care practices: “Compared to control physicians, intervention physicians significantly improved TWO of 11 [clinical] quality indicators …[and] ONE of ten efficiency indicators.” (Capitalization in the original.) They add, “There were no significant cost savings.”

Hey, who are you going to trust, icons from an advocacy group or your own eyes?

In another criticism of the JAMA study, the PCPCC takes the researchers to task for failing to use “measures related to patient-centeredness.” That’s a curious suggestion if you’re familiar with the literature on that topic. A nationally representative sample of individuals with chronic diseases and physician practices found “no association between PCMH processes and patient experience.”

Another study found “fewer than a third of patient-centered medical home practices engage patients in quality improvement.” A third study found improved patient-centeredness only when “lean” quality improvement techniques were combined with the PCMH.

As I’ve written previously, putting “patient-centeredness” in the name doesn’t make it so.

To summarize what the PCPCC would like policymakers and others to believe: a “true” PCMH might save money and improve care, but being accredited doesn’t mean you are one, not being accredited doesn’t mean you aren’t one and the requirements for accreditation “must continue to evolve.”

In addition, a “fair” study would balance original research in JAMA with the icons the PCPCC uses to characterize research listed in its annual report.

Though these arguments are laced with Humpty-Dumpty logic, that doesn’t mean the PCMH concept is headed for an irreparable fall. There’s widespread agreement that primary care needs to be organized more effectively and that primary care physicians should be paid appropriately for transitioning from fee-for-service to pay-for-value care.

There will be tweaks along the way, perhaps by concentrating on those patients for whom care coordination is most critical (which the PCPCC also suggests) or by constructing a “Primary Care 2.0,” as Paul Keckley calls it.

But today, as in the topsy-turvy world of Alice in Wonderland, the math connected to the PCMH specifics doesn’t yet add up. When four times five equals twelve (as with Alice), it’s tough persuading outsiders that something isn’t wrong.

Rather than denouncing or dredging data, not to mention endangering its credibility with dubious definitions, the PCPCC should heed the advice of Dr. Thomas L. Schwenk, dean of the University of Nevada School of Medicine.

In an editorial accompanying the JAMA study, he writes: “Before confidently promoting the PCMH as a core component of health care reform, it is necessary to better understand which features and combination of features of the PCMH are most effective for which populations and in what settings.”

It’s time for PCMH advocates to travel back through the looking glass and re-engineer the PCMH to thrive in the real world. As Schwenk puts it: “The study… has done a great service for advocates of the PCMH by effectively ending promotion of this care model as a generic, low-level, unselective approach to health care delivery for all.”

Michael L. Millenson is president, Health Quality Advisors, LLC.  This article originally appeared on Forbes.com.