New research blows the lid on China's claim to have stopped using prisoners and groups such as Falun Gong for organ donation, finding that China appears to have systematically falsified its official data.
The Australian National University research, published on Friday, said analysis of the data implied "deliberate human intervention", showing centrally coordinated data falsification "has clearly taken place".
Simply, the rise in the numbers of transplants was "too neat to be true" and appeared to be generated using a simple quadratic equation, familiar to high school students.
"The only plausible explanation that accounts for all of our observations is that the three datasets were manufactured and manipulated from the central levels of the Chinese medical bureaucracy," the paper from Matthew Robertson, a PhD student and China expert, Canberra statistician Dr Raymond Hinde, and Tel Aviv heart transplant surgeon Jacob Lavee, concludes.
"The goal of these elaborate efforts appears to have been to create a misleading impression to the international transplantation community about the successes of China's voluntary organ donation reform, and to neutralise the criticism of activists who allege that crimes against humanity have been committed in the acquisition of organs for transplant."
Mr Robertson said China had violated the trust of the international transplantation community and international medical groups should reconsider their decision to welcome Chinese surgeons back.
He has analysed the three available datasets of 12 that are kept on Chinese transplants, finding inconsistencies, anomalies and implausible and medically impossible claims.
In technical terms, the data showed "mirroring of quadratic formulae, stubborn adherence to arbitrary ratios, anomalies that abrogate the mathematical integrity of data series, unsubstantiated growth patterns, and other irregularities".
"It is difficult to imagine how such data from three sources could have come to possess these qualities if not for deliberate, ongoing and imperfect human intervention," the paper, published on Friday in the BMC Medical Ethics journal, said.
China announced in January 2015 that it would only take organs from volunteers and no longer use prisoners (it has also been accused of using Falun Gong, Uighur and other persecuted groups).
Its national COTRS database of donors and transplants has shown "extraordinary success", with the number of voluntary donors up from 34 in 2010 to 6316 in 2018.
The data has been welcomed by international transplant groups and resulted in invitations to the head of China's transplant reforms, Dr Huang Jiefu, to present at international conferences.
But doubts have persisted, with most of China's transplant data remaining secret, and "no independent, scientific examination of China's ambitious program of organ transplant reform" until now, according to Mr Robertson's paper.
It finds that the figures that Dr Huang presented showing fast-rising donor numbers showed "an extremely close adherence to a simple mathematical function, specifically a quadratic equation". The pattern was out of step with data from 50 other countries and its mathematical precision was implausible in a complex, geographically scattered industry such as organ transplants.
"The finding that China's data for voluntary deceased donors, kidney transplants, and liver transplants, conform to three almost perfect quadratic equations is highly surprising," they said.
The explanation of deliberate manipulation to fit a target was given more heft last year when updated COTRS numbers were released, matching an even more simple mathematical formula (for the mathematicians, y equals a times x squared, where x=0 corresponds to 2010, the year in which Chinese authorities said they began voluntary organ donation).
The formula explained 99.7 per cent of the variation in the data, Mr Robertson said.
Asked why China would do something so obvious, Mr Robertson said it was very difficult to falsify an entire data series with "some semblance of internal coherence among competing bureaucracies" and it seemed China had made a mistake.
"If they had added 10 per cent more random variation we wouldn't have such strong findings," he said. "The fact that it was so clean is simply a mistake. It's a monumental error on their part."
The ANU researchers also found anomalies in China's Red Cross dataset, including medically impossible 21.3 number of transplants per donor in March 2016, data inputs that matched an apparent pattern of "correcting" for a consistent rate of 2.75 transplants per donor, and other changes suggesting manipulation.
Mr Robertson concludes the COTRS data was "falsified through a top-down process", and the Red Cross data manipulated to match and "maintain a semblance of congruence".
However, the anomalies betrayed the ruse. The data appeared to have been "handed down as quotas - albeit quotas that were imperfectly implemented across a fractured bureaucratic and administrative apparatus, thus exposing the discrepancies identified".
Mr Robertson said his paper had been sent to China for comment, but none had been made.
It was also reviewed by a top statistician in Britain, Professor Sir David Spiegelhalter, of Cambridge, who backed the analyses.
While there were almost always recording errors and delays in data in government data, the anomalies found by Mr Robertson "follow a systematic and surprising pattern", Sir David said.
"The close agreement of the numbers of donors and transplants with a quadratic function is remarkable, and is in sharp contrast to other countries.
"... This could, of course, just be coincidence, although it is difficult to quantify how surprising such a pattern is without a model for the "natural" development of a transplant program. But I cannot think of any good reason for such a quadratic trend arising naturally."