Publishing the performance data of thousands of surgeons across England fails to pick up those whose practice is causing high death rates, experts say.
A review of the death rates for patients in six key health areas found that even those surgeons whose performance is deemed "acceptable" may actually have too many patients dying needlessly.
In 2013, Health Secretary Jeremy Hunt launched the My NHS website for patients, enabling them to search for individual surgeons, assessing factors such as the death rate of patients within 90 days of surgery.
He said that publishing the data "will not only drive better care for patients" but could "literally save lives".
However, the move has proved controversial, with critics saying death rates are a "crude measure" for assessing a surgeon's performance.
In January 2015, heart surgeons wrote to NHS England asking for a rethink of the policy of publishing death rates, claiming it was causing some colleagues to avoid risky operations.
In the new study, published in the journal BMJ Open and funded by the Medical Research Council, researchers from the University of Edinburgh looked at death rates for inpatients and at 30 and 90 days post-surgery for six common procedures between 2010 and 2014.
The procedures were surgery for bowel cancer, removal of a part or the whole of the stomach (gastrectomy) or oesophagus, aortic aneurysm repair, hip replacement, removal of the thyroid gland (thyroidectomy) and weight-loss surgery.
The team found that the current data fails to identify those surgeons with an above-average death rate because each individual surgeon does not perform enough procedures.
For example, when it comes to hip replacements, weight-loss procedures and thyroidectomy, fewer than 20% of surgeons with death rates five times higher than the national average would be detected using the current system.
Each hip replacement surgeon would need to carry out 500 hip replacements every year if just one failing surgeon was to be detected. At present, they perform about 48 to 75 operations per year.
The researchers said: "At these rates, it is unlikely that a surgeon would perform a sufficient number of procedures in his/ her entire career to stand a good chance of detecting a mortality rate five times the national average."
They concluded: "At present, surgeons with increased mortality rates are unlikely to be detected. Performance within an expected mortality rate range cannot be considered reliable evidence of acceptable performance."
The researchers said records of patient outcomes and death rates are not consistent between hospitals and units, which also makes the figures unreliable.
They called for more focus on tracking recovery after surgery as well as measuring patient satisfaction. A s death rates for all surgical procedures continue to fall, they argued, measuring death rates will become less useful for assessing surgeons.
Ewen Harrison, of the University of Edinburgh's department of clinical surgery, said: "Publishing surgeons' mortality rates is a step towards transparency in medical care, but it offers little help in identifying poor performance.
"We must use this data as part of a wider initiative to keep the quality of care in UK hospitals high."
Professor Derek Alderson, vice president of the Royal College of Surgeons, said: " Individual surgeons' mortality rates are published in the interests of transparency, however they cannot be relied on as an indicator of how well a surgeon is performing.
"When looking at how to improve patient care in hospitals, surgeon mortality figures must be viewed in the context of wider measures including unit and relevant patient outcomes."
A Department of Health spokesman said: "We make no apology for our drive to make the NHS the safest health service in the world - there is no shortage of evidence showing that transparency is a key driver of improvement, supporting both better accountability and patient care."