Doctors do kill a disturbing number of patients from avoidable mistakes, but the comparative statistics in the claim are mostly meaningless
Before looking at the actual statistics on medical errors it is important to dispose of some of the meaningless statistics in the claim. "doctors are 9,000 times as deadly than gun owners" is a meaningless comparison, for example, as there is nothing comparable between owning a gun and being a doctor. Most doctors interact with hundred or thousands of patients a year; most gun owners won't use their gun at all. And what does the percentage of deaths per physician mean?
However, if we avoid silly percentages we can look at the number of avoidable deaths. The classic US study of this is To Err is Human: Building a Safer Health System from the year 2000. Their headline number (which is the source of many press reports) is described in context thus:
• Sizable numbers of Americans are harmed as a result of medical errors.
Two studies of large samples of hospital admissions, one in New York
using 1984 data and another in Colorado and Utah using 1992 data, found
that the proportion of hospital admissions experiencing an adverse event,
defined as injuries caused by medical management, were 2.9 and 3.7 percent,
respectively. The proportion of adverse events attributable to errors
(i.e., preventable adverse events) was 58 percent in New York, and 53 percent
in Colorado and Utah.
• Preventable adverse events are a leading cause of death in the United
States. When extrapolated to the over 33.6 million admissions to U.S. hospitals
in 1997, the results of these two studies imply that at least 44,000 and
perhaps as many as 98,000 Americans die in hospitals each year as a result of
Note the method: detailed studies in local hospitals extrapolated to the whole USA. This might justify putting even bigger error bounds on those totals, but the numbers are disturbing even if they have big error bars.
It is also worth noting that many studies or reported statistics might underestimate the real avoidable deaths as any admission of error might lead to legal liability (medicine seems to adopt the opposite approach to aviation where reporting of near misses and mistakes in encouraged so procedures can be tightened to avoid future errors). So we have to be wary of many of the numbers.
The ballpark figures from the USA don't appear out of line with other studies. An analysis done for the NHS was reported in this BMJ paper in 2004 (NB the links to the references were broken when I checked the article). It uses several sources and comes up with estimates of up to 40,000 deaths (from about 30% of the number of admissions as the US system) from one source to only about 4,000 from another (but excluding infections which are a major killer).
A more recent BMJ paper suggests the UK is again broadly similar the the USA but doesn't give overall estimates. A 2005 survey by the UK's National Audit Office provides several useful numbers for judging the scale of the problem and conveniently summarises both the estimates and some of the problems with them:
A retrospective study of patient records in two English
hospitals found 10.8 per cent of patients experienced an
adverse incident; of which around half (5.2 per cent) were
judged to have been preventable. These adverse incidents
caused permanent impairment in six per cent and contributed
to death in eight per cent of cases.
Our analysis of trust surveys found that 169 trusts were able
to provide data on the number of deaths as a result of patient
safety incidents. This showed that in 2004-05 there were some
2,181 deaths recorded but it is acknowledged that there is
significant under reporting of deaths and serious incidents.
Other published estimates of death as a result of patient safety
incidents range from 840 to 34,000 but in reality the NHS
simply does not know.
These estimates are broadly consistent with the estimates from the USA.
Another perspective is the Institute for Healthcare Improvement's 100,000 lives campaign which set a target of (crudely) avoiding 100,000 deaths in hospitals over a two year period.
Yet another perspective that provides some quantification of how many deaths are avoidable comes from the use of aviation-style checklists in surgery (NEJM article from 2009) where the rates of death from complications were reduced from 1.5% to 0.8%. This study doesn't extrapolate directly to all hospital admissions, but the size of the gain suggests a large number of avoidable deaths in the current system.
It wouldn't be outrageous to say that the rates of accidental death across several health systems seem to be between 0.1% and 0.4% of hospital admissions (compared to the numbers used in the original question in the USA, this is equivalent to a range of about 30,000- greater than 120,000 deaths).
So, in summary, it is hard to estimate the number of avoidable deaths in hospitals exactly, but it is likely to be large and is probably one of the top ten causes of death.