The guy who did the "43 times" study, Arthur Kellermann, was criticised for not sharing his statistics for replication (for example, today American Economic Review will not publish an article if the data and math are not released pre-publication for replication by other researchers; in 1986 medicine allowed researchers to withold data until they decided they had no further studies to produce from the data).
12 Jun 1986, New England Journal of Medicine, Arthur Kellerman, M.D., and Donald Reay, medical examiner, Kings County, Washington State, six years 1978-1983, medical examiner and police reports; 398 gunshot deaths in the residences where the gun was kept, 9 justifiable homicide (self defense), 12 accidents, 41 nonjustifiable homicides, 333 suicides, a questionable 3 either accident or suicide. So the "43 times" comes from 1 justifiable homicide versus 1.33-1.67 accidents, 4.56 criminal homicides, and 37.33 suicides.
There are problems assuming that a sample of homes that include unusual numbers of suicides plus homicides represent otherwise ordinary households that happen to own a gun for self-defense. Another Kellermann study weighted for other factors, such as: households with a member who uses illicit drugs; rented homes; prior violence within the household; living alone; household member with arrest record.
The 43:1 is highly dependent for shock value on the ratio of 37 suicides to one justifiable homicide; as though the suicides were committed with guns kept as protection against criminals, versus guns acquired for the intent of committing suicide. Or that people in high crime neighborhoods were more likely both to own a gun for protection and to potentially be a victim.
There are some problems with assuming that police report all self defense killings as justifiable homicide. Most justifiable homicides (self-defense) are adjudicated much higher in the judicial system than by police report; Gary Kleck has estimated that for every homicide adjudicated by police report as justifiable, the judicial system will eventually adjudicate four or seven times that number of voluntary manslaughters as justifiable self defense.
In a totally different study*, researchers looked into the question of why the district attorney did not charge murder in 481 out of 1247 homicides as determined by the medical examiners office in a Wisconsin jurisdiction. Of a selected sample of the non-prosecuted homicides looked at in the study, half were adjudicated by the prosecutor as self-defense. That would imply 1 out of 6 homicides adjudicated at the DA level as self-defense, not tracing cases through the judicial system to trial jury or appellate court level where other cases could be adjudicated a self defense. Most crime stats are not reported past the police report level and adjudication can take years. The FBI Uniform Crime Report table of "killing of a felon during commission of a felony" by a citizen adjudicated by police does not reflect adjudication by coroner, ME, DA, grand jury, judge, trial jury or appeals court. Criminologist Marvin Wolfgang found that in isolated jurisdictions that did track homicides all the way, 20 to 30 percent were self defense. Kellermann's sample was 9 justifiable homicides and 41 criminal homicides of a subsample of 50 (sample was gunshot deaths in a home where a gun was kept) actually pretty close to 20%.
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* PROCEEDINGS of the American Academy of Forensic Sciences February 2003
"Discrepancy Between the Legal and Medical Definitions of Homicide" by Jeffrey M. Jentzen, MD, of Milwaukee County Medical Examiner's Office
and three co-authors.