Previous articles by the authors of this current study1–4 and by others5–13 have examined the frequency of different gunshot wound characteristics as indicators to determine the manner of death, specifically homicide or suicide. It has been shown that there are significant differences between aspects of wound location, range, and number of shots that are more likely in either homicide or suicide.1,3–8,10,12,14,15 These differences vary by the type of firearm used—rifle, shotgun, or handgun.2 These cited studies gave a probability of homicide or suicide for each variable examined.
Probabilities are often used and assigned in scientific research and analysis. Even if unknowingly, forensic pathologists assign probabilities while performing autopsies or when testifying in court with statements such as “In my experience, contact gunshot wounds are more common in suicides.” But if questioned about how certain they are of their opinion, a precise answer can often be difficult to support. When there is a single characteristic to be considered, such as the range of shot, the relative probabilities of homicide and suicide are reasonably simple to assess. In practice, however, there is a need to assess a number of different features in combination, such as range of shot, location of the wound, and type of firearm used. The variability in these features shown by the previous studies cited means that the assessment in combination is a complex task. It becomes even more complex if the combination of features includes some that are more likely to be homicide with some that are more likely to be suicide.
Bayesian analysis is used in clinical medicine and forensic science alike. For example, Klein et al16 devised a Bayesian network to assess the likelihood of venous thromboemboli in low-risk patients, and Biedermann and Taroni17 applied Bayesian analysis to gunshot residue interpretation. Internationally, there is strong support for use of this approach (“the likelihood ratio framework”) for the evaluation of forensic evidence (e.g., Evett18). But what is Bayesian analysis, and how can forensic pathologists apply it to their work?
Most medical practitioners will be aware of “relative risk,” which is a comparison of the risk of a particular event (such as developing a disease) for different groups of people. Relative risk is calculated using Bayes’ theorem and when used for forensic science is generally called a likelihood ratio (LR). In essence, Bayes’ theorem provides a formalized way of comparing 2 hypothetical situations (such as homicide and suicide) and measuring the impact of pieces of evidence on the relative likelihood of each.
More technically, Bayes’ theorem states that the subjective posterior odds that a hypothesis is true (ie, the odds after incorporating data about a particular factor or piece of evidence) can be determined by multiplying the prior odds (or the odds before incorporating the new data) by the ratio of
- a. the probability that the data would have been observed if the hypothesis were true to
- b. the probability that the data would have been observed if the hypothesis were not true.
The LR is the ratio of (a):(b).
Using P to represent probability, Bayes’ theorem is:
The full version of the theorem is therefore
where P = probability, E = evidence, H= the hypothesis, = “not the hypothesis.”
Use of Bayes’ theorem can generate a probability of how likely something (such as suicide) is to be true compared with an alternative (such as homicide), when given evidence that something else (such as a contact range shot) is known to have occurred.
This allows the pathologist to consider multiple variables in combination when analyzing a situation, as the process can be repeated to combine the effect of several known factors (such as a known range, known firearm type, known wound location). The calculations for each included variable are iterative. So, by way of explanation, if H1 = suicide, H2 = homicide, and the iterative evidence is
- E1 = head shots (given a fatal shot)
- E2 = temple shots (given a fatal shot to the head)
- E3 = left temple shots (given a fatal shot to the temple);
then a sequence of calculations is performed as follows:
Thus, a net likelihood for each of the competing hypotheses (such as homicide and suicide) can be produced.
Use of Bayes’ theorem to address multiple evidential factors requires a Bayesian network. For a simple example of how a network might be constructed, one might try to assess what the probability is that it will rain today, given that it is June, there is a drought, it has not rained for weeks, the weather forecast is predicting rain, and there are few clouds in the sky. A diagram of this example is illustrated in Figure 1; where each factor included is represented by a node. Given the right data, a probability can be calculated for each node individually using Bayes’ theorem. The probability thus derived for each individual “node” becomes the “prior probability” for the next node or nodes in the network. Bayesian analysis is particularly appropriate when the factors being examined have to be calculated from data with a lack of independence, such as with some gunshot wound locations.
Bayes’ Theorem and Medicolegal Death Investigation
Bayes’ theorem can be applied to medicolegal death investigations. For example, a forensic pathologist testifying that in his/her assessment a particular gunshot wound resulted from suicide may be asked how certain he/she is of that opinion. Bayesian analysis can define that certainty by deriving a specific LR from the known probabilities of the features of the wound. This study was designed to apply Bayesian analysis to gunshot wound interpretation as pertaining to manner of death.
MATERIALS AND METHODS
A systematic search was made for published studies and “gray” literature (i.e., studies and reports not indexed in commercial publication databases19), which reported homicidal and/or suicidal deaths by firearm, and which reported the frequency of number of shots, range of fire, and location of wounds. Studies were included if they were published since 1980, were in English, had been peer reviewed, and gave sufficient detail to permit data extraction. Studies were excluded if they did not meet the inclusion criteria, and/or if they were about specific subpopulations (e.g., military personnel in action) or atypical firearms (such as home-made guns) or did not distinguish between different types of firearms.
Data extracted from individual studies were pooled to provide larger data sets. Likelihood ratios were calculated for individual characteristics (range, wound location, and number of shots) being indicative of homicide or suicide. Analysis of combined characteristics was performed using specialist software (GeNIe 2.0; Decision Systems Laboratory of the University of Pittsburgh, Pittsburgh, Pa) to construct Bayesian networks; nodes in the networks were populated with data from the pooled data sets. Because of the incomplete nature of the data, separate networks are necessary for homicide and suicide. The networks generated probabilities for homicide and suicide for each combination of variables and the probabilities used to calculate LRs.
A total of 47 potential studies were identified. On review, 19 met the criteria for inclusion. From these, data could be extracted for a total of 5600 deaths by firearm: 3707 suicides and 1893 homicides. Of the suicides, 2779 were by handgun, 587 by shotgun, and 341 by rifle, whereas of the homicides, 1036 were by handgun, 568 by shotgun, and 289 by rifle.
Multiple Versus Single Shots
Suicide is substantially more likely than homicide to result from a single shot for all firearm types. More than 98% of handgun suicides were single shots (LR = 2.3), compared with fewer than 42% of homicides (LR = 0.4). For rifles, more than 97% of suicides were single shot (LR = 1.7), and 58% of homicides (LR = 0.6). For shotguns, all except one of the suicides (99.8%) were single shot (LR = 2.8), and fewer than 36% of the homicides (LR = 0.4).
Similarly, suicide is substantially more likely than homicide to result from a shot at contact range for all firearm types. More than 96% of handgun suicides (LR = 9.6) were at contact range but only 10% of homicides (LR = 0.1). For rifles, nearly 99% of suicides were contact (LR = 16.9) compared with fewer than 6% of homicides (LR = 0.06), and for shotguns nearly 97% were suicides (LR = 24.9) compared with fewer than 4% of homicides (LR = 0.04).
Wound Location—Head and Chest
Head Versus Elsewhere on Body
Suicidal fatalities are substantially more likely than homicidal to result from shots to the head rather than other body locations. For handguns, more than 81% of suicidal shots were to the head rather than elsewhere on the body (LR = 3.2), compared with only 25% of homicidal shots (LR = 0.3). For rifles, nearly 76% of suicidal shots were to the head (LR = 3.4), but fewer than 23% of homicides (LR = 0.3), whereas for shotguns, 62% of suicides (LR = 3.0) compared with only 21% of homicides (LR = 0.3) were shots to the head.
Chest Versus Elsewhere on Body
Fatal shots to the chest do not differentiate well between homicide and suicide. For handguns, 14.5% of suicidal shots were to the chest, compared with just over 15% of homicidal shots, meaning a shot to the chest was slightly more likely to be a homicide (LR = 1.05). With rifles, homicide was again slightly more likely (LR = 1.09) as 16% of suicidal shots and nearly 18% of homicidal shots were to the chest. However, shotgun fatalities showed a greater difference in manner of death, and homicide (26%) was about a third more likely (LR = 1.3) than suicide (21%) as manner of death for people with fatal shot wounds to the chest.
Specific Locations on the Head
Table 1 shows the locations of shots to the head for handguns, rifles, and shotguns by suicides and homicides.
For all types of firearm, occipital shots were least frequent in suicide (<1% of cases). For every other head location, there was variability between the different firearm types, with the side of the head being the most frequent site for suicidal handgun and rifle shots, and the mouth the most frequent site for suicidal shotgun shots. There is similar variability in the homicidal locations, with mouth and submental being least frequent for all firearm types. Shots to the side of the head were most frequent for homicidal handgun and rifle shots, whereas the face was most frequent for homicide by shotgun. Some studies allowed identification of which side of the head—right or left—was the location in temporoparietal shots, and the division is shown in Table 2.
Data about specific head locations are a subset of wounds to the head, and data for which side of the head is a subset of the data for wounds to the side of the head. Because of this lack of independence, Bayesian analysis was used to derive probabilities and LRs for the locations, and these are tabulated. Table 3 shows the probabilities and LRs for homicide and suicide for the different head-wound locations for handguns. Table 4 shows the same for rifles, and Table 5 for shotguns.
Table 3 shows that when handguns are used, and only the location of the fatal wound considered, suicide is more likely given a fatal headshot located to the side (both right and left), mouth or submentally. Homicide is more likely given shots to the face or the back of the head. Table 4 shows that when rifles are used and only the location of the fatal wound considered, homicide is more likely for all locations except mouth and submental, where all cases were suicidal. Table 5 shows that like rifles, when shotguns are used and only the location of the fatal wound considered, homicide is more likely for all locations except mouth and submental. These two latter locations are more likely suicide.
Bayesian Application—Case Examples
Shot to the Head
A case was presented where a person has died of a rifle shot. It is known that the death was not accidental and was either suicide or homicide. There was a single shot (more likely suicide), at contact range (also more likely suicide), to the left side of the head (more likely homicide). Because the head location data are not independent, a Bayesian network was developed to produce net probabilities for this combination of factors being suicide or homicide. As Figure 2 shows, each factor is represented by a node. The data in this study provided the probability for each factor. The resulting probabilities of suicide (P = 0.0371) and homicide (P = 0.0010) show that suicide is more probable than homicide, giving an LR = 36.4. That is, a case with this combination of features is more than 36 times more likely to be a result of suicide than of homicide.
Now consider if the death had been the result of 2 shots rather than 1—what difference would that make in the analysis? In that case, the resulting probabilities of suicide (P = 0.0010) and homicide (0.0007) show that suicide is still more likely than homicide, but only very slightly (LR = 1.4). If the firearm used had been a shotgun rather than a rifle, again, with a single shot to the same location, then suicide (P = 0.0311) is more than 78 times more likely (LR = 78.3) than homicide (P = 0.0004). That is, the likelihood of suicide is even stronger for a shotgun than a rifle. However, if a shotgun is used, and there are 2 shots rather than 1 shot, while the other factors remain the same, the calculation shows that the probable manner of death reverses, and homicide (P = 0.0007) is 10 times more likely than suicide (P = 0.0001).
Shot to the Chest
A second example is a case where someone has died of a handgun shot. Again, it is known that the death was not accidental and was either suicide or homicide. There was a single shot (more likely suicide), at contact range (also more likely suicide), to the chest (more likely homicide). In this case, the data are independent, and a Bayesian network is not necessary. Instead, the LRs for suicide for the different factors can be multiplied together to produce a net LR: single shot (LR = 2.34) × contact range (LR = 9.58) × chest location (LR = 0.96) = 21.5. That is, a death by handgun with these features is more than 21 times more likely to be suicide than homicide.
However, we know that shots to the chest are more likely to be homicide when a shotgun is used when gun type is considered in isolation. Using the same features but for a shotgun rather than a handgun produces a net LR for suicide: single shot (LR = 2.8) × contact range (LR = 24.9) × chest location (LR = 0.78) = 54.3. Thus, although a shotgun shot to the chest considered in isolation is more likely to be homicide, in fact, when considered in combination with the other factors, it is more than 54 times more likely to result from suicide. But the probable manner of death depends on the combination of factors. If the death had been by shotgun but not at contact range, the net LR for suicide becomes0: single shot (LR = 2.8) × noncontact range (LR = 0.04) × chest location (LR = 0.96) = 0.09. That is, homicide is substantially the more likely manner of death (LR = 12.7).
The current study with pooled data finds that for all firearm types, shots at contact range are strongly more likely to be suicidal, whereas shots at other than contact range, multiple shots, and shots to the back of the head are strongly more likely to be homicidal. For all gun types, shots to the head are 3 times more likely to be suicide than homicide. This is broadly consistent with previous studies: for example, Karger et al8 found that head wounds occurred in more than 82% of suicides but only 33% of homicides (LR = 2.5), and Desinan and Mazzolo11 and Fedakar et al20 found similar proportions. When wound location is considered on its own, shots to the face and back of head are more likely to be homicide than suicide for all gun types, whereas intraoral and submental shots are more likely to be suicide than homicide. These findings are consistent with the authors’ previous studies1–4 and with others.10,21
However, the larger samples from pooled data support the authors’ previous finding that there are differences between firearm types.2 These differences may be absolute: that a certain factor is more indicative of suicide for 1 firearm type but of homicide for another; for example, when location is considered alone, shots to the side of the head are more likely to be homicide than suicide for rifles (LR = 2.2) and shotguns (LR = 2.6), but for handguns, that location is more likely to be suicide (LR = 5.6). In most factors, however, the difference between firearm types is the effect size: that is, the factor is more strongly indicative of manner of death when 1 type of firearm is used than another. For example, the likelihood of shots to the face being homicide, although true for all gun types, varies in how strong that indication is between rifles (LR = 17.2), shotguns (LR = 10.7), and handguns (LR = 1.5). Variability in the effect size is obviously important for inferences drawn by the pathologist, as, for example, if considering whether a case with a shot to the face is suicide or homicide, that location carries more weight in the overall decision for rifles than it does for handguns where it is marginal. Many studies have not distinguished between firearm types (eg, see Stone,6 de la Grandmaison et al,12 and Thoresen14), and pathologists should be aware of this when considering the conclusions of those studies.
Previous published studies have focused on individual features and have not addressed the need in practice to consider various features in combination. Basing a conclusion on probable manner of death on a single criterion alone may be incorrect, as this study demonstrates. For example, multiple shot wounds may be assumed to be homicide if only that 1 factor is considered. However, suicide may be more likely when considered with other factors. Bayesian analysis allows us to consider several variables in combination and compare outcomes—to produce a net LR for the combination. This may be applied in practice in a case where a person has died, and the pathologist is asked to determine whether it is more likely to be homicide or suicide. The information about the type of firearm used, the range at which the shot was fired, the number of shots sustained by the victim, and the location of the fatal shot can be used to derive a likelihood of homicide or suicide.
The LR can provide a measure of the strength of the conclusion as to manner of death. The closer the LR is to “1” for a particular feature or combinations of features, the less differentiating between homicide and suicide is that feature (or combination of features). In the absence of any other information, if the LR is 1 or very close to 1, the pathologist should consider the manner of death is undetermined.
It will be observed that there is considerable variability in the total data from which the proportions are derived. This is because the included studies reported data differently depending on the purpose of each study. For example, some studies reported only homicides, whereas others reported only suicide, and when reporting wound locations, some studies reported only locations to the head. Many studies had to be excluded from the analysis because of lack of uniformity in reporting data and data being reported in ways that prevented deriving particulars. Pooling data is hindered by the lack of reporting data by many organizations, as well as by the lack of standardization when it is reported. For example, one of the current authors has personally observed homicidal intraoral wound locations for all 3 types of guns, but this is not reflected in the available data. The benefits of standardization of reporting formats warrants consideration, as increasing the data will increase confidence in the accuracy of the findings. Nonetheless, the eligible data produce sizable pooled data sets, which are the current best evidence and allow for strong inferences.
In addition, this study addresses only suicide and homicide as manner of death: there was not sufficient reporting of the accidental deaths in the literature to allow for its inclusion. The present study also analyzes only death from gunshots to the head and chest by type of gun, wound location, and range. There are many other variables that could potentially contribute in a similar way if data are available to derive probabilities, such as other wound locations, pathology findings, crime scene evidence, and psychological factors.
Obviously, every case should be considered in the context of what information is available, and other evidence from the scene of death is important when determining manner of death. However, when a case is ambiguous and other information is inconclusive, the assessment becomes necessarily probabilistic. This study illustrates how a single variable within a case can alter the overall assessment and may lead to a change in the proper conclusion being drawn. In addition, this variable may not necessarily be the feature with the strongest apparent effect (such as range). It is demonstrably important to consider each case with its particular variables as a whole. If data are available to derive probabilities, the factors to be combined in assessment of individual cases could be extended to include other aspects such as trajectory data and psychological evidence. The more factors specific to the cases that are included, the more precise the conclusion would be. The benefits of standardization of reporting formats to support pooling of data warrant consideration.
While every case should still be assessed on an individual basis, the pathologist should consider the variables for that case in the light of research findings. The Bayesian approach can offer us some probabilistic parameters with which to view the case as a whole. To return to the hypothetical pathologist being questioned in court about how certain they are of their opinion: the approach taken in this study will allow them to give an unambiguous and robust scientific answer: “Based on pooled research data, the LR is….”
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