Journal of Substance
Use 6:218-228, 2001
THE SHARE OF VIOLENCE ATTRIBUTABLE TO DRINKING:
What do we need to know and what research is needed?
Ingeborg Rossow, PhD
The relation of alcohol to violence
has long been a subject of controversy. There is no argument that a large
proportion of the perpetrators of crimes had been drinking at the time of the
crime was committed. For example about 40 percent of violent offenders in state
and local jails in the
One source of controversy about the
causal nature of alcohol in violent crime has been the definition of “cause”,
with some researchers requiring that in order to be considered causal, the
presence of alcohol must be necessary and sufficient in order for a violent
crime to occur. Rather than adopting such a stringent position, it seems much
more reasonable to consider the epidemiology of violence in the same way one
would consider the epidemiology of disease. For example, while it is clear that
smoking is an important, if not the most important, causal factor in the
occurrence of lung cancer, not all smokers get cancer and not all cancer
victims are smokers. In the same way, not all violent crimes involve alcohol
and not all people under the influence of alcohol commit violent crimes.
However, ample evidence exists that more drinking tends to result in more
violence and less drinking in less violence.
The role of alcohol in violence is
complex and relates not only to the offender’s drinking but also to that of the
victim as well as others in the social context or the gathering of people in
drinking places. When assessing the share of violence that can be attributed to
alcohol, this complexity is probably better reflected when the relationship
between alcohol and violence is estimated at the aggregate level, preferably
time series analyses. In the end, the policy question behind the attributable
fraction concept is: if a certain fraction of consumption, or of high-risk
drinking occasions, could be taken away, how much would the rates of the
adverse events fall? from this perspective, the most direct measurement of
attributable fraction is from studies at the population level, rather than
studies of individual events. over the past decade several studies on changes
at the population level have demonstrated that an increase in the population’s
alcohol consumption is followed by an increase in rates of violence in that
population.
Estimates of the degree to which
alcohol contributes to violent crime vary from study to study and country to
country. For example, studies of assaults in the
Until recently, the literature on
the relationship between alcohol use and violence has assumed a single relative
risk for a given volume of drinking. This model is based on the assumption that
the relationship between alcohol and violence is similar to the relationship
between alcohol and physical disease, such as cirrhosis of the liver. Recently,
however, it has become apparent that social problems from drinking are more
closely related to pattern of drinking than to the overall volume. That
is, more violence is likely to occur when an individual drinks a large quantity
of alcohol at one time.
The patterns of drinking associated
with different cultures are likely to affect the relationship between overall
drinking levels and violence. It is also clear from the research that people in
different cultures behave very differently when under the influence of an equal
amount of alcohol. Thus the relative risk of violence for a given pattern of
drinking can vary from culture to culture.
Studies of different countries
confirm these different patterns in the influence of drinking on violence. For
example, one study found that the impact of alcohol on homicide was highest in
Further study of the potential
impact of reductions in alcohol use is needed, yet difficulties in studying
this issue exist. Current methods of estimating the share of violence
attributable to alcohol use based on individual level data have two flaws.
First, while it is possible to determine the presence of alcohol in a
violent event and to determine whether participants believe that alcohol
played a role, it is not yet possible to determine objectively whether the
event would have occurred in the absence of alcohol. A second flaw is that we
have not yet found means to measure all the ways in which alcohol may play a
causal role. For example, alcohol consumption by the victim as well as by the
perpetrator has been found to be important. But in addition, alcohol use by bystanders
has been found to play a role. Alcohol may affect a range of interactional and
situational aspects of the violent event, but currently we cannot measure this
role or establish its causal role. Therefore, studies of changes in alcohol
consumption and the relationship with violence can be complicated. For example,
a particular policy change may alter not only the quantity of alcohol consumed
but also the drinking contexts and the cultural expectancies about the effects
of drinking.
It may be useful in examining the
role of alcohol in violence to consider three different classes of violent
situations:
·
domestic
violence involving sexual partners or other family and domestic relationships
in which drinking is often a significant feature of the relationship
Each of these types of violence may
yield to different approaches to prevention.
More aggregate level studies are
needed to track the impact of policy changes. In addition, individual and
event-level studies are needed, including
Given that a significant proportion
of violent incidents can be attributed to alcohol consumption, the question
remains as to the best policy options for reducing alcohol consumption and by
what mechanism will these policy changes achieve a reduction in violence. For
example, while it may seem logical that policies aimed at curbing drinking by
heavy drinkers would have the greatest impact on violence, this may not, in
fact, be the case. Since moderate drinkers greatly out number heavy drinkers,
even changes in drinking among people who are not heavy consumers may result in
a significant reduction in violence. there is support for this application of
the “prevention paradox”, but there is also reason to believe that
alcohol-related violence is most often associated with intoxication and
therefore that reducing incidents of intoxication would be an effective
strategy for preventing violence.
While more study may help further
define the proportion of violent incidents in which alcohol plays a role, too
much attention to exact estimates of the relationship may only divert attention
from the more important issues of how to prevent alcohol-related violence. A
detailed understanding of the various causal pathways and of potential points
of intervention that can be used in preventing violence is needed to make a
difference in the rate of alcohol-related violence.
A number of studies have
demonstrated significant and positive associations between alcohol consumption
and rates of criminal violence (Skog & Bjørk, 1988; Lenke, 1990;
Parker & Rebhun, 1995; Norström,
1998; Parker & Cartmill, 1998). A large proportion of violent offenders had
been drinking before the violence occurred. About 40 percent of such offenders
in state and local jails in the
The causal significance of these
findings, however, is still a matter of dispute. The 19th-century temperance
literature, for instance, states that three-quarters of all crime was due to
drinking (Levine, 1983:136-138). On the other hand, perhaps partly in reaction
against these views, many criminological discussions deny that alcohol has been
shown to cause violence. Thus the
Canadian Supreme Court could cite a number of sources to support its conclusion
that “studies demonstrate that the consumption of alcohol is not the cause of
the crime” (Room, 1996).
The argument is primarily about the
meaning of “causation”. One view, which
rules out alcohol as a causal agent, is that the term “cause” should only be
used with respect to human agency.
Related to this has been the concern, in the context of discussions of
male violence against women, that a formulation like “alcohol causes violence”
is among “many distracting theories of violence which act as obstructions to
social change” by diverting responsibility from the perpetrator (McGregor,
1990).
Another view which rules out alcohol
as a cause of violence is a requirement that the relation be necessary and
sufficient before using the term “cause”.
The criminology literature often tends towards this restrictive view of
causal connections. In this vein, Lipsey
et al. (1997:277-278) review a variety of publications, each of which, they
acknowledge, provide “evidence of an alcohol-violence association which
is consistent with a causal interpretation”, yet shy away from attributing
causation: “the causal issue is still cloudy and uncertain”. From their discussion, it seems clear that
they hanker for a “broad, reliable, ‘main effect’ of alcohol on violence”, and
are reluctant to use causal language in its absence.
At the other end of the spectrum is
public opinion about alcohol and violence, which is nearly unanimous, at least
in
Somewhere between these polar
positions is the stance of the epidemiological literature. Epidemiology hews to
guidelines for attributing cause that require neither a necessary nor a
sufficient relation. This reflects the fact that it is quite typical for many
factors to play a role in an illness or death, and for a particular kind of
illness or death to occur also in the absence of a putatively causal factor. Thus not all cigarette smokers get lung
cancer, and not all patients with lung cancer have been cigarette smokers. In an epidemiological framework, then, causes
are often multiple and indeed conditional, and at a population level the causal
connection is probabilistic rather than all-or-nothing. Sets of guidelines to determine causal
attribution are commonly explicitly stated in epidemiology; one of the most
used was formulated by Bradford Hill (Hill, 1965)[1].
Using an epidemiological frame, we
contend that ample evidence now exists in the empirical literature to regard
alcohol as a cause of violence. This
does not mean that, at the level of particular events, the relationship is
either necessary or sufficient. Usually,
the relationship is conditional: it is drinking in combination with other
factors that is implicated. Nor does the
relationship necessarily operate through a psychopharmacological action in a
perpetrators brain. For one thing, drinking
by the victim is often a crucial factor, and this factor is often involved in
the causal chain. More generally, the relationship may operate through drinking
as a cultural and circumstantial practice, that is, through the understandings
and behaviors that are part of the drinking occasion. At a population level, however -- the level
that matters for epidemiology and public health -- we can say with some
confidence that more drinking tends to result in more violence, and less
drinking in less violence (Room, 1983).
Though the strength of this relationship varies in different cultural
contexts, new evidence at the aggregate level indicates a relationship across a
broad range of cultural contexts (Rossow, 2001).
In the epidemiological literature,
the potential impact of a risk factor for some disease (or other outcome
measure) is defined as the “proportion of all new cases in a given period that
are attributable to the risk factor of interest” (Kleinbaum et al., 1982). This
is often termed the “attributable fraction” (Ouellet et al, 1979)[2].
“Attributable”, in this formulation, is “the difference between all new
cases in a period and the number of new cases that would have occurred in the
absence of the exposure” (Kleinbaum et al., 1982). This is a meaningful concept from a policy
point of view, because it implies the potential to prevent the occurrence of
new cases by eliminating the particular risk factor. This is also in line with
Pernanen's (1995) suggestion that the causal role of alcohol in violence
is more fruitfully approached when applying a more inclusive term that “coincides
with the idea of 'had it not been for alcohol'”, rather than a “single-minded
focus on hard-science direct causal connections.”
The attributable fraction (AF) can be calculated on the basis of two estimates derived from analyses of empirical data: an estimate of the association between the exposure (alcohol) and the outcome (violence), and an estimate of the magnitude of the exposure (alcohol). This calculation can be done either on individual level data[3] or on aggregate level data[4]. The primary problem in applying these formulae lies in the question of how to measure the association only where the drinking is causally significant. Arriving at “sound” estimates of the association between alcohol consumption and violent behavior is hampered by various kinds of methodological problems.
Studies based
on individual-level data have generally suggested that a substantial proportion
of violence is somehow related to alcohol consumption (e.g. Roizen, 1981). But
although many studies have found that a high proportion of violent offenders
were under the influence of alcohol at the time of the violent crime, it may
well be argued that many of these violent crimes might have taken place even if
alcohol were not a part of the event. To the extent this is true, the
proportion of violent incidents where alcohol was somehow involved is larger
than the proportion of incidents that could be attributed to alcohol use. This
has been demonstrated, for instance, by Norström (1998), who found that some
75-80 percent of those committing criminal assaults in
An alternative to individual-level studies as a strategy for assessing attributable fractions is to apply time series analyses of aggregate-level data. A number of such studies of alcohol and violence have been carried out over the past decade or so (e.g. Skog & Bjørk, 1988; Lenke, 1990; Norström, 1993; Parker and Rebhun, 1995; Norström, 1998; Parker and Cartmill 1998; Rossow, 2001). These studies have generally demonstrated that an increase in the populations drinking level (or an indicator of this) is followed by an increase in rates of violence in that population. The findings are interpreted as a reflection of two underlying mechanisms: an increase in total consumption implies an increase in the proportion of people who are drinking heavily and in that state are more prone to behave aggressively or violently; and an increase in total consumption also implies an increase in the number of drinking occasions that lead to acute intoxication, which may trigger violent behavior among otherwise moderate consumers. Particularly when the analyses are based on differenced time series, the effect estimate reflects the impact of a change in alcohol consumption on the change in rates of criminal violence. It is assumed that a spurious correlation due to various individual or social environment characteristics would not be not reflected in annual changes at the aggregate level (Lenke, 1990; Norström, 1998). Thus, the estimated effect or association based on such analyses can be taken to indicate the causal impact of alcohol consumption on violence. Causality in this respect would also include what Pernanen (1995) refers to as second order causality, for instance the impact of alcohol on violence that is generated through alcohol's role as a 'social attractor' (the gathering of people in specific places) or as a 'courage enhancer'. We should, however, also keep in mind that there is often a problem of Type II error (missing a relationship that is really there) and of huge confidence intervals around the point estimates from time series analyses on differenced data, due to measurement problems or insufficient length of the data series. Moreover, the estimate of an attributable fraction is also based on extrapolation from the empirical data. Thus, the estimates of association, as well as the attributable fractions, from these kinds of analyses should be interpreted with some caution.
Spatial correlations or cross-sectional aggregate level analyses have also been applied in a number of studies on alcohol and violence (e.g. Lester, 1995; Parker & Rebhun, 1995; Stevenson et al, 1999). Such analyses generally test for the finding that the higher the alcohol consumption, the higher the violence rate across geographical areas. But, as rates of violence most probably result from a complex of factors, control of all relevant confounders is difficult, and hence the results offer much weaker evidence concerning the existence and strength of a causal relationship.
With many multifactorial phenomena it can be argued that the impact of a specific risk factor depends on other (risk) factors. As we have indicated, this is also the case with alcohol and violence (Skog & Bjørk, 1988; Lenke, 1990). Both experimental studies and observational studies indicate that the impact of alcohol in aggressive or violent behavior depends on the presence of other factors which may trigger or facilitate violence (see Lenke, 1990; Graham et al, 1996 for reviews). This implies that cases of violence may not be attributed to one single risk factor, but often to the co-occurrence of several risk factors. In turn, this means that summing up the attributable fractions for various risk factors would yield more than 100 percent (Rothman, 1986, p.14). However, this may not gainsay that alcohol makes a substantial contribution, and one that is potentially preventable. The issue around multiple causation, attributable fractions, and the implications for potential to prevent new cases has been discussed by O'Carroll (1993) in relation to suicide. He argues that even though a very large proportion of cases can be attributed to one or two single factors, this does not mean that little potential exists to prevent new cases by strategies directed towards other risk factors, as these other factors may also contribute significantly and thus be subject to preventive strategies. His arguments are just as relevant with respect to violence.
Individual level data:
In a few
review studies over the past decade, some estimates have been given on the
proportion of violent assaults that are attributable to alcohol consumption. In
their review of
Concluding a
literature search for material relevant to estimating attributable fractions
for alcohol and other drugs in relation to crimes in
Aggregate level data:
Based on time
series analyses of aggregate level data, Lenke estimated that a little more
than half of the assaults in
Large
confidence intervals surround these estimates; and hence apparent similarities
as well as differences should not be given too much weight until they are
further validated. However, there is no doubt that the impact of alcohol
consumption on rates of violence is substantial, and that incidents of violence
can be prevented by significant reduction in the overall intake of alcohol
and/or heavy drinking episodes. Corroborating evidence comes from data from
sudden and large changes in alcohol consumption (“natural experiments”). Von Hofer and Tham (1989) observed that when
Swedish alcohol consumption fell dramatically from about 6 to 1 liter per
capita during World War I (due to rationing), assault rates fell from 70 to 40
per 100 000 inhabitants, and they found no other explanation than the huge
decrease in alcohol sales (cited in Lenke, 1990). Such evidence is much in line with Lenke’s
estimate that around half of assaults in
Despite all these studies, a more systematic description of associations between alcohol consumption and violence is still needed from both individual level and aggregate level data and from various countries and drinking cultures. Parker and Rebhun’s analysis (1995), using a combination of time-series with cross-sectional data, and Parker and Cartmill’s (1998) study of beverage specific effects on homicide rates are among the very few studies using time-series methods on population-level data in North America.
Until now, the literature on attributable fraction for alcohol has usually implicitly assumed that there will be, in principle, a single relative risk applicable everywhere for a given volume of drinking. The attributable fraction would then vary in different populations only according to the proportion of the population at each level of volume of drinking (as in the approach taken by English et al., 1995). This algorithm has been modeled on the assumptions about the relation between volume of drinking and such chronic diseases as cirrhosis of the liver. Recently, however, it has become apparent that casualties and social problems from drinking are often more closely related to the pattern of drinking -- particularly whether large amounts are drunk on an occasion -- than to the volume of drinking (e.g., Room et al., 1995; Midanik et al, 1996). Alcohol epidemiologists have thus called for substantial attention to patterns of drinking, as well as the overall volume, in future epidemiological studies (Rehm, 1998). The influence of pattern of drinking on the link with many social and health problems means that the attributable risk may vary between two societies or groups with the same level of volume of drinking, if their patterns of drinking vary.
Beyond this, with respect to violence in particular, it is clear from the ethnographic record (MacAndrew and Edgerton, 1969) that people in different cultures behave very differently when under the influence of an equal amount of alcohol. What MacAndrew and Edgerton call “changes-for-the-worse” in behavior after drinking, including violent behavior, is thus influenced not only by individual and situational factors, but also by specific cultural expectations and patterns. This implies that the relative risk of violence for a given pattern of drinking (and thus also the attributable fraction) may vary from one culture to another.
While the literature offers some typologies of the cultural position of drinking and some hypotheses about the relation of rates of violence to them (Room and Mäkelä, 2000), empirical work on testing and refining such hypotheses is still at its beginning.
Lenke's
comparative analyses of alcohol sales and assaults in four Nordic countries and
in
A variety of
studies in the
From the
European analyses, it seems that a stronger impact of alcohol on violent crimes
is found in drinking cultures where acute intoxication to a larger extent
characterizes the drinking pattern. It is worth noting that parallel
cross-cultural variations can be found with respect to the alcohol and suicide
association. Again based on time series analyses, a generally stronger
association between alcohol consumption and suicide rates has been found in the
more explosive drinking cultures in
Challenges for the future
Attributable fraction is in the end a population-level concept. It asks what proportion of cause of death or other adverse condition is attributable to a particular risk factor, regardless of whether or not the factor can be causally implicated in particular deaths or adverse events. In the end, the policy question behind the attributable fraction concept is: if a certain fraction of consumption, or of high-risk drinking occasions, could be taken away, how much would the rates of the adverse events fall? From this perspective, the most direct measurement of attributable fraction is from studies at the population level, rather than studies of individual events.
In estimating attributable fraction, studies at the level of individual events have two major flaws.
Studies of change over time in a given polity have the potential to overcome these flaws of individual-level studies. The causal attribution is based on a direct measurement of how much the dependent variable changes when the alcohol variable changes. Obviously, interpreting this covariation as causal depends on all else being equal. The different aggregate-level studies have different ways of controlling for other factors. One major control, used by the strongest studies, is to look at variation over time in a single polity. This automatically controls many of the particular cultural and socioeconomic features which might otherwise enter into the explanation. ARIMA-type analyses typically use differenced data to control out long-term trends. Studies of particular events in the alcohol market -- for instance, liquor store strike studies -- are often able to use a control period in the same population in another year.
Nevertheless, estimates from aggregate-level studies have their own drawbacks. Cross-sectional aggregate analyses are particularly vulnerable to influence by unmeasured variables, and in our view are of little value for estimating attributable fractions. But the studies of change over time have problems, too, even if they are less serious. As we have already mentioned, the small numbers of data points in many ARIMA analyses make the confidence intervals large, and the conservative procedures used also raise the possibility of important relationships remaining statistically insignificant. It should also be kept in mind that the cause of the change that is registered in the studies may be a broad penumbra of effects related to whichever particular alcohol variable is measured (often, the per-capita consumption). The attributable fraction measured by these aggregate studies is not the fraction attributable to ethanol as a psychoactive substance, but rather to amounts and practices and the social interactions that are attached to drinking. The attributable fraction thus tells us something about the size of the problem, but does not dictate the policies which might counteract it. Besides changing the overall amount of drinking, policy options may include, for instance, changes in drinking contexts, or in cultural expectancies about behavior while drinking.
As we have
mentioned, some North American studies show at the aggregate level the effects
of changes in drinking, but this tradition of studies has been much more
strongly developed in the Nordic countries.
While the Nordic countries have particularly rich data for such
analyses, much can be done with the data available in any developed society, as
the current European Comparative Alcohol Study is showing (Rossow, 2001). Future applications in
The patterns
of change in the aggregate-level analyses can also contribute hints about the
social processes involved, and thus about potential targets and entry-points
for efforts at social change. The
dramatic fall in homicides in the Gorbachev era in
The policy implications
Given that a significant proportion of violent incidents seem to be attributable to alcohol consumption, a question for policy is whether preventive strategies should be aimed at particular high-risk individuals or the whole population -- i.e., should the focus be on what are generally termed high-risk strategies or on population strategies? This will basically depend on what the risk curve between alcohol exposure and violent behavior looks like, but given a (more or less) straight linear risk function, it can be assumed that those with a moderate volume of consumption are responsible for the majority of the violent incidents that are due to alcohol (see Skog, 1999 for details). This is often referred to as the prevention paradox (Rose, 1981; Kreitman, 1986; Skog, 1999). Doubts have been raised with regard to whether the prevention paradox is valid for various acute alcohol problems (Stockwell et al, 1996). However, several individual level studies have indicated that there seems to be a (more or less) linear relationship between alcohol consumption and violent behavior, implying that the prevention paradox may be valid for violent behavior (e.g. Room et al., 1995; Rossow, 1996a; Rossow et al., 1999). One might therefore argue that a prevention strategy aimed at all consumers (population strategy) would yield a larger reduction in violent incidents than a prevention strategy aimed only at high-risk individuals (high-risk strategy). Norström (1995) argued that the advantage of a population strategy is most marked in connection with accidents and suicide (which probably have a risk function more like that for violence than like that for cirrhosis). But even a high-risk strategy, he felt, would yield a significant impact on accidents and suicide as well. Since alcohol-related violence is associated particularly with intoxication, preventive strategies might be aimed not only at reducing overall consumption but also at preventing drinking events becoming occasions of intoxication (Grover, 1999). However, a need still exists for more studies evaluating the outcome of such strategies.
In studying patterns of connection between alcohol and violence, an important step is to differentiate between different kinds of violence, since the patterns of linkages between the violence and the drinking may well differ for different types of violence. A rough differentiation which may prove useful is between three classes of violent situations:
We have already marked on the need
for further aggregate-level studies, and in particular for the tradition of
differenced time-series studies on aggregate data to be used more extensively
on North American data -- for instance on
We are thus still a considerable distance from being able to assign relative risks and attributable fractions for alcohol’s role in violence in a given society, on the basis of a well-developed epidemiological literatures for a range of types of societies. It is worth keeping in mind, however, that the search for defensible attributable risks applicable cross-culturally is not the end of our journey, and too much fetishistic attention to this search may divert us from more important paths. In the end, the exact size of an attributable risk is primarily of importance to politics rather than to policy or public health programming. A large attributable risk may serve to draw political attention to a factor otherwise neglected -- what is sometimes called the gee whiz factor. The ability to compare attributable risks for different factors which are computed according to common principles may have some importance in priority setting in the policy process. Conceivably, doing this might be used to elicit support for general policy measures – for instance, alcohol rationing or higher alcohol taxes – for which there is evidence of effects on alcohol-related violence, but which are at present politically unpopular or inconceivable. in an era where political realities favor strategies that prevent the violence without substantially interfering with the drinking (Room, 2000) a detailed understanding of the various causal pathways, and of the potential points of intervention in them, is needed to make a difference in the rate of alcohol-related violence.
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Table 1. Parameter estimates of the association between alcohol consumption and indicators of violence from time series analyses (ARIMA) in various countries or areas.
|
Country/area |
Violence indicator |
Parameter estimate |
Skog & Bjørk, 1988 |
Norway 1930-1982 |
Assault rates |
.18 (.05) |
Lenke, 1990 |
|
Assault rates |
.02 (.007) |
Lenke, 1990 |
|
Assault rates |
.06 (.03) |
Lenke, 1990 |
|
Homicide rates |
.11 (.055) |
Norström, 1998 |
|
Assault rates |
53.76 (25.15) |
Norström, 1998 |
|
Homicide rates |
0.14 (0.06) |
Rossow, 2001 |
|
Homicide rates |
.124 (.038) |
Rossow, 2001 |
|
Homicide rates |
.085 (.023) |
Rossow, 2001 |
|
Homicide rates |
.055 (.017) |
Note: The estimates in the studies by Skog & Bjørk (1988), Lenke (1990) and Rossow (forthcoming) are based on semi-logarithmic models, which means that the parameter estimate indicates a relative (i.e. percentage) change in the dependent variable with a one unit (1 liter pure alcohol per inhabitant > 15 yrs) change in the independent variable, whereas Norströms study is based on linear models, which means that the parameter estimate indicates the absolute change in the dependent variable. Moreover, the estimates in Rossows study are based on pooling of estimates across several countries (i.e. North Europe comprises Finland, Sweden and Norway; Central Europe comprises Austria, BRD, Denmark, Netherlands, Belgium, UK and Ireland; and South Europe comprises Italy, France, Spain and Portugal).
End notes:
[1]. Hill
criteria for causal inference from associations: 1) strength, 2) consistency,
3) specificity,
4)
temporality, 5) biologic gradient, 6) plausibility, 7) coherence, 8)
experimental evidence, 9) analogy.
[2]. The terms
used by various authors have differed.
Other terms used have included: “attributable risk” (Levin, 1953);
“population attributable risk percent” (Cole & MacMahon, 1971); “etiologic
fraction” (Miettinen, 1974), and “attributable proportion” (Rothman, 1986).
[3]. (1) AF= q(RR-1)
q (RR-1) + 1
where q is the proportion of the population exposed to the risk factor and RR is the relative risk (Lilienfeld & Lilienfeld, 1980).
[4]. (2) AF= bX
Y
where b is the (unstandardized) regression coefficient, X is the risk factor, and Y is the outcome measure, when a straight linear model is specified, or
(3) AF= 1 B e -bX, when a semi-logarithmic model is specified (Norström, 1989).
[5]. Lenke
(1990) applied the term alcohol-related for violent crimes that “probably not would have been committed
without the presence of alcohol” in contrast to the term “alcohol involvement”
implying that one or more of the persons involved had been drinking prior to
the crime.