Content uploaded by James Nolan
Author content
All content in this area was uploaded by James Nolan on Apr 26, 2016
Content may be subject to copyright.
NOTICE WARNING CONCERNING COPYRIGHT RESTRICTIONS
The copyright law of the United States [Title 17, United States
Code] governs the making of photocopies or other reproductions of
copyrighted material. Under certain conditions specified in the
law, libraries and archives are authorized to furnish a photocopy or
other reproduction. One of these specified conditions is that the
reproduction is not to be used for any purpose other than private
study, scholarship, or research. If a user makes a request for, or
later uses, a photocopy or reproduction for purposes in excess of
"fair use," that use may be liable for copyright infringement. This
institution reserves the right to refuse to accept a copying order if,
in its judgement, fullfillment of the order would involve violation
of copyright law. No further reproduction and distribution of this
copy is permitted by transmission or any other means.
Article
Lifetime Likelihood
Computations With
NIBRS
Yoshio Akiyama
1
, James J. Nolan
2
, Karen G. Weiss
2
,
and Stacia Gilliard-Matthews
3
Abstract
This article explores the conditions and assumptions under which it is possible to use
National Incident-Based Reporting System (NIBRS) in lifetime crime computations,
particularly for nonfatal violent crimes. We describe methods for using NIBRS to
study lifetime risk for a variety of crimes and show how researchers and policy makers
can apply these methods using readily available software such as Microsoft Excel.
Finally, we demonstrate in two different studies how NIBRS can be used to estimate
lifetime risk at the state and national levels. In doing so, we introduce the concept of
the ‘‘average person’’ in each age–sex–race grouping to calculate the risk of victimi-
zation for this hypothetical person only.
Keywords
UCR, NIBRS, Lifetime Likelihood
Introduction
Lifetime risk estimations are important tools in the field of public health. They provide
assessments of risk at various points along the life course based on age, race, and sex
for particular diseases such as cancer, schizophrenia, and heart disease, among many
others. Lifetime risk computations help policy makers better understand the nature
1
Retired from teaching and government service
2
West Virginia University, Morgantown, WV, USA
3
Rutgers University, Camden, NJ, USA
Corresponding Author:
James J. Nolan, West Virginia University, Morgantown, WV, USA.
Email: jim.nolan@mail.wvu.edu
Justice Research and Policy
2015, Vol. 16(2) 129-146
ªThe Author(s) 2016
Reprints and permission:
sagepub.com/journalsPermissions.nav
DOI: 10.1177/1525107115623505
jrx.sagepub.com
and extent of diseases and how best to respond to them. They also provide ways to
quantify the success or failures of public policy aimed at reducing risk for everyone
in a population or for subgroups in the population which experience risk dispropor-
tionate to their representation. Groups like the National Cancer Institute (NCI) regu-
larly publish reports that reflect disparity in risk for diseases across age, race, and sex
groupings. For example, a recent NCI report indicates that although African Ameri-
cans are 6%less likely than White Americans to develop cancer over their lifetime,
they are more likely than Whites to develop stomach and prostate cancer by 39%and
38%, respectively (Howlader et al., 2014). Clearly, this is important information for
public policy makers whose goal is to help reduce this risk.
Crime victimization is another form of health risk that affects the population differ-
ently, especially by age, sex, and race. But the limitations of the existing national crime
data often prevent this type of analysis. Lifetime likelihood computations are possible via
the National Crime Victimization Survey (NCVS), the Summary Uniform Crime Report-
ing (UCR) Program,
1
and the National Incident-Based Reporting System (NIBRS) but
with qualificationsand specific limitations. The NCVS lifetime likelihood computations
are only national in scope and do not include children under 12 or victims of murder. Sum-
mary UCR data can be used to compute the likelihood of murder victimization over a life-
time for all ages and age groupings. But thisis not possible for any other UCR index crime
category because information about the age, sex, and race of the victim is not captured.
Since NIBRS does collect age, sex, and race data from the victims of violent crime, it
is now possible to compute the lifetime risk of violent crime victimization. Using the
methods we describe in this article, estimates of risk can be made frombirth to a specific
age, such as 18 or 25 or for any other age over a lifetime. Risk estimates can also be estab-
lished from a specific age, say 45, through the rest of a person’s life.
The purpose of this article is to explore the conditions and assumptions under
which it is possible to use NIBRS in lifetime crime computations, particularly for non-
fatal violent crimes such as intimate partner violence and aggravated assault. Just as
assessing risk is an important tool for health research, understanding lifetime risk is
relevant to crime research and policy.
In the pages that follow, we briefly outline findings from the few lifetime risk stud-
ies conducted using NCVS and summary UCR data. We then describe methods for
using NIBRS to study lifetime risk for a variety of crimes and also show how research-
ers and policy makers can apply these methods using readily available software such
as Microsoft Excel. Finally, we demonstrate in two different studies how NIBRS can
be used to estimate lifetime risk at the state and national levels. In doing so, we intro-
duce the concept of the ‘‘average person’’ in each age–sex–race grouping to calculate
the risk of victimization for this hypothetical person.
Lifetime Risk Estimates With National Crime
Victimization Data
In 1987, the Bureau of Justice Statistics (BJS) published Lifetime Likelihood of Victi-
mization which reported estimates of the likelihood of victimization in the United
130 Justice Research and Policy 16(2)
States over a lifetime. The study was based on data from the National Crime Survey
(NCS)
2
and the National Center for Health Statistics between 1975 and 1984 (Koppel,
1987). In this report, the probability that a person would be the victim of a crime at a
particular age was based on rates of survival and victimization for specific age, sex,
and race categories. Table 1 depicts the lifetime likelihood of violent crime victimiza-
tion by race and sex based on NCS victimization rates from 1975 to 1984.
3
The report
predicted that the vast majority of citizens (i.e., five of six) would become victims of
violent crime in their lifetime. According to the data, Black men have the highest risk
of victimization over their lifetime (92%). In addition, Table 1 presents the total risk of
violent crime victimization to a more fine-grained risk estimate, that is, one, two, or
three or more violent crime victimizations by race and sex.
Using data from the same study, Table 2 presents the risk of violent crime victimi-
zation starting at various ages and continuing over a lifetime. For example, from age
12 through 70, people in the United States have an 83%chance of being the victim of a
violent crime. As the table indicates, the risk drops off as people age. By the time indi-
viduals in the United States reach the age of 50, their risk drops to 22%for the rest of
their lives (assuming they live to the average age). If they live to 60, the risk for the
remainder of a normal life drops to 14%.
Some researchers have been critical of the methodology used in the BJS report,
stating that the estimates are ‘‘implausibly high’’ due to the inclusion of repeat victi-
mization for nonfatal violent crimes and property crimes (Lynch, 1989, p. 263). Lynch
argues that the NCS was not designed with lifetime computations in mind and that
only a longitudinal survey of persons could allow for accurate lifetime victimization
estimates. The NCS study was also challenged on its basic assumptions that victimi-
zation rates remain constant from year to year and that the risk of victimization is
equally likely for all members of the age, race, and sex groupings. The author of the
Table 1. Lifetime Likelihood of Violent Crime Victimization (Based on NCS Victimization
Rates From 1975 to 1984).
a,b
One or More
Victimizations
One
Victimization
Two
Victimizations
Three or more
Victimizations
Total population 83% 30% 27% 25%
Male 89 24 27 38
Female 73 35 23 14
White 82% 31% 26% 24%
Male 88 25 27 37
Female 71 36 22 13
Black 87% 26% 27% 34%
Male 92 21 26 45
Female 81 31 26 24
Note. Adapted from BJS Technical Report (Herbert Koppel, 1987). NCS ¼National Crime Survey.
a
In this table, violent crime was defined as rape, robbery, and assault.
b
Victimization rates for the crime of
rape were calculated based on NCS victimization rates from 1973 to 1982.
Akiyama et al. 131
BJS study (Koppel, 1987) acknowledges these limitations in the publication. In addi-
tion, the NCS (now NCVS) is limited in other ways too; for example, it does not
include children under the age of 12, highly mobile populations, and incarcerated
people (Addington, 2008).
Lifetime Victimization Studies With UCR
In recent years, the FBI conducted two studies of the two lifetime risk of murder vic-
timization one conducted in 1978 and the other in 1997 (Federal Bureau of Investiga-
tion [FBI], 1999). Using homicide data from the FBI’s Supplemental Homicide
Reports, population data from the U.S. Bureau of Census, and survival data from the
National Center for Health Statistics, the FBI researchers calculated homicide rates by
age, sex, and race. When the number of survivors
4
in a particular age category was
divided by the total number of murders for each age category, the resulting number
was the reciprocal odds ratio for victimization likelihood. For example, based on the
number of murders reported in 1978, individuals born alive that year would have a 1 in
157 chance of being the victim of a homicide over their lifetime. Based on the number
of homicides in 1997, the lifetime chance for homicide victimization starting at age 0
was 1 in 240 (see Table 3).
In both of these studies, the researchers applied a single year’s murder rate into a
lifetime frame. As shown in Table 3, the lifetime risk of homicide victimization chan-
ged dramatically from 1978 to 1997 which exposes the limitations of using a single
year experience for making lifetime projections. For example, a person born in
1978, whose lifetime risk was assessed according to the 1978 experience, turned 19
years of age in 1997. Because conditions were different in 1997, his or her chances
of homicide around age 20 changed from 1 in 172 to 1 in 291, a 41%lower risk than
originally estimated. Notwithstanding this limitation, lifetime risk computations for
the crime of murder can be useful in conveying what a single year experience will
mean over a lifetime if conditions remain the same. This is true in public health studies
Table 2. Lifetime Likelihood of Violent Crime Victimization From Current Age to Rest of Life.
Current Age
(Years)
One or More
Victimizations, %
One
Victimization, %
Two
Victimizations, %
Three or More
Victimizations, %
12 83 30 27 25
20 72 36 23 14
30 53 35 13 4
40 36 29 6 1
50 22 19 2 —
60 14 13 1 —
70 8 7 —
a
—
Note. Adapted from BJS Technical Report (Herbert Koppel, 1987).
a
‘‘—’’ indicates less than .5%.
132 Justice Research and Policy 16(2)
too. As conditions affecting health problems such as heart disease change, so do the
estimates of risk over the lifetime.
Lifetime Computations Using the NIBRS
Where the summary UCR program enables researchers to examine lifetime risk for
only the crime of homicide, NIBRS provides data to make estimates for a variety
of nonfatal violent crimes in a variety of contexts at both national and subnational lev-
els. NIBRS provides an opportunity to extend the lifetime risk of violent crime victi-
mization in the United States as a whole, or in smaller jurisdictions such as cities and
states, beyond homicides to include nonfatal violent crimes such as aggravated
assault.
5
Similar to the analytical methods used in the BJS and UCR studies mentioned
above, our computations using NIBRS consider how the crime/victimization rate in a
given period of time (i.e., 1 year) translates into a lifetime frame. Of course, we under-
stand that NIBRS data are generated by police reports which are notoriously under-
counted. Therefore, our model is limited to estimating the risk of being a victim of
a crime that gets reported to and recorded by the police. Unlike the BJS study, we
do not assume that all individuals in a particular age–sex–race group share the same
risk, which of course they do not. Clearly, there are those individuals whose routine
activities put them at higher (or lower) risk than others. Therefore, we introduce the
concept of the average person in each age–sex–race grouping and calculate the risk
of victimization for this hypothetical person only.
Poisson Distributions and the Average Person
In order to use NIBRS for lifetime victimization computations, we introduce the con-
cept of the average person.
6
We must do this because we cannot determine the number
of people who were repeat victims and, therefore, we cannot treat the crime rate (No.
of victimizations/population) as the probability of victimization. The average per-
son—as we describe in this article—is a hypothetical person whose risk of victimiza-
tion is determined by the per person crime rate. By identifying this statistically
Table 3. Lifetime Risk for Murder Victimization in 1978 and 1997.
Age to Rest of Life 1978 1997
0 157 240
10 160 250
20 172 291
30 242 487
40 365 786
50 602 1,287
60 1,021 2,033
Note. Adapted from FBI, Crime in the United States, 1999.
Akiyama et al. 133
average person, we are able to compute his or her risk of violent crime victimization
over a lifetime using methods described below.
Our model assumes that the number of violent crime victimizations for an individ-
ual person is Poisson distributed with a parameter greater than 0. The average person
at age a(again, a hypothetical person) has a Poisson parameter, l, which is equal to
the per person crime rate for that particular age. Since the violent crime rate is an aver-
aged number, an average person is a ‘‘standardized’’ or ‘‘averaged’’ existence. The
number of violent crime victimizations for an average person at age ahas a Poisson
density function given by
fðxÞ¼ellx
x!;ð1Þ
where x¼the number of victimizations (e.g., 0, 1, 2, 3) and l¼R(a) (the per person
crime rate at age a).
Since Poisson is a single parameter distribution, the mean and the variance are the
same and equal to R(a). This implies that the per person crime rate R(a) is a measure of
the annually expected number of victimizations for the average person at age a. This
crime rate is not a measure of the probability of victimization, although it is often mis-
interpreted as such. Instead, the probability of violent crime victimization is 1—prob-
ability that x¼0or1f(0). From Equation 1, we can compute the probability of 0
victimizations as f(0) ¼e
l
and the probability of one or more victimizations as 1
f(0) ¼1e
l
. Moreover, the probability that a person will be victimized 1 or more
times is smaller than the crime rate due to the fact that some citizens are victimized
more than once and counted as separate victims for each reported incident (l¼
R(a)>1e
l
).
The Independence Assumption
The model assumes that the annual Poisson victimization variables for an individual
are independent. In other words, if the average person lives to age a, he or she is cumu-
latively exposed to the Poisson victimization process with the parameter:
TðaÞ¼RðaÞþRðaþ1ÞþRðaþ2ÞþRðaþ3Þþ ... þRðaþ98Þ:ð2Þ
Equation 2 is based on the following theorem: Poisson distribution is ‘‘reproduc-
tive,’’ that is, the sum of kindependent Poisson distributions is a Poisson distribution
with its parameter being equal to the sum of kparameters (Stuart & Ord, 1987). There-
fore, under the independence assumption, if the average person lives to age a, then the
probability of his or her facing violent crime victimization xtimes is described by the
Poisson density function with the parameter l¼T(a).
This computational method for estimating the lifetime risk of violent crime victimi-
zation can be interpreted from two main perspectives: (1) from age athrough the rest of
life (see Figure 1) and (2) from birth to age a(see Figures 2 and 3). Lifetime computa-
tions provides an estimate of the total amount of risk an average person would have if he
or she lives an average lifetime. For example, if you select a certain age, say 30, our
134 Justice Research and Policy 16(2)
estimates will show how much risk this person has remaining in his or her life (the first
perspective) and how much he or she has already endured (the second perspective).
Calculating Lifetime Risk With Microsoft Excel
In this section, we demonstrate how to use readily available, off-the-shelf software
like Microsoft Excel to compute lifetime violent crime risk with NIBRS. We provide
this section to help researchers and policy makers replicate these methods.
Figure 4 is a screenshot of a Microsoft Excel spreadsheet intended to show how to
calculate lifetime risk estimates with NIBRS. In this example, we show how to calcu-
late age-specific risk estimates and an age-group risk estimate using Equations 1 and 2
described above. Due to space limitations, we show only columns A through O and
rows 1 through 19. In column A, we list all possible ages from 0 to 98 (stopping at
age 17 in this example). In column B, we list the total number of people in the pop-
ulation for each age. The population data were obtained from the U.S. Bureau of Cen-
sus. In column C, we list the total number of victims in each age-group for a given year
and calculate the age-specific victimization rate in column D. The victimization data
in this example come from the 2011 West Virginia NIBRS. Column E is calculated
according to Equation 2. Columns F through I are the probabilities of 0, 1, 2, and 3
victimizations for the average person at each age. They are calculated according to
Equation 1.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1 5 9 131721252933374145495357616569737781
Black Females
White Females
Figure 1. Lifetime risk of violent crime victimization for the Average female by race where the
offender is an intimate partner (presented as risk from age athrough the rest of life).
Akiyama et al. 135
Similarly, columns L through O are the computed probabilities of 0, 1, 2, and 3 vic-
timizations for the average persons in each age grouping in column J. Column K is the
Poisson parameter for the average person in the 0–17 age-group and is computed via
Equation 2.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81
Black female
White female
Figure 2. Lifetime risk of violent crime victimization for the Average female by race where the
offender is an intimate partner (presented as risk from birth to age a).
0
0.1
0.2
0.3
0.4
0.5
0.6
1 5 9 131721252933374145495357616569737781
White males
White females
Black females
Black males
Figure 3. The ‘‘average person’s’’ risk of aggravated assault victimization over a lifetime by age,
sex, and race (presented as risk from birth to age a).
136 Justice Research and Policy 16(2)
Figure 4. Lifetime Computations Using Microsoft Excel.
137
Two Studies as Examples: Computing State and National
Victimization Estimates
In this section, we present two studies of crime victimization applying our lifetime risk
computations with NIBRS data. The purpose of these studies is to demonstrate how
lifetime computations can be made and interpreted at the state level and at the national
level. The first study is from the state of West Virginia and focuses on nonfatal inti-
mate partner violence. We picked this state because all law enforcement agencies in
West Virginia report crime data in NIBRS format and Intimate Partner Violence (IPV)
is a serious problem in this state. This situation is optimal because there is no need to
add ‘‘weights’’ to account for populations not covered by NIBRS reporting agencies.
The second study is intended to demonstrate how to compute lifetime risk estimates
when only a part of the data comes from NIBRS. We use the national NIBRS data
from the FBI along with national estimates of crime volume provided by summary
UCR to make and interpret these computations.
In both studies presented below, all calculations are made for the average person in
each age, sex, and race group. In presenting our findings, statements such as ‘‘
...Black males are the most at-risk group’’ are sometimes made. This may be mis-
leading since we are not really talking about ‘‘Black males’’ per se but are referring
to the average Black male and the crimes that are reported to and recorded by the
police. It is true, however, that the average person in each group indirectly reflects the
group’s risk, since the group with the most at-risk average person is also the group
with the highest risk overall.
Study 1: Computing State Estimates of Intimate Partner Violent
Crime Victimization
In this first lifetime risk study, using NIBRS, we apply the methods described above to
a full NIBRS reporting state, West Virginia, to demonstrate how these estimates can
be computed and interpreted. We did this both to demonstrate the flexibility of NIBRS
for computing lifetime risk for a variety of crime types and to focus on a crime of
interest in a state that is known to have a high rate of domestic crime. The computa-
tions were made using Microsoft Excel as described in Figure 4.
Data and method. We obtained a single year (2011) of NIBRS violent crime data from
the state UCR program in West Virginia. The data include female victims and include
the following offenses: forcible rape,
7
forcible sodomy, sexual assault with an object,
forcible fondling, aggravated assault, simple assault, and intimidation. We selected
only female victims for this study, who were assaulted by an intimate partner. There
were 5,420 White female victims and 468 Black female victims included in this study.
The per person rates for intimate partner violence at each age in each of these groups
were calculated using U.S. Census population estimates for 2011. Although NIBRS
allows for the reporting of victim ages up to 98, we included calculations only to age
80. The impact of lifetime computations of violent crime victimization on ages above
138 Justice Research and Policy 16(2)
80 are negligible since victimization rates above the age of 80 approximate 0. It is
important to remember that only crimes that are reported to and recorded by the police
make it into the NIBRS data. This is clearly a limitation of using NIBRS for lifetime
risk computations, suggesting that the estimates may actually be higher especially for
crimes such as rape and other sexual assaults.
Findings. In Figure 1, we depict the lifetime risk of violent crime victimization for the
average Black and White females where the offender was a boyfriend, husband, or
same-sex partner. The way to read the figure is from age ato the rest of the person’s
life. For example, at birth, the average Black female has a 69%chance of being the
victim of one of the violent crimes listed above during her lifetime. In contrast, the
average White female has a 40%chance of victimization over her lifetime—that
is, a 42%lower risk than the average newborn Black female. Although the risk drops
for both groups each decade as they advance in age, a similar disparity exists though
the 20s, 30s, and 40s and up to the 50s. From age 20 through the rest of her life, the
average Black female has a 75%greater risk of this type of violent victimization than
the average White female. At age 30 and at age 40, the risk for Black females is still
91%higher than for White females. Even at age 50, when the risk is low for both
groups, the average Black female still has an 81%greater risk of victimization than
the average White female. However, by age 55, the average Black female and White
female share the same low risk of this form of violent crime victimization over the rest
of their lives.
Using the same data, but plotted from birth to age a, one can easily compare the
trajectory of victimization risk between White and Black females in West Virginia
(see Figure 2). In Figure 2, the vertical arrow indicates the different levels of risk
at the same age of 28. By the age of 28, the average Black female has already expe-
rienced a 40%risk for violent crime victimization (as indicated by the vertical arrow).
This level of accumulated risk (i.e., 40%) does not occur for an average White female
until three decades later, at the age of 58 (see the horizontal arrow).
Study 2: Computing National Estimates of Lifetime Risk of Aggravated
Assault Victimization
Data and method. In this section, we demonstrate how to compute national estimates of
violent crime victimization with NIBRS when only a proportion of police agencies
submit data in NIBRS format.
8
The data used in this example come from three
sources, all in the year 2000. The 2000 NIBRS file obtained from the FBI
9
contains
information about the age, sex, and race of aggravated assault victims. The annual
UCR crime report, Crime in the United States, 2000, provides the national estimates
of aggravated assault victims,
10
and the U.S. Bureau of Census provides the popula-
tion totals by age, sex, and race for the year 2000. The same methods used in this
example apply to any given year where complete data from all three sources are
available.
Akiyama et al. 139
In the year 2000 NIBRS data, there were 111,751 victims of aggravated assault.
These aggravated assault victims were distributed by sex and race at each age from
0 to 98. This distribution of NIBRS aggravated assaults by age, sex, and race was then
applied to the estimated number of aggravated assault offenses in Crime in the United
States (FBI, 2001). According to UCR counting rules, the number of offenses for these
crimes against persons is equal to the number of victims (see Notes 5 and 10). The age-
specific rates for each race/sex group are calculated using the 2000 National Census
population as the denominator.
The number of NIBRS violent crime victims distributed by age, sex, and race cate-
gories is denoted here by V(a, s, r).
11
V¼SVða;s;rÞð3Þ
Let Equation 3 represents the total number of aggravated assault victims reported
in NIBRS. Vis smaller than the national UCR estimate of aggravated assault,
denoted as ~
V, primarily due to the partial coverage of the NIBRS data. But the above
noted exclusion of victims with unknown age, sex, or race should be added as a sec-
ondary reason (see Note 11). ~
Vis the estimated number of aggravated assault
offenses reported in Crime in the United States. Again, according to UCR counting
rules, the number of offenses for these particular crimes is equal to the number of
victims.
The national estimate of the number of violent crime victims is calculated by:
~
Vða;s;rÞ¼ ~
VVða;s;rÞ
V
:ð4Þ
The annual per person crime rate, R(as,r), is defined as follows:
Rða;s;rÞ¼
~
Vða;s;rÞ
Popða;s;rÞ;ð5Þ
where the denominator in Equation 5 is the 2000 National Census population for a
given age, sex, and race.
12
Findings for aggravated assault. Aggravated assault is defined by the UCR Program as an
unlawful attack by one person upon another wherein the offender uses a weapon or
displays it in a threatening manner, or the victim suffers obvious severe or aggra-
vated bodily injury involving apparent broken bones, loss of teeth, possible internal
injuries, severe laceration, or loss of consciousness. We chose this crime because it
is the most frequent type of violent crime against person reported to the FBI as an
index crime.
In Table 4, we show the estimated risk for aggravated assault victimization by age,
sex, and race grouping. The most vulnerable age-group is 21–30 years (see Table 4).
At this age, Black males have the highest risk, that is, a 19%chance of one or more
aggravated assault victimizations (1–0.8112). Black females are the second most vul-
nerable group with a 16%chance of one or more aggravated assault victimizations. In
140 Justice Research and Policy 16(2)
this same age-group, White males are more at risk for being victimized than are White
females (7%and 5%, respectively). The risk of one or more victimizations subsides
for all groups by age 50.
In Figure 3, we plot the results of this study from birth through the rest of life. Over
the life course, Black males have the highest probability of aggravated assault victi-
mization. If the average Black male lives to age 80, he has a 51%chance of being the
victim of one or more aggravated assaults. Black females are the second most vulner-
able group with a 40%chance of aggravated assault victimization. Over the life
course, the risk of aggravated assault victimization for White males is 21%and for
White females 15%.
The risk for aggravated assault victimization begins earlier for Black men than for
the other race/sex groups. For example, from birth to age 25, Black males have a 23%
chance of one or more aggravated assault victimizations. Compare this with the risk in
the other groups: Black females (19%), White males (10%), and White females (6%).
In fact, Black males are more at risk in this time frame (birth to 25) than White males
and White females are from birth through the rest of their lives.
Table 4. National Estimates for Aggravated Assault Victimization Risk by Age, Sex, and Race
Using NIBRS.
Age
Black Females Black Males
p¼0
a
p¼1p¼2p¼3p¼0p¼1p¼2p¼3
Birth to 10 .9861 .0138 .0001 .0000 .9802 .0196 .0002 .0000
11 to 20 .8902 .1035 .0060 .0002 .8659 .1247 .0090 .0004
21 to 30 .8432 .1438 .0123 .0007 .8112 .1697 .0178 .0012
31 to 40 .8936 .1005 .0057 .0002 .8550 .1340 .0105 .0005
41 to 50 .9432 .0552 .0016 .0000 .8920 .1019 .0058 .0002
51 to 60 .9798 .0200 .0002 .0000 .9507 .0481 .0012 .0000
61 to 70 .9908 .0092 .0000 .0000 .9760 .0237 .0003 .0000
71 to 80 .9930 .0070 .0000 .0000 .9888 .0111 .0001 .0000
81 to 90 .9953 .0047 .0000 .0000 .9941 .0059 .0000 .0000
White females White males
Birth to 10 .9932 .0068 .0000 .0000 .9905 .0095 .0000 .0000
11 to 20 .9615 .0377 .0007 .0000 .9377 .0603 .0019 .0000
21 to 30 .9496 .0491 .0013 .0000 .9258 .0714 .0028 .0001
31 to 40 .9631 .0362 .0007 .0000 .9535 .0454 .0011 .0000
41 to 50 .9809 .0189 .0002 .0000 .9739 .0258 .0003 .0000
51 to 60 .9930 .0070 .0000 .0000 .9883 .0116 .0001 .0000
61 to 70 .9967 .0033 .0000 .0000 .9947 .0053 .0000 .0000
71 to 80 .9983 .0017 .0000 .0000 .9969 .0031 .0000 .0000
81 to 90 .9987 .0013 .0000 .0000 .9984 .0016 .0000 .0000
Note. NIBRS ¼National Incident-Based Reporting System.
a
p¼0 means the probability of 0 victimizations,p¼1 indicates the risk of 1 victimization,and so on up to p¼3.
Akiyama et al. 141
Discussion
In both studies described above, we demonstrate a method for using NIBRS to com-
pute the risk of violent crime victimization over a lifetime. Since there are no unique
victim identifiers in NIBRS, it is impossible to know the number of people in a pop-
ulation who are victimized more than once. For this reason, we cannot treat the crime
rate as the probability of crime victimization and so we have introduced the concept of
the average person. As indicated above, the average person is a hypothetical person
whose victimization experience—in quantifiable terms—is the average per person
crime rate. Using methods described in this article, the risk of victimization over a
lifetime for the average person can be computed with NIBRS data for a variety of
age–sex–race groupings. This type of analysis enables researchers and policy makers
to compare the risk of crime victimization across demographic groups and across
places with varying structural conditions, such as levels of poverty, home ownership,
unemployment, teen pregnancy, or single-parent homes. Examining lifetime compu-
tations from birth to age a(i.e., Figures 2 and 3) enables researchers and policy makers
to clearly see the onset and trajectory of risk as it begins at a young age, plateaus at
midlife, and trails off to near zero toward the end of life. From the reverse direc-
tion—from age athrough the rest of life (i.e., Figure 1)—one can see how risk slowly
diminishes as we age and how vast disparities in risk between groups (e.g., race and
sex) in early ages of life can shrink later in life such as in middle age or later.
The methods presented in this article may be of particular interest to researchers and
policy makers in states that report all crime data in NIBRS format. As of 2013, there
were 15 such states. In these states, the risk of lifetime victimization for certain crimes
can be computed with NIBRS similar to our approach in Study 1. When all crime data
come from NIBRS (rather than a mix of summary UCR and NIBRS), there is no need to
adjust estimates for the non-NIBRS places. However, at the national level, where only a
portion of the crime data is in NIBRS format, we need an additional step in our methods.
Our second study (using Equations 3–5) demonstrates how to weight the estimates to
100%. In applying the distribution of NIBRS crimes by age, sex, and race to the sum-
mary UCR offense counts for crimes against persons (excluding murder), we assume
that NIBRS places are similar to non-NIBRS places which may not be the case. Accord-
ing to an FBI report in 2013, 6,328 law enforcement agencies, representing coverage for
nearly 93 million U.S. inhabitants, submitted crime data in NIBRS format. The same
study reports that about 34.4%of all law enforcement agencies that participate in UCR
submit their data via NIBRS (FBI, 2014). This is a large number of NIBRS reporters,
but it is still not considered a probability sample, and therefore national estimates of life-
time risk by age, sex, and race may not be valid. As mentioned previously (Note 8), the
FBI and the BJS have recently initiated the National Crime Statistics Exchange (NCS-
X), a program designed to generate nationally representative incident-based data on
crimes reported to law enforcement agencies. This will add validity to estimates of life-
time risk that may not exist at the present time.
In addition, although the concept of the average person enables us to compute life-
time victimization risk with NIBRS data, it is important to note that the average
142 Justice Research and Policy 16(2)
person’s risk is not the community’s risk. To estimate the community’s risk, one
would need to know the number of people in the populations who have experienced
0, 1, 2, 3, ...,kvictimizations. This is not possible with NIBRS, but with NCVS,
it is. Perhaps future studies can utilize the methods presented in this article to examine
NCVS to see how its estimates of lifetime victimization risk compare with NIBRS.
Policy Applications/Implications
In the field of public health, risk assessments are commonplace and offer opportunities
to assess the overall health risks in a community at particular stages of life, tailor pol-
icies and interventions to the right times and to the right groups, and to assess progress
along the way. Within certain limits, NIBRS provides the same opportunities for gov-
ernment officials and public policy makers concerned with the lifetime risk of harm
due to violent crime. As we have demonstrated, NIBRS can help identify the age at
which members of certain sex and racial groups begin experiencing risk for violent
crime victimization and compute projections of risk over a lifetime—given that social,
economic, and other structural conditions remain the same. In our first study, we
demonstrate that Black females in West Virginia are twice as likely as White females
to experience intimate partner violence in the period between ages 18 and 28 (see Fig-
ure 4). This is significant and could be used to direct policy and educational support to
this vulnerable group.
NIBRS is adaptable to many different types of risk assessments based on crime
type (e.g., aggravated and sexual assault), location types (e.g., at home, school, or pub-
lic places), victim–offender relationship (e.g., intimate partner, family member,
acquaintance, stranger, and friend), or any combination of the above. Further, lifetime
computations can be used to compare the risk of violent crime for different age–sex–
race groups in a variety of geographic areas—within or across cities, counties, states,
or regions of the United States. These analyses may add new insights about the rela-
tionship between crime and place.
In addition, lifetime risk computations maybeausefuladditiontoinformation
provided by government officials for public awareness campaigns, particularly
those aimed at mobilizing people to help prevent violent crime. The information
provided by lifetime risk assessments with NIBRS may also aid in community
dialogueandactionfocusingonprotecting the most vulnerable groups in a com-
munity or neighborhood. Further, they may be useful for public officials deve-
loping training programs and implementing and assessing the effectiveness of
anti-violence programs.
Conclusions
In presenting the methods and examples described in this article, we imagine that they
can be used by researchers especially interested in studying crime victimization from a
life course or routine activities perspective. We provided the section ‘‘Calculating
Lifetime Risk with Excel’’ to show researchers and policy makers how to use these
Akiyama et al. 143
statistical methods for data analysis. The methods may also be useful to criminologists
or sociologists who study social inequality and its impact on crime victimization. Pol-
icy makers and government officials may also find these methods useful for identify-
ing risk patterns by age, sex, and race over time in the same way public health officials
examine health risks over time.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship,
and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of
this article.
Notes
1. Summary Uniform Crime Reporting (UCR) refers to the original crime reporting system
developed in the late 1920s and continues today. The summary UCR provides aggregate
crime counts of eight index crimes that are reported to and recorded by the police working
in local jurisdictions. These crime counts are then combined to compute county, state,
regional, and national estimates of crime volume and crime rate. Summary UCR includes
the count of the number of murders. For the crime of murder, police agencies submit addi-
tional information about the crime under the subprogram of summary UCR known as Sup-
plemental Homicide Reports (SHR). Through the SHR, additional information for each
homicide is captured, including the age, sex, and race of the victim. NIBRS also comes
under the UCR Program which is managed by the FBI. NIBRS is an incident-level crime
reporting system that captures the age, sex, and race of victims and offenders.
2. The National Crime Survey (NCS) was the predecessor of the current National Crime Vic-
timization Survey.
3. In this study, violent crime was operationalized as rape, robbery, and aggravated assault.
4. The term ‘‘survivor’’ refers to the number of people in birth cohort who each year survive
death by natural or other causes.
5. Lifetime victimization cannot easily be computed for property crimes because of NIBRS
counting rules. For crimes against person, NIBRS counts one victim for each offense. For
property crimes, there may be multiple victims for each offense. The counting rules are
detailed in the FBI publication UCR Handbook (2004) available online at https://www2.
fbi.gov/ucr/handbook/ucrhandbook04.pdf
6. The concept of the ‘‘average person’’ was developed by Yoshio Akiyama in the late 1990s.
It was prepared as a technical paper in 2000 but was never published. The focus of the pres-
ent article is to explicate the concepts, methods, underlying assumptions, and limitations of
lifetime computations with NIBRS as originally developed by Akiyama.
7. The FBI has recently changed the definition of sexual violence to remove the word ‘‘for-
cible,’’ but the data in this study predated this change.
8. The methods used in this example assume that the age, sex, and race distribution of violent
crime victims is the same in NIBRS and non-NIBRS agencies. At the present time, this
144 Justice Research and Policy 16(2)
assumption may not hold true. In 2000 (the year used in this example), only about 14%of
the United States was covered by law enforcement officers who reported crimes in
NIBRS format. Even though the number of violent crimes reported that year via NIBRS
was large, it is not a probability sample of the United States. Recently, BJS has initiated
the National Crime Statistics Exchange, a program designed to generate nationally rep-
resentative incident-based data on crimes reported to law enforcement agencies. For more
information about this program, please go to the following link: http://www.bjs.gov/con-
tent/ncsx.cfm
9. The data for this study were obtained directly from the FBI. However, the NIBRS data are
readily available for download at the National Archive of Criminal Justice Data at the Uni-
versity of Michigan.
10. Because UCR counts one victim per offense for crimes against persons, the annual count of
crimes against persons (i.e., murder, rape, and aggravated assault) is equal to the number of
victims of those crimes. While murder is a violent crime, it is excluded from the current
study since the lifetime model presented considers ‘‘repeated victimizations’’ which does
not apply to this crime. Although the crime of robbery is a violent crime, it is counted
by UCR as a crime against property and, therefore, cannot be used to estimate the number
of robbery victims.
11. When any of the information relating to a victim’s age, sex, and race is unknown, the victim
is not counted. In NIBRS aggravated assault incidents, about 1.3%of victim age, 0.4%of
victim sex, and 2.5%of victim race are missing. When these three variables are combined,
about 3.4%of victims are excluded from the analysis.
12. In Equation 3, it is assumed that the population covered by NIBRS data is similar to the
nation in terms of age, sex, and race. If we could establish the age, race, and sex distribu-
tions of populations covered by NIBRS, Equation 3 could be refined.
References
Addington, L. (2008). Current issues in victimization research and the NCVS’s ability to study
them. Report from the Bureau of Justice Statistics Data User Workshop. Retrieved http://bjs.
gov/content/pub/pdf/Addington.pdf
Akiyama, Y. (2000). The ‘‘average person’’ in crime victimization computations. Unpublished
technical paper.
Federal Bureau of Investigation. (1999). The chances of lifetime murder victimization, 1997.
Crime in the United States. Washington, DC: GPO.
Federal Bureau of Investigation. (2001). Crime in the United States. Washington, DC: GPO.
Federal Bureau of Investigation. (2014). Summary of NIBRS 2013. Retrieved June 18, 2015,
from https://www.fbi.gov/about-us/cjis/ucr/nibrs/2013/resources/summary-of-nibrs-2013
Howlader, N., Noone, A. M., Krapcho, M., Garshell, J., Miller, D., Altekruse, S. F., ... Cronin,
K. A. (Eds.). (2014). SEER cancer statistics review, 1975-2012. Bethesda, MD: National
Cancer Institute. Retrieved from http://seer.cancer.gov/csr/1975_2012/
Koppel, H. (1987). Lifetime likelihood of victimization. Washington, DC: The Bureau of Justice
Statistics.
Lynch, J. P. (1989). An evaluation of lifetime likelihood of victimization. Public Opinion
Quarterly,53, 262–264.
Akiyama et al. 145
Stuart, A., & Ord, J. K. (1987). Kendall’s advanced theory of statistics (5th ed.). London,
England: Griffin.
Author Biographies
Yoshio Akiyama earned a PhD in Mathematics at the University of Minnesota. Later, he taught
Mathematics at the University of Wisconsin at Madison, Florida State University, and George
Washington University. He is currently retired from teaching and government service.
James J. Nolan is a Professor in the Department of Sociology and Anthropology at West Vir-
ginia University where he teaches courses on the topic of crime and social control. His research
currently focuses on urban policing, intergroup relations, and the measurement of crime.
Karen G. Weiss is an Associate Professor in the Department of Sociology and Anthropology at
West Virginia University. Her research focuses on violence and victimization, and most
recently, intoxication and bystander intervention.
Stacia Gilliard-Matthews is an Assistant Professor in the Department of Sociology, Anthro-
pology & Criminal Justice at Rutgers University in Camden, NJ. Dr. Gilliard-Matthews teaches
classes on policing and research methods. Her research focuses on the impact of politics and
policies on race, gender, and class inequalities in society and police behavior and discretion.
146 Justice Research and Policy 16(2)