Measuring child maltreatment risk in communities: a life table approach

Child Abuse & Neglect 28 (2004) 967–983

Measuring child maltreatment risk in communities: a life table approach夽 William Sabol, Claudia Coulton∗ , Engel Polousky Mandel School of Applied Social Sciences, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA Received 2 July 2003; received in revised form 21 February 2004; accepted 5 March 2004

Abstract Objective: The purpose of this article is to: (1) illustrate the application of life table methodology to child abuse and neglect report data and (2) demonstrate the use of indicators derived from the life tables for monitoring the risk of child maltreatment within a community. Method: Computerized records of child maltreatment reports from a large, urban county in Ohio are cumulated for 11 years and linked for each child. Life table methods are used to estimate the probability that children from birth to age 10 will be reported victims of maltreatment by age, race, and urban or suburban residence. Results: Using life tables, the estimates in the county of this study are that 33.4% of African American children and 11.8% of White children will appear in substantiated or indicated child abuse or neglect report(s) by their 10th birthday. The age-specific probability of a maltreatment report is highest in the first year of life for both groups. The probability of a child being reported for a substantiated or indicated incident of maltreatment before his or her 10th birthday is more than three times higher for city dwellers than for suburbanites in the urban county studied here. Conclusions: Life table methodology is useful for creating child well-being indicators for communities. Such indicators reveal that a larger portion of the child population is affected by maltreatment reports than would be concluded from examining cross-sectional rates and can be used to identify racial or geographic disparities. © 2004 Elsevier Ltd. All rights reserved. Keywords: Social indicators; Community; Child maltreatment; Life tables

夽 ∗

Grants from the Cleveland Foundation and the George Gund Foundation helped to support this study.

Corresponding author.

0145-2134/$ – see front matter © 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.chiabu.2004.03.014

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Introduction The recognition that there are serious disparities in outcomes for children has prompted many communities to launch prevention and health promotion efforts (National Research Council & Institute of Medicine, 2000; Schorr, 1997). Such community-based efforts require measures of the conditions and status of children to plan, mobilize and assess their progress (Daro & Harding, 1999; Fawcett, Schultz, Carson, Renault, & Francisco, 2003). National surveys and government reports are not appropriate data sources for this type of measurement because they seldom have large enough samples within local communities to make reliable estimates. Under such circumstances, communities working to improve conditions for children often use administrative records to craft indicators of child well-being (Coulton, 1997; Goerge, 1997). However, the methodologies of crafting child well-being indicators from administrative records have not received as much attention as have measures based on survey and observational data. Depending on the methods used, though, indicators may be more or less revealing of change or disparities among groups and communities. This article illustrates the use of life table methods to craft measures of child well-being in one community. Life table techniques are applied to 11 years of child abuse and neglect reports and population data from a large urban county in Ohio. The article presents estimates of the likelihood that the population of the metropolitan area will become victims of maltreatment from birth to 10 years of age. The life tables are also disaggregated by race and residential location to demonstrate the usefulness of the technique in identifying disparities. The advantage of life table methods over the more usual cross-sectional analysis is that they allow a community to gauge the condition of children over their childhood years rather than during a point in time. Such measures better reflect the reality that events may affect the course of child development for multiple years, not simply in the year they occur. Life tables and childhood perspective Life tables are tools that can be applied to routinely collected data—such as that from the census. These tables allow for examination of the degree to which specific events occur across intervals of time and permit estimation of life course patterns and probabilities. Life tables are a commonly used method in epidemiology and demography to describe mortality, fertility, marriage and other occurrences in populations (Namboodiri & Suchindran, 1987; Preston, Heuveline, & Guillot, 2001). Yet, they have not been applied to the estimation of risks for child maltreatment within communities. However, as Rank and Hirschl (1999) illustrate in their application of life table methods in their study of child poverty, many more children are affected when such problems are viewed over the entire period of childhood than when they are estimated cross-sectionally. Racial disparities in poverty also take on a greater magnitude when viewed from this longitudinal childhood perspective. The period life table methods demonstrated in this article make it possible to estimate risk during the first 10 years of childhood without actually tracking research subjects longitudinally. Most efforts to estimate the extent of child maltreatment capture a point-in-time, such as 1 year. The surveys and federal and state data systems that have been used for the research do not explicitly track children and families over multiple years, so it has been difficult to craft longitudinal measures. Moreover, studies that gather data on families over time are difficult to carry out and are prohibitively expensive, especially for local communities. For this reason, most community social indicators for children reflect a snapshot of the status of the child population each year rather than over time.

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Child maltreatment data and rates Official child abuse and neglect reports have been used widely in efforts to determine the scope and distribution of child maltreatment. Most of these studies have focused on a 1-year period and have calculated various types of maltreatment rates. For example, the National Child Abuse and Neglect Data System (NCANDS) of the Children’s Bureau has been gathering case level data from states on reports of child abuse and neglect since 1988. Reports of child abuse and neglect that are investigated and determined by the states to be substantiated or indicated are used to estimate national and state victimization rates. In 2000, the victimization rate for the US was 15.7 per thousand for children birth to age 3 and 13.3 per thousand for children age 4–7 (US Department of Health and Human Services, 2002). In addition, localized studies have used official reports to study child maltreatment. They have demonstrated higher incidence rates in poor and distressed neighborhoods and among minority populations (Coulton, Korbin, Su, & Chow, 1995; Drake & Pandey, 1996; Garbarino & Sherman, 1980; Zuravin, 1989). Neglect, which comprises the majority of officially investigated reports, is more highly concentrated in poor neighborhoods and populations than physical or sexual abuse. There has also been considerable debate about whether there are racial differences in the incidence of child maltreatment. Using NCANDS and census data, racial and ethnic groups have been compared on the ratio of children reported for maltreatment to the size of the child population in the racial or ethnic group, leading to the conclusion that African American children have higher maltreatment rates than White children (Fluke, Yuan, Hedderson, & Curtis, 2003). However, other studies have suggested that the question of racial differences in maltreatment is quite complex. For example, racial disparities have been shown to be larger when comparing the rate of maltreatment reports than when comparing races on the proportion of maltreatment reports that are actually substantiated by Child Protective Services (CPS). Moreover, there is a significant interaction between race and dependence on public assistance in explaining racial differences in maltreatment reports and substantiations (Ards, Myers, Chung, Malkis, & Hagerty, 2003; Ards, Myers, & Malkis, 2003). Counts or rates of child maltreatment reports are often used by communities as indicators of the well-being of children, and preventing child maltreatment is often an explicit objective of community initiatives to support children. Communities typically calculate child maltreatment indicators as yearly rates. In other words, the number of individual children with child maltreatment reports are counted for a year and divided by the number of children at risk (e.g., US Department of Health and Human Services, 2002). This rate is interpreted as the portion of children in a particular age group that experienced at least one child maltreatment report in that year. Yearly maltreatment rates resemble what is known as incidence rates in epidemiology (English, 1998), but incidence rates are meant to reflect “new cases.” If child maltreatment were actually an event with a beginning and end such as influenza, the analogy would be a reasonable one, but the course of child maltreatment is actually quite varied. Another difficulty with the cross-sectional approach is that the entire child population is assumed to be “at risk” in any given year but, once a child has been reported for maltreatment earlier in life, an additional report in the following year may not represent a new case in the epidemiological sense but a continued situation (National Research Council, 1993). An alternative way of thinking about the magnitude of the problem of maltreatment in a community is to consider the chances that individuals will become victims of maltreatment during their childhood years. Such a life course perspective is particularly relevant since a substantial amount of research demonstrates that maltreatment has later consequences for child development and repeated reports and ongoing maltreatment are not uncommon (DePanfilis & Zuravin, 1999; Fluke, Yuan, & Edwards, 1999; National

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Research Council, 1993). Young children who have experienced child maltreatment are likely to be at risk or require services for an extended period that is underestimated in cross-sectional incidence studies. A longitudinal measure provides a better indication of the magnitude of the impact of maltreatment on the community’s children. Although communities may recognize the importance of such a longitudinal view, few have crafted child well-being indicators that reflect this perspective. Longitudinal indicators are more difficult to calculate than cross-sectional measures and present some complications in terms of the kinds of data that are needed to estimate the at-risk population and the children who are maltreated. Child abuse and neglect reports made to official agencies are typically the data source for these indicators. Although there is the concern that these events may be subject to reporting bias, they constitute a rich and important source of local data because they are nearly universally available and have been collected for many years (Barth, Locklin-Brown, Cuccaro-Alamin, & Needell, 2002; Murphey & Braner, 2000; National Research Council, 1993). Moreover, even though some instances of neglect and abuse are surely missed by the reporting system, official reports represent a real need to which the community must respond. Thus, child abuse and neglect reports are useful for calculating child well-being indicators that can be tracked over time in communities.

Methodology This study uses period life table methods (Namboodiri & Suchindran, 1987; Preston et al., 2001) to estimate the cumulative and age-specific rates of maltreatment during early childhood. This method is demonstrated for one metropolitan area in Northeast Ohio, so while the method is applicable elsewhere, the findings themselves are not generalizable. The term life table comes from their most widespread application, which is to the estimation of the likelihood of mortality across age groups. The period life table estimates in this study are based on the experiences of children whose age was between birth and 10 in a particular period, in this case 1999 through 2001. A period life table approach is in contrast to studying true cohorts, which would reflect the actual experiences of birth cohorts as they age. The main limitations of a true cohorts approach are that the estimates may not be timely and the fact that they can be affected by short term external influences or chance (Preston et al., 2001, p. 19). For example, to obtain true cohort measures of maltreatment up to age 10, children born in 1991 would have to be tracked until 2001. This would raise questions about how relevant the experiences of children born in 1991 are for estimating the outcomes 10 years later. Conversely, if a recent cohort were tracked, for example, the 1999 birth cohort, then by the year 2001, actual experiences would be available only for 2 years. A single event, such as a scandal at a child care center or a temporary change in agency practice might unduly affect age-specific maltreatment rates of a single cohort while these differences are smoothed using what is essentially synthetic cohorts. We use this term to emphasize the fact that the estimates derived from the period life table are modeled estimates of what would happen to a cohort if the set of conditions observed persisted throughout the life of the cohort. Thus, the period life table uses events from a defined period and for specified age groups to construct a synthetic cohort, which serves as an estimate of the likelihood of the events occurring over time in the population. The experiences of the synthetic birth cohorts described by the period life table estimates are not necessarily identical to the actual experiences of children in birth cohorts. This is because the life table estimates rely on the assumption that age-specific probabilities of maltreatment are constant into the

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future. If future experiences depart from the historical information that is used to generate the period life table estimates, actual maltreatment outcomes may differ from those projected from the period life table. By comparing actual outcomes to those projected from the life table, it is possible to explore the reasons for the departures. Data sources The site for this study is Cuyahoga County, Ohio. Cleveland is the central city in the county, which also contains over 40 suburban municipalities. Two data sources are used for this analysis: Child maltreatment reports, and population counts from the US Census. Child maltreatment reports. Under a strict confidentiality contract, the Cuyahoga County Department of Children and Family Services (DCFS) provided their computerized files of maltreatment reports that were accepted for investigation from 1990 through 2001. The procedures for securing these files were approved by the Institutional Review Board at Case Western Reserve University. The files contain a record for each reported incident that includes a child identifier. For this analysis, the incidents were linked across years for children (using the child identification number) because the methodology required determining whether reports in the study period (1999–2001) were indeed first time reports for each child. For example, if a child who was age 9 had a child abuse or neglect report in 1999, data from 1990 through 1998 were examined to determine whether the report in 1999 was the first report. The study separately estimates the life tables using all reports and substantiated or indicated reports since both have been shown to be predictive of negative outcomes for children later in life (Leiter, Myers, & Zingraff, 1994). It should be noted that Ohio has three possible disposition codes; unsubstantiated, indicated, and substantiated. Therefore, maltreatment rates calculated using such codes may differ from those in states using only two levels. The estimates of all reports were based on the first time that a child appears in any report of maltreatment during the child’s life. The estimates of substantiated and indicated reports were unduplicated to find the first report in the child’s life of a substantiated or indicated incident of maltreatment. Age-specific population data. To compute the life table estimates, it was necessary to know the size of the population at risk of having a first incident of maltreatment in 1999–2001. This requirement led to the development of estimates of the age-group specific sizes of population for the years 1999–2001. The 1990 and 2000 census counts of children in each age group were the starting point for these estimates. Linear interpolation methods were used to calculate estimated populations for each inter-censal age group, which were benchmarked to the yearly population estimates for the county. Life table analysis The period life table estimates in this study take into account the maltreatment reports that occurred during the study years, 1999–2001, and extrapolate from these experiences to generalize about the experiences of the child population if the conditions that existed during the 1999–2001 period were to continue. Conceptually, these life table estimates trace the experiences of synthetic birth cohorts through their first 10 years of life. The life table estimates are derived from the age-specific rates of child maltreatment that occurred from 1999 to 2001. These rates reflect the chances that a child in one of the age groups has a first experience in his or her life of a reported case of maltreatment during the study years. These age-specific

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rates are converted to probabilities of experiencing maltreatment, and assuming a “steady-state,” these yield the projected maltreatment probabilities for county residents from birth to age 10. The period life table uses current or point in time data to estimate the outcomes for a synthetic birth cohort under the assumption that what happened to the population at the point in time in which it was observed persists throughout the life of the synthetic cohort. This requires that the maltreatment reports observed during the period or point in time be transformed into the life table of the synthetic cohort. This transformation is done by converting a set of observed period age-specific maltreatment rates (n Mx ) into a set of age-specific probabilities of being maltreated (n qx ) for the synthetic cohort from birth to age 10. The details of these calculations appear in Appendix A. The main adjustment to the life tables is in the estimate of the number of children in each age group with prior maltreatments. This quantity is subtracted from the age group’s population to yield the population at risk of a first maltreatment, or the quantity n Nx . The life table used census estimates of the age-group specific population that take into account net migration, so it was unnecessary to make further adjustments. We also prepared separate life tables for African American children and White children and for children residing in the inner city and the suburbs. It was not possible to compute multivariate life tables since there were too few African American children in the suburbs to produce stable estimates. However, there was a correlation between race and location (Phi = .19, p < .001). Also, although multivariate methods, such as survival models, can be applied to true cohorts that are studied longitudinally, they cannot be applied to these life tables because they estimate synthetic cohorts in which the children who are not maltreated are never directly observed.

Results Between 1999 and 2001, there were 18,574 child maltreatment reports that were determined to be first reports for children birth to age 10 in Cuyahoga County. Table 1 presents descriptive information on all first reports and on those first reports that were found to be substantiated or indicated. Approximately 55.1% of the reports are on children classified as African American, 38.3% as White, and 6.6% as other races. More than 64% of the children with reports live in the central city of Cleveland. The category of maltreatment that was alleged in the case of reports, or concluded at disposition in the case of substantiated or indicated reports is also examined in Table 1. Neglect is the predominant type of maltreatment, particularly among the youngest children. The life table estimates of the chances that children birth to age 10 will become the subject of a child maltreatment report appear in Table 2. These estimates are presented separately for the probability of any maltreatment report and the likelihood of a substantiated or indicated report. The age-specific percentage is indicative of the percentage of children who would be expected to experience their first report in that age interval. The cumulative percentage reflects the percent of all children who will experience a report prior to their 10th birthday. It is estimated that 31% of all children in the county will have experienced at least one maltreatment report before they reach their 10th year. The greatest chance of a maltreatment report occurs in the birth to age 1 interval. The probability of a report declines in each yearly age interval up to ages 5 through 7 when there is a slight increase. This may reflect the point at which most children enter elementary school. The life table method allows for the comparison of selected groups on their risk of child maltreatment reports. In Table 3, cumulative percentage comparisons are made by children’s race and by whether they

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Table 1 Characteristics of first maltreatment reports for children birth to age 10, 1999–2001, Cuyahoga County, Ohio Any report of maltreatment

Substantiated or indicated incident

Race (%) African American White Other

55.1 38.3 6.6

59.4 35.0 5.6

Residence (%) City of Cleveland Suburban jurisdictions

64.3 35.7

68.0 32.0

Category of reporter (%) Family/self Neighbor/friend Social service professionals Health professionals School Day care/foster care Legal authorities Anonymous/unknown

17.2 8.0 20.0 8.2 6.1 1.2 13.3 26.0

16.4 5.1 25.2 9.0 6.5 1.1 19.8 16.8

62.8 20.3 7.2 9.8

64.3 13.5 6.7 13.5 2.2

Type of maltreatment (%) Neglect only Physical abuse only Sexual abuse only Emotional maltreatment only More than 1 N

18, 574

11, 551

reside in the central city versus the suburbs at the time of their first report. The cumulative percentage of children experiencing a maltreatment report is presented separately for African American and White children. There are too few children in other racial groups to calculate specific rates for them. Similarly, children who reside in the suburbs at the time of their first report are compared with children who reside Table 2 Life table estimates of the likelihood of maltreatment, birth to age 10, 1999–2001, Cuyahoga County, Ohio Age at incident

0–1 1–2 2–3 3–4 4–5 5–6 6–7 7–8 8–9 9–10

Any report of maltreatment

Substantiated or indicated incident

Age-specific percent

Cumulative percent

Age-specific percent

Cumulative percent

8.2 4.8 3.9 3.4 3.0 2.9 3.0 2.7 2.5 2.0

8.2 12.6 16.0 18.8 21.3 23.6 25.8 27.8 29.6 31.0

5.0 2.5 2.2 1.9 1.8 1.8 1.8 1.8 1.5 1.2

5.0 7.3 9.3 11.1 12.7 14.2 15.8 17.2 18.5 19.5

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Table 3 Cumulative percents of children experiencing maltreatment by race and residential location Age group

African American

White

City of Cleveland

Suburban jurisdictions

Any report of maltreatment 0–1 13.7 1–2 21.0 2–3 26.2 3–4 30.4 4–5 34.2 5–6 37.6 6–7 41.1 7–8 44.3 8–9 47.1 9–10 49.1

4.9 7.8 10.1 12.2 13.9 15.5 17.1 18.4 19.6 20.7

12.5 19.3 24.4 28.7 32.4 35.9 39.2 42.1 44.8 46.6

4.7 7.2 9.2 11.0 12.5 14.0 15.4 16.8 17.9 19.0

Substantiated or indicated incident 0–1 9.2 1–2 13.3 2–3 16.7 3–4 19.6 4–5 22.2 5–6 24.7 6–7 27.4 7–8 29.8 8–9 31.8 9–10 33.4

2.6 4.0 5.1 6.3 7.3 8.3 9.3 10.2 11.1 11.8

8.0 11.9 15.0 17.8 20.4 22.9 25.4 27.7 29.7 31.1

2.6 3.8 4.9 5.8 6.7 7.6 8.4 9.3 10.1 10.7

within the central city. African American children are nearly 2.4 times more likely than White children to have a child maltreatment report by age 10. The racial differences in the chances of a substantiated or indicated report are somewhat higher, approaching 3–1. The cumulative percentage quite starkly portrays the magnitude of the total impact in the African American population. It shows that virtually half the African American children in the county are likely to be the subject of a child maltreatment investigation by age 10. Comparing the cumulative percentage of children receiving a maltreatment report in the city and the suburbs also reveals a sizeable difference. Children in the central city are 2.5 times more likely to be reported for maltreatment than their suburban counterparts. City children are three times more likely than suburban children to have a substantiated or indicated report. Also, it should be noted that race and place are confounded in these bivariate analyses. According to data from the 2000 US Census, African American children represent about 59.6% of the city and 19.2% of the suburban population in Cuyahoga County. Figures 1 and 2 display the age-specific hazard rates of becoming a victim of a first substantiated or indicated maltreatment report by age broken down by race and residential location. Unlike the cumulative percentages in Table 3, these figures show the chance of a child who had not previously had a maltreatment report experiencing a report in each age interval. It can be seen that the groups differ not only in their overall likelihood of maltreatment but also in the ages at which that likelihood rises and falls. Specifically, there is a very marked disparity in the first year. For example, the disparity between White and African American children is nearly four fold surrounding birth, and then levels off. It should also be noted that

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Figure 1. Estimated age-specific hazard rates for substantiated or indicated maltreatment for synthetic cohorts, 1999–2001, for African American and White children.

Figure 2. Estimated age-specific hazard rates for substantiated or indicated maltreatment for synthetic cohorts, 1999–2001, for City of Cleveland and Suburban Jurisdictions.

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Table 4 Cross-sectional maltreatment rates for children birth to age 10, Cuyahoga County, Ohio Total percent

African American percent

White percent

Cleveland percent

Suburban percent

9.7 10.1 10.1

3.7 3.9 4.0

9.4 10.4 10.3

3.2 3.2 3.3

Substantiated or indicated incident 1999 2.8 4.8 2000 3.0 5.2 2001 3.2 5.5

1.7 1.7 1.9

4.5 5.1 5.4

1.5 1.5 1.6

Any report of maltreatment 1999 5.9 2000 6.2 2001 6.2

the population at risk shrinks more at older ages for the African American group because those who have already had a maltreatment report are no longer at risk of having a first report, although they may have received additional reports at a later date. As mentioned earlier, the most common way that communities now use child abuse and neglect reports is to calculate a yearly maltreatment rate. For the purpose of contrasting the longitudinal and cross-sectional findings, Table 4 presents the point in time child maltreatment rates for children birth to age 10 in each of the study years: 1999, 2000, and 2001. These rates are calculated by summing the number of children under age 10 in the calendar year that have at least one child abuse or neglect report in that year and dividing by the population in the age range of birth to 10 at the mid-point of the year. Racial and geographic disparities are apparent in both Tables 3 and 4, and they are of similar magnitude. African American children and central city children are between two and three times more likely to be subjects of a maltreatment investigation each year. The profound difference between the two approaches, though, is in the magnitude of the involved population. Whereas cross-sectional rates make child maltreatment seem like a relatively rare event, the cumulative percentages show that experience with maltreatment or maltreatment investigations is practically endemic in some communities.

Discussion Life table methods applied to child maltreatment reports provide a life course perspective that is not seen in cross-sectional studies. In the community studied here, life table methods revealed the following patterns that could not be seen in yearly rates: (1) The first recognition of child abuse and neglect peaks at particular ages and (2) Over time during childhood, a very sizable portion of the population is likely to be the subject of a maltreatment report. In fact, by age 10, 33.4% of African American and 11.8% of White children will appear in a substantiated or indicated report of child maltreatment. This study demonstrates that life table methods can be applied to official records of child maltreatment reports. Although this demonstration of life table methods was confined to one metropolitan area, it does illustrate a practical tool for communities to understand the scope of the problem of child maltreatment. Life tables can be calculated with data that are available in most states or locales: official child abuse and neglect reports and census estimates of the size of the age-specific population of children. The methods presented here construct synthetic cohorts using recent reports of child maltreatment so that the

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findings can be relatively current and timely. Because the at-risk population is estimated using census data, expensive population surveys are not required. By using several years’ worth of reports, the findings regarding the synthetic cohorts are less subject to aberrations or chance occurrences than would occur using maltreatment reports from a shorter time period. These methods also have important limitations. Life table methods are best known for their application to national mortality records where there is little concern about missing cases or false reports, but child abuse and neglect reports are quite imperfect in this regard. Official maltreatment reports reflect the processes of recognition, reporting and investigation, all of which can be subject to error and bias. Nevertheless, children and families who become the subject of a maltreatment investigation are an important risk group who are the appropriate concern of prevention and health promotion efforts in the community. Another drawback of the life table that is estimated for a particular community population rather than the nation as a whole is that estimating the at-risk population is more difficult. Inter-censal age-specific population estimates have a higher margin of error at the local level than for the nation as a whole. Also, children who have been reported for maltreatment may move into or out of the state, introducing the possibility of error into the determination of age at first maltreatment event. An additional limitation of these methods is in their generalization to a community’s children in the future. The life table generates estimated chances of reported maltreatment for a synthetic cohort based on past events. These projections will be accurate into the future only insofar as conditions remain similar. For example, any changes in reporting behavior or child welfare agency practice in terms of accepting or classifying reports would change the estimates of risk in the future. Thus, it may be necessary to revise the life tables frequently. Another shortcoming of this study is that it relied on official maltreatment reports. While official reports are commonly used to study the abuse and neglect that is known to the authorities, there is general agreement that they under-represent the problem. Surveys that ask parents to self-report behaviors toward their children that are aggressive or violent generally conclude that child abuse occurs much more frequently than official reports suggest (Gallup, Moor, & Schussel, 1997; Straus & Gelles, 1986). Retrospective self-reports by adults on their mistreatment in childhood also confirm higher rates than official reports (Carlin et al., 1994; Fergusson, Horwood, & Woodward, 2000). Moreover, when official reports are combined with counts of children whom professionals believe have been harmed by abuse and neglect but not reported, the rates are measurably higher as well (Sedlak & Broadhurst, 1996). As such, official abuse and neglect reports represent only that portion of maltreated children who are recognized and reported to the public child protection system. Despite limitations, life table methods can be useful to communities in addressing issues in child maltreatment. Life tables more starkly illustrate that the impact of reported child maltreatment is greatest in central city and minority communities where the sheer magnitude of the involvement is extremely high. If nearly half the children in a neighborhood may be the subject of a child maltreatment investigation between birth and their 10th year, the problem touches virtually everyone. Even those families who do not directly experience maltreatment have a strong chance of having an acquaintance, relative or neighbor who has been involved in an investigation. In addition to revealing the magnitude of the reported maltreatment problem and racial and geographic disparities, the life table analysis raises some important issues for prevention efforts. One relates to the consequences of widespread involvement with child maltreatment investigations on particular neighborhoods or communities. Does the high likelihood of reported maltreatment in the population impact how prevention programs are perceived and accepted by families? Does the high level of surveillance

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and presence of child protection in particular communities have implications for how prevention is introduced and managed? The life course perspective also signals that prevention efforts will take many years to measurably impact the prevalence of maltreated children in a community where the proportions are already quite high. The greatest returns on prevention may come from targeting the ages at which children have the greatest likelihood of experiencing their first report and the groups and communities that have shown sizeable overall risk over the life course. Life table methods provide useful information for planning programs that take into account the risk of child maltreatment over the years of childhood and for determining whether communities are making progress on reducing that risk.

Acknowledgement Amy Billing provided research assistance on an earlier version of this analysis.

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Garbarino, J., & Sherman, D. (1980). High-risk neighborhoods and high-risk families: The human ecology of child maltreatment. Child Development, 51, 188–198. Goerge, R. M. (1997). Potential and problems in developing indicators on child well-being from administrative data. In R. M. Hauser, B. V. Brown, & W. R. Prosser (Eds.), Indicators of children’s well-being (pp. 457–471). New York: Russell Sage Foundation. Leiter, J., Myers, K. A., & Zingraff, M. T. (1994). Substantiated and unsubstantiated cases of child maltreatment: Do their consequences differ? Social Work Research, 18(2), 64–82. Murphey, D. A., & Braner, M. (2000). Linking child maltreatment retrospectively to birth and home visit records: An initial examination. Child Welfare, 79(6), 711–728. Namboodiri, K., & Suchindran, C. M. (1987). Life table techniques and their applications. Orlando, FL: Academic Press. National Research Council & Institute of Medicine. (2000). Healthy development through intervention, In J. P. Shonkoff & D. A. Phillips (Eds.), From neurons to neighborhoods: The science of early childhood development (pp. 337–3380). Committee on Integrating the Science of Early Childhood Development. Washington, DC: National Academy Press. National Research Council, Panel on Research on Child Abuse and Neglect, & Commission on Behavioral and Social Sciences and Education. (1993). Understanding child abuse and neglect. Washington, DC: National Academy Press. Preston, S. H., Heuveline, P., & Guillot, M. (2001). Demography: Measuring and modeling population processes. Oxford: Blackwell Publishers, Ltd. Rank, M. R., & Hirschl, T. A. (1999). The economic risk of childhood in America: Estimating the probability of poverty across the formative years. Journal of Marriage and the Family, 61(4), 1058–1067. Schorr, L. B. (1997). Common purpose: Strengthening families and neighborhoods to rebuild America. New York: Anchor Books, Doubleday. Sedlak, A. J., & Broadhurst, D. D. (1996). Third national incidence study of child abuse and neglect: Final report. Washington, DC: US Department of Health and Human Services, Administration for Children, Youth, and Families. Straus, M. A., & Gelles, R. J. (1986). Societal change and change in family violence from 1975 to 1985 as revealed by two national surveys. Journal of Marriage and the Family, 48(3), 465–479. US Department of Health and Human Services, Administration on Children, Youth and Families. (2000). Child maltreatment 2000. Washington, DC: US Government Printing Office. Zuravin, S. (1989). The ecology of child abuse and neglect: Review of the literature and presentation of data. Violence and Victims, 4, 101–120.

R´esum´e Objectif: Le but de cet article consiste a` :1. illustrer l’application de la m´ethodologie des tables de mortalit´e aux donn´ees venant des signalements de mauvais traitements et de n´egligence envers les enfants et 2. d´emontrer l’utilisation des indicateurs tir´es des tables de mortalit´e pour la surveillance des risques de mauvais traitements a` l’int´erieur d’une communaut´e. M´ethode: Les dossiers informatis´es comportant les signalements issus d’un grand comt´e de l’Ohio sont cumul´es sur une dur´ee de 11 ans et li´es pour chaque enfant. La m´ethode des tables de mortalit´e est utilis´ee pour estimer la probabilit´e selon laquelle des enfants, de la naissance a` l’ˆage de 11 ans et selon leur aˆ ge, leur origine ethnique et leur lieu de r´esidence, en ville ou en banlieue, seront signal´es comme victimes de mauvais traitements. R´esultats: En utilisant les tables de mortalit´e on estime que, dans le comt´e e´ tudi´e, il y a 33.4% d’enfants Am´ericains Africains et 11.8% d’enfants Blancs qui avant leur dixi`eme anniversaire apparaissent dans un ou des signalements pour maltraitance avec preuves ou indices seulement. La probalit´e selon l’ˆage, d’un signalement sp´ecifique pour mauvais traitements concerne la premi`ere ann´ee de vie pour les deux groupes. La probabilit´e pour un enfant de faire l’objet d’un signalement avec preuves ou indices concernant un incident de mauvais traitements avant son dixi`eme anniversaire est plus de trois fois plus e´ l´ev´e chez les habitants des villes que chez ceux des banlieues dans le comt´e urbain e´ tudi´e ici.

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Conclusions: La m´ethode des tables de mortalit´e peut eˆ tre utilis´ee pour e´ tablir des indicateurs de bien-ˆetre de l’enfant dans une communant´e. De tels indicateurs r´ev`elent qu’une plus grande partie de la population est concern´ee par les signalements pour mauvais traitements que ne l’indiquerait l’examen des taux calcul´es a` partir d’un e´ chantillon repr´esentif. Il peuvent eˆ tre utilis´es pour identifier les diff´erences selon l’origine ethnique ou g´eographique. Resumen Objetivo: El prop´osito de este art´ıculo es (1) ilustrar la aplicaci´on de la metodolog´ıa “life table” a los datos notificados de maltrato y abandono infantil, y (2) demostrar el uso de indicadores derivados de las “life tables” para observar el riesgo de maltrato en una comunidad. M´etodo: Los archivos informatizados de notificaciones de maltrato en un Condado urbano y grande de Ohio fueron acumulados durante 11 a˜nos y unificados para cada ni˜no. Los m´etodos de “life table” son utilizados para estimar la probabilidad de que los ni˜nos de entre 0 y 10 a˜nos sean notificados como v´ıctimas de maltrato en funci´on de la edad, la raza y la residencia urbana o suburbana. Resultados: Siguiendo esta metodolog´ıa, se puede estimar que un 33.4% de los ni˜nos afroamericanos y un 11.8% de los ni˜nos blancos aparecer´an en una notificaci´on de sospecha o confirmaci´on de maltrato o abandono antes de cumplir los 10 a˜nos de edad. La probabilidad de una notificaci´on de maltrato es m´as alta en el primer a˜no de vida en ambos grupos. La probabilidad de notificaci´on de sospecha o confirmaci´on de maltrato antes de los 10 a˜nos es tres veces m´as alta en este Condado para los habitantes de zonas urbanas que zonas suburbanas. Conclusiones: La metodolog´ıa “life table” es u´ til para crear indicadores de bienestar infantil en la comunidad. Tales indicadores revelan que una proporci´on de la poblaci´on infantil m´as amplia de lo esperable puede estar afectada por situaciones de maltrato. Esta metodolog´ıa puede ser u´ til para identificar disparidades geogr´aficas o raciales.

Appendix A The mechanics of arriving at the specific probabilities for the life table are as follows. For each year of the study (i.e., 1999–2001) we have information about the age, race, and residential location of the children who have a first child abuse or neglect report. We also have estimates of the county’s population by age interval for each year of the study and these estimates are also broken down by race and central city and balance of the county. We need to convert that information to a synthetic cohort (i.e., birth to age 10) for the life tables. For each age interval, we want to estimate the proportion of children who will have a first maltreatment event during that interval. We also want to calculate the cumulative proportion of children who will have a first event by the time they reach the end of that age interval. Table 5 shows the detailed calculations for one of the life table estimates. Specifically, this is the table for maltreatment reports for all races and geographic locations in 1999. The results reported in the article are based on averaging the outcomes of the 1999, 2000, and 2001 life tables. The definitions for the columns in the table are: 1. Age interval (x); this defines the age groups used in the calculations. 2. Mid-year population estimate for the age interval.

Table 5 Life table calculations, 1999, any maltreatment report, all children, Cuyahoga County, Ohio Estimated population, Cuyahoga County, 1999 (2)

0–1 1–2 2–3 3–4 4–5 5–6 6–7 7–8 8–9 9–10

18,184 18,169 18,380 18,318 18,917 19,063 19,676 20,269 20,618 20,948

Number of children with at least one prior reported maltreatment by age (3)

0 1353 2102 2741 3203 3665 4482 5035 5572 5717

Number of children “at-risk” of maltreatment (4) = (2) − (3)

18,184 16,816 16,278 15,577 15,714 15,398 15,194 15,234 15,046 15,231

Number of children first reported during 1999 (5)

1362 652 583 517 482 441 477 394 371 161

Age-specific rates of first report in 1999 (6) = (5)/(4)

Age-specific probability of being reported (7)

Age-specific probability of not being reported (8)

Estimated number in the synthetic cohort that do not appear in maltreatment reports (9)a

Cumulative percentage synthetic cohort appearing in maltreatment reports (10) (%)

0.0749 0.0388 0.0358 0.0332 0.0307 0.0286 0.0314 0.0259 0.0247 0.0106

0.0712 0.0380 0.0352 0.0326 0.0302 0.0282 0.0309 0.0255 0.0244 0.0105

0.9288 0.9620 0.9648 0.9674 0.9698 0.9718 0.9691 0.9745 0.9756 0.9895

20,000 18,577 17,870 17,241 16,678 16,175 15,718 15,232 14,843 14,482 14,329

7.1 10.6 13.8 16.6 19.1 21.4 23.8 25.8 27.6 28.4

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Age at first report of maltreatment, age x (1)

a

Although the size of the synthetic cohort can be any positive arbitrary constant, we used 20,000 as the starting size of the synthetic cohort, as this number approximates the size of birth cohorts in Cuyahoga County, Ohio. This number is used to calculate the percentages of the synthetic cohort that survive and that appear in reports.

981

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3. From the child abuse and neglect records, number of children in each age group that had at least one maltreatment report prior to 1999. 4. n Nx = (2) − (3)—number of children at-risk for a first ever maltreatment report. To calculate the number at risk of a first ever maltreatment, it is necessary to subtract from the population in the age interval, the number of persons in the age interval that had a prior maltreatment report. 5. n Dx —From the child abuse and neglect records, a count of the number of children experiencing the first maltreatment report in their life between ages x and x + n during 1999. 6. (5)/(4) Calculate n mx , the age-specific maltreatment rate, which is approximately equal to n Mx , which equals the number of first maltreatments ever in the age interval x and x + n divided by the mid-year at-risk population in age interval x to x + n:mx =n Dx /n Nx 7. The probabilities of having a first in lifetime maltreatment report between ages x and x + n. The probabilities are computed from the age-specific maltreatment rates by applying a factor that adjusts for the number of person years lived during an age interval, or n ax . In other words, the probability, n qx , equals n×n mx /[1 + (n−n ax )×n mx ]. We set the term n ax equal to 0.5 for all age intervals above the 0–1 age interval under the assumption that half of the maltreatment reports occurred during the first half of the year and half occurred during the second half of the year. (This corresponds roughly to the monthly reports of abuse and neglect.) For the 0–1 age interval, we set the term n ax equal to 0.3; this value implies that half of the maltreatment reports occurred during the first 3/10ths of the year and the remaining half in the last 7/10ths of the year. We arrived at this distribution of events within a year from the relatively large number of reports that occurred during the first 7 days of life. (Note: Because we used single-age intervals and because of our assumptions about the values for n ax , the effects of the n ax term on the life table estimates of maltreatment are small. Hence, others wishing to construct life table estimates of the prevalence of maltreatment can drop this term from their calculations if they have reason to believe that there is a relatively equal distribution of reports over time within given years.) 8. Compute n px , the probability of surviving (i.e., not being maltreated) from age x to x + n, which equals: px = 1−n qx . 9. Select the (constant) size of the synthetic cohort—lx . (This can be any number but we choose a number that is about the size of a typical birth cohort in Cuyahoga County): l0 = 20,000; changes in the size of the hypothetical population are calculated by applying n px , the probability of surviving to the next age interval to lx , the number not maltreated (number of survivors) at age x, or lx+n = lx ×n px . 10. Compute the cumulative percentages of children by age grouping that can expect to appear in maltreatment reports. For example, 7.1% of the synthetic cohort is expected to appear in maltreatment reports by the end of the 0–1 age interval; 10.6% of the synthetic cohort is expected to appear in reports by the end of the 1–2 age interval; and so on. The percentages in column (10) are derived from the data in column (9), which report the estimated number of children in the synthetic cohort that are expected “to survive,” that is, not to appear in a maltreatment report; hence, the percentages in column (10) represent the compliment of surviving a year without a report. To obtain the percentages in column (10), first we use the data in column (9) to calculate the percentage of the synthetic cohort that survives at the end of each age interval. For example, in column (9), we start with a synthetic cohort of size of 20,000; this represents the number of children in the 0–1 age interval. After applying the probabilities of surviving, we expect that 18,577 of the cohort will survive until the 1–2 age interval. The ratio of the number surviving until 1–2 (18,577) to the number in the synthetic

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cohort (20,000) times 100% yields a survival rate of 92.9%. The compliment of this—100% minus the survival rate—equals 100% minus 92.9%, or 7.1%. The 7.1% therefore represents the percentage of the synthetic cohort that “did not survive,” or which appeared in maltreatment reports during the age interval 0–1, and this number appears in column (10). Similarly, the expected number of the synthetic cohort that is expected to survive until the end of the 2–3 age interval, or 17,870, represents a 2-year survival rate of 89.4% (or 17,870/20,000 × 100%). The compliment of this 2-year survival rate (or 100% minus 89.4%) equals 10.6%, which is the cumulative percentage of the synthetic cohort that appears in reports through age interval 1–2. The rest of the percentages in column (10) are calculated in a similar fashion. Note, however, that the cumulative percentages of appearing in a maltreatment report that are associated with each age interval do not equal the sum of age-specific probabilities of appearing in a report. The reason for this is that in calculating the cumulative percentages, the base number is the size of the synthetic cohort, which in this case equals 20,000. On the other hand, the age-specific probabilities of appearing in reports use as their denominators the agespecific number of persons in the synthetic cohort that survived (or did not appear) in maltreatment reports.