An incidence-based (victims estimated by incidence), top-down approach (or attributable risk approach, measuring the proportion of a disease that is due to exposure to risk factor) was applied in this study from a societal perspective [18]. We employed the following steps to estimate the total economic burden, constituted by direct and indirect costs:
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1.
Population attributable fraction (PAF) was generated to estimate long-term impacts/costs attributed to child maltreatment.
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2.
Short-term and long-term direct medical costs were assessed by using national expenditure databases.
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3.
Indirect costs measured include productivity loss caused by abusive head trauma and economic burden deriving from DALYs.
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4.
Finally, sensitivity analyses were performed for the plausible range of the discount rate and the incidence / prevalence.
Estimating PAF
In the top-down approach, PAF for each disease i measured that how health outcomes and their associated costs may be attributed to child abuse, using the following formula [19, 20]:
$$ PAFi=\frac{P\left({RR}_i-1\right)}{P\left({RR}_i-1\right)+1} $$
(P: prevalence of child abuse; RR: the relative risk of the outcome i in those who experienced child abuse compared with those who did not)
Risk ratio (RR) or odds ratio (OR)
Several previous related systematic reviews and meta-analyses summarised the relevant health consequences [5, 15, 21, 22]. As adverse childhood experiences (ACEs) often intertwine with child maltreatment, cluster in children’s lives and cumulatively lead to poor health outcomes, we pooled the ORs from a recent systematic review and meta-analysis for the effect of multiple ACEs on health [5], rather than that for each category of child maltreatment.
The pooled prevalence
A literature review was performed to synthesize the evidence on epidemiological characteristics the consequences in Japan. The review focused on those published between December 2010 and March 2018 on Medline (PubMed), Web of Science, SCOPUS and CiNii Articles (Japanese literature). Details of the search strategy, search terms used, and inclusion and exclusion criteria are provided in the Additional file 2. We combined our review results with those studies in Japan included in an existing systematic review [23], and calculated the simple size-weighted mean incidence/prevalence. In addition, the median value was also calculated to examine the robustness (Supplementary Table 1). The annual incidence rate was obtained by the formula: [24].
$$ \mathrm{Incidence}\ \mathrm{rate}=\frac{\mathrm{Prevalence}}{\mathrm{Average}\ \mathrm{duration}} $$
Due to the lack of local data on the average duration, we adopted that published in Australia [12]: the average 5.6 years for physical abuse and 2.9 years for sexual abuse. Based on this finding, the weighted average of 4.6 years was used for other categories of abuse.
Direct medical costs
Short-term medical costs
For abusive head trauma (AHT) is the leading cause of death due to child abuse among children younger than 5 years old, [25] we estimated its hospitalization costs as short-term medical costs by multiplying the incidence of AHT under 3 years old [26], the age-specific population in 2016 [27], and admission medical fee per case [26].
There were two reported incidences: one is the “possible” incidence considering countable possibility of AHT cases at most and another one is the “presumptive” incidence representing victims had intracranial injuries or intentional injuries with certain ICD-10 code. We used the “possible” incidence for the general calculation and the latter one in sensitivity analysis. The total possible AHT cases aged under 3 years was about 8 times of the presumptive counterparts [26].
Long-term medical costs
For long-term medical costs, we used National healthcare expenditures 2016 and Patient Survey 2014 to simulate disease burden of relevant health consequences by sex and age group (0–14, 14–44, 45–64, above 65), and then multiplied with PAFs to calculate the attributable costs in the victim cohort of 2016 [5, 26, 28]. On the other hand, we did not include self-harm and collective violence because of the limitation to distinguish the two in the reported overall injury cases.
Indirect costs
In this study, we considered differential and loss of earning as a result of human capital depreciation is caused by mortality and morbidities. It was presented as a monetary value of DALYs and GDP per capita [15, 29]..
DALYs and its monetary value
The disease burden indicator DALY aggregates years of life lost for premature death and years lost due to disability for morbidities [19]. Related data were obtained from the WHO Global Burden of Disease (GBD) [30]. Using the pooled ORs as described by Karen et al. (2017) [5], we matched each related health outcome [5] with the cause of disease burden in the WHO GBD categories, though it was difficult to match some outcomes with the cause of GBD (Supplementary Table 2).
Then, monetary value was converted from DALY attributable to child maltreatment by multiplying DALY and GDP per capita [17] with adjustment of purchasing power parity in 2016 [31].
Productivity losses due to AHT fatal cases
Productivity loss due to fatal cases of child maltreatment was calculated based on the reported fatal cases, which figure was obtained from official data [32], and the average lifetime income subject to discounting. In 2016, there were 67 abuse-related deaths reported in Japan (not including family suicide), with the average onset age of 2 years [32]. The discounted lifetime income (from 18 to 65 years old) was calculated by assuming the long-term growth in labour productivity to be 1% per year [10].
DALYs losses of survival AHT
For disease burden due to survival AHT, we considered sequelae such as vision loss, brain damage, and reduced life span [33], and long-term health consequences as developing diseases in adulthood. We calculated the disease burden of AHT in 2016 by multiplying average cases and the estimated mean lifetime DALY loss per case at different severity (mild, moderate and severe) [33].
Long-term DALYs losses of other diseases
Then the long-term health consequences were calculated using the following formula:
$$ {\displaystyle \begin{array}{l}\mathrm{DALY}\ \mathrm{losses}=\Sigma \left({\mathrm{PAF}}_{\mathrm{i}}\ast {\mathrm{original}\ \mathrm{DALY}}_{\mathrm{i}}\right)\\ {}\left(\mathrm{i}:\mathrm{different}\ \mathrm{child}\ \mathrm{abuse}-\mathrm{related}\ \mathrm{health}\ \mathrm{outcome}\right)\end{array}} $$
Sensitivity analyses
A discount rate of 2% is generally performed which was recommended in the domestic guideline for cost-effectiveness analysis [34]. Whereas especially in the US, a discount rate of 3% has been selected and applied in the cost estimate reports of Centers for Disease Control and a best practices for the Social Return on Investment analysis recommended by experts and guidelines [9]. As such the parameter potentially affects the finally results, we adopted a plausible range of 0, 2 to 3% for sensitivity analysis.
In addition, we also calculated costs and disease burden using the incidence/prevalence data based on officially reported child abuse cases. To calculate the conservative incidence of child abuse by categories, we obtained the official data of victim cases reported by child consultation facilities in 2016 [2] and then divided them by the total population number in corresponding age [27]. Data by sex were not available. Co-current information was not available and the overlapped cases were not considered (Supplementary Table 3). The initial victim age is assumed to be 7 years old, according to an age-weighted incidence calculation based on official reported cases [2]. We assumed the probable abuse-related death cases to be 8 times of the reported cases based on the ratio of the presumptive and the possible incidence of AHT cases among children aged under 3 years [26].