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Title

Calculating disability-adjusted life years (DALY) as a measure ofexcess cancer risk following radiation exposure

Author(s)Shimada Kazumasa, Kai Michiaki

Citation

Journal of Radiological Protection, 35(4), p.763-775

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https://jopss.jaea.go.jp/search/servlet/search?5049038

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https://doi.org/10.1088/0952-4746/35/4/763
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Japan Atomic Energy Agency

Calculating Disability-Adjusted Life Years (DALY) as a
Measure of Excess Cancer Risk Following Radiation
Exposure
K Shimada1 and M Kai2
1

Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokaimura, Nakagun, 319-1195 Ibaraki

Prefecture, Japan
2

Oita University of Nursing and Health Sciences, 2944-9 Megusuno, Oita City, Oita Prefecture,

870-1201, Japan
E-mail: shimada.kazumasa@jaea.go.jp
Abstract
This paper has proposed that disability-adjusted life year (DALY) can be used as a measure of radiation
health risk. DALY is calculated as the sum of years of life lost (YLL) and years lived with disability(YLD). This multidimensional concept can be expressed as a risk index without a probability measure to
avoid the misuse of the current radiation detriment at low doses. In this study, we calculated YLL andYLD using Japanese population data by gender. DALY for all cancers in Japan per 1 Gy per person was
0.84 year in men and 1.34 year in women. The DALY for all cancers in the Japanese baseline was 4.8 in
men and 3.5 in women. When we calculated the ICRP detriment from the same data, DALYs for thecancer sites were similar to the radiation detriment in the cancer sites, excluding leukemia, breast andthyroid cancer. These results suggested that the ICRP detriment overestimate the weighting fraction ofleukemia risk and underestimate the weighting fraction of breast and thyroid cancer. A big advantage overthe ICRP detriment is that DALY can calculate the risk components for non-fatal diseases without thedata of lethality. This study showed that DALY is a practical tool that can compare many types of diseases
encountered in public health.

Keywords
DALY, Radiation risk, Cancer, Japan, ICRP, DetrimentIntroduction
Lifetime cancer mortality, incidence rate, and lives lost have been the previous indices ofhealth risk associated with radiation protection[1]. ICRP defined the detriment in Publication 60
by considering non-fatal cancers and the number of lives lost due to the difference in latent1

times [2]. The detriment has been used in estimating tissue-weighting factors anddetriment-adjusted nominal risk coefficients [3] and has been a measure of radiation risk used
for radiation protection. However, the detriment has the disadvantage that it can neither beappropriately interpreted nor used. Behind invention of the detriment, there are some historicalreasons on estimation of the cancer risk for radiation protection. The cancer incidence data has
been available to estimate the risk rather than the mortality risk[2]. It has become evident that
non-fatal cancers such as breast and thyroid cancers can be susceptibly increased by radiation
exposure[2].
For radiation protection, a multi-dimensional concept has been emphasized as a measure ofradiation risk. In particular, the question was the comparison of risks between fatal and non-fatal
cancers. ICRP (2007) considered the lethality and quality of life. Furthermore, ICRP considered
the length of life lost when evaluating the detriment of leukemia. As the other components, asocial judgment is involved when inferring the detriment in addition to the scientificinformation. A modifying factor is used for calculating the detriment by considering the qualityof life (QOL) for non-fatal cancer. ICRP judges that cancers should be weighted not only bylethality but also for pain, suffering, and any adverse effects of cancer treatment [2].
The concept of the detriment can be only used for comparison purposes between different
doses. The number of radiation-induced cancer deaths has been sometimes incorrectly inferredusing the detriment-adjusted nominal risk coefficient multiplied by the size of the populationthat received radiation exposure. Since the detriment is a multi-dimensional risk index, thedetriment-adjusted nominal risk does not mean the number of radiation-induced cancer deaths.
The calculated detriment expresses only a relative numerical value in an exact sense. In addition,
the detriment does not mean the risk of a population considered since it is calculated in ahypothetical population with both sexes, different ages and ethnic diversity [2]. The detriment isgiven as risk coefficients like a probabilistic quantity. These issues would be brought by thedefinition specific to radiation-related cancer risk.
It appears that the misuse partly occurred due to the probabilistic quantity and that themultidimensional concept as a measure of health risk failed to be properly communicated withpeople because ICRP defined the relative quantity specific to radiation protection. Risk
comparison does not work appropriately when one compares with other health risks that are
expressed by cancer incidence or mortality. Based on these reasons, it can be said that the
detriment as a risk measure has some disadvantages, if the detriment will be used not only forrisk comparison and but also for understanding of radiation risk.
After the Fukushima accident, the key issues regarding the use of detriment-adjusted nominal
risk coefficients have been identified [4]. Further, a misunderstanding of radiation risk may
occur from methods of determining low-dose risk and from the interpretation of the meaning. In
2particular, the probability measure of the detriment-adjusted nominal risk coefficients would
have led to misuse and misinterpretation in the Fukushima accident. The essential lessons
learned are that people want to quantitatively know whether future health effects will occur. The
cautionary notice that health effect calculation should be avoided would be not effective fromthe viewpoints of risk communication. Risk quantification of radiation would be required so as
to easily compare with other risk. The same method would be desirable as radiologicalprotection purpose
In common public health, measuring disease burden in a population requires a composite
metric for both premature mortality and the prevalence and severity of illness [5]. As a risk
measure of both common health and environmental health [6], there is a disability-adjusted life
year (DALY) that is developed from concepts of life lost. DALY is defined as the number ofyears lost due to ill-health, disability, and/or early death. DALY was developed by Harvard
University in 1990 and was further adopted to establish an order of priority for health issues by
the World Health Organization (WHO) [7, 8]. In this study, we calculated DALY to estimate
radiation cancer risk and compared this with the radiation detriment to discuss the effectivenessof DALY.
Calculation methods of DALY for cancer risk following radiation exposure
DALY is a measure of overall disease burden, expressed as the number of healthy years lost
due to premature death and disability by disease or unexpected accidents. To use DALY,
mortality and morbidity are combined into a single, common metric. Therefore, mortality can becompared with morbidity by DALY. The basic formula of DALY is expressed as the following
equations[9]:DALY=YLL+YLD(1)

YLL=Nm ×LE(2)

YLD=Ni ×DW×YD(3)

DALY: Disability adjusted life year (year)
YLL: Years of life lost due to premature mortality (year)
YLD: Years lived with disability (year)
Nm: Number of deaths (person)
LE: Standard life expectancy at age of death (year/person)
Ni: Number of incident cases (person)
DW: Disability weight
YD: Mean years of disability (year/person)

3

YLL due to be exposed to radiation is expressed with the following equations [10]:YLL(e,d)= CYLL(e,d)⁄N(e)g
CYLL(e,d)= ∫e+L Mi (e,d,a)∙RC(a)∙N(a)∙ S(a)⁄S(e) ∙LE(a)daYLL(d)= ∑g0 YLL(e,d)∙N(e)�∑g0 N(e)

(4)
(5)
(6)

e: Age at exposure

d: Radiation dose (Gy)a: Attained age (the age at which a cancer might occur)
CYLL: Collective year of life lost (person·year)
g: Standard life expectancy at birth is set at 80 years for men and 86 for women
L: Minimum latent period (year)
S: The probability of surviving
Mi: The excess absolute risk of cancer incidence exposed
RC: Ratio of cancer mortality per incidence
N: Age population distribution (person)
In DALY’s calculation, life expectancy is defined as one which occurs before the age to which
the dying person could have expected to survive if they were a member of a standardized model
population with a life expectancy at birth equal to that of the world’s longest-surviving
population, Japan.[8] In this calculations, life expectancy at birth was set 86 years for womenand 80 years for men using the Japanese life table as a reference. The minimum latent period L
was set at five-years for solid cancers and was set at two-years for leukemia [10]. For
calculating LE, the survival rates, S (t), were used in Equation 7:∞

LE(x)= T(x)⁄S(x) , T(x)= ∫x S(t)dt(7)

YLD(e,d)= CYLD(e,d)⁄N(e)(8)

Next, YLD due to be exposed to radiation was expressed as the following equations:g
CYLD(e,d)=DW·YD· ∫e+L Mi (d,e,a)·N(a)· S(a)⁄S(e) dagg

YLD(d)= ∑0 YLD(e,d)·N(e)�∑0 N(e)

(9)
(10)

CYLD: Collective years lived with disability (person·year)
DW: Disability weight
YLL and YLD for a population are calculated as a weighted average of the age-at-exposure
specific Mi. The weights are proportional to the number of people, N(e), who would be exposed
at age e.
The mean years of disability (YD) were calculated from the survival fraction exceeding 5
years (SF) as following equation (See Appendix. A):
4

YD=

log2

�

-0.2×logSF(11)

We separately calculated the excess absolute risk for cancer incidence Mi based on the Excess
Relative Risk (ERR) and Excess Absolute Risk (EAR) models and then combined the results
using an arithmetic mean [11, 12]. The parameters of these models were established in the
Tables A4.6 and 4.7 in ICRP Pub.103 [3]. The dose and dose rate effective factor was set at 2 forsolid cancers referencing ICRP.
The ratio of cancer mortality per incidence (RC) was expressed as the following equation:
RC(a)= λm (a)⁄λi (a)(12)λm : Cancer mortality baseline rate of Japaneseλi : Cancer incidence baseline rate of JapaneseCancer-specific incidence, mortality rates, and the survival fractions exceeding 5 years havebeen based on data from the National Cancer Center in Japan. The cancer-specific incidence andmortality rate statistics were from 2010 in Japan [13]; the survival fractions exceeding 5 years
were from 2003 to 2005 in Japan [14]. These baseline incidence and mortality rates wereobtained using spline interpolation from per 5 years to per 1 year. N was the number of people,
based on census data, in the Japanese population at age “e” for a reference year (2010) [15].
Figure 1 shows the age distribution of the Japanese population in 2010(N). For calculating
survival probabilities (S), the Japanese life tables for the year 2010 were used (Figure 2).

5Figure 1. Age population distribution in Japan in 2010

Figure 2. Number of surviving people per 100,000 in Japan in 2010
We used disability weights (DW) of cancer according to stage diagnosis/therapy in the WHOtable [16]. We established the DW of all cancer sites shown in Table 1.
6

Table 1. Disability Weight (DW) of each cancer site

Calculation results of DALY for cancer at single exposure to 1 Gy
Table 2 illustrates the results of DALY for each cancer site for Japanese after exposure at 1 Gydose per person. Furthermore, the ratio of DALY for each cancer site per DALY for all cancers
and the ratio of YLL per DALY for each cancer are shown in Table 2. Furthermore, in thesecalculations, we used the classification of cancer sites where they had the ERR or EAR model
parameters from the Tables A.4.6 and A.4.7 of ICRP Pub.103. In ICRP Pub.103, leukemia isexpressed as marrow. The other solid sites were set by subtracting the sum of each solid cancersite from all solid cancers.
Table 2. Calculation results of DALY for each cancer in the Japanese population exposed
at 1 Gy, the attributable fraction (%) of DALY for each cancer site in DALY for all cancers,
and those of YLL in DALY for each cancer

7

DALY for all cancer sites in the Japanese population exposed at 1 Gy was 0.84 per men. Inmen, lung cancer had the largest proportion at 13% of total DALY, followed by leukemia at 13%
and colon cancer at 12%. In women, DALY for all cancer sites in Japan at 1 Gy per women was
1.34. In women, breast cancer had the largest proportion at 27% of total DALY, followed bylung cancer at 16% and stomach cancer at 12%.
Compare calculation results of DALY with detriment
We have also discussed the validity of the calculation of DALY for radiation exposure. The
validity of these calculations was demonstrated by the comparison of the calculation results with
the ICRP detriment for the same condition. Note that there is a difference of calculations
between the ICRP detriment and YLD. The lethality fraction of cancer is used to represent QOL
in the calculation of ICRP detriment. On the other hand, YLD are able to consider QOL with
DW instead of the lethality fraction of cancer.
Radiation detriment for a tissue DT is calculated using Eqs.(13) , (14) and (15) .[3]𝐷𝐷𝑇𝑇 = 𝑅𝑅𝑇𝑇 �𝑘𝑘 𝑇𝑇 + 𝑞𝑞𝑇𝑇 (1 − 𝑘𝑘 𝑇𝑇 )�𝑙𝑙 𝑇𝑇

𝑞𝑞𝑇𝑇 = 𝑞𝑞𝑚𝑚𝑚𝑚𝑚𝑚 + 𝑘𝑘 𝑇𝑇 (1 − 𝑞𝑞𝑚𝑚𝑚𝑚𝑚𝑚 )g
g
g
𝑅𝑅𝑇𝑇 = �∫0 S(e)∙ ∫e+L Mi (e,a)∙ S(a)⁄S(e) da��∫0 S(e)

(13)
(14)
(15)

where、RT is the lifetime risk of excess absolute cancer incidence for a tissue exposed. In thispaper, in order to compare between DALY and ICRP detriment, we used RT which was
calculated based on the Japanese baseline incidence data of cancer instead of the nominal risk
coefficients that are averaged across seven western and Asian populations. kT is the lethality
fraction for a tissue. These values of 𝑘𝑘 𝑇𝑇 are used on the table 3. 𝑞𝑞𝑇𝑇 is a non-fatal weight(between 0 and 1) reflecting the reduced quality of life associated with living with a serious

illness, 𝑞𝑞𝑚𝑚𝑚𝑚𝑚𝑚 is 0.1 without thyroid cancer, 𝑞𝑞𝑚𝑚𝑚𝑚𝑚𝑚 of thyroid cancer is 0.2[3] and 𝑙𝑙 𝑇𝑇 is theaverage life lost due to the disease relative to normal life expectancy, expressed relative to theaverage over all cancers. These values of 𝑙𝑙 𝑇𝑇 are used on the Table 4. [3] Table5 shows theresults of detriment for each cancer site for Japanese exposed at 1 Gy.

Table 3. Calculation results of the lethality fraction for a tissue of cancer mortality per
incidence (𝒌𝒌𝑻𝑻 ) in Japan8

Table 4. The values of relative life lost 𝒍𝒍𝑻𝑻 from ICRP pub103, Table A4.5[3]9Table 5. The results of ICRP detriment for each cancer site in the Japanese population
exposed at 1 Gy and the ratio of the detriment in each cancer site per detriment for all
cancers

In these calculations, leukemia was the highest of cancer sites in the detriment due to radiation
exposure. Figures 3 and 4 show comparisons of the attributable fraction of the DALY and ICRP
detriment. The descending order for the detriment was almost same from that of DALY without
leukemia, breast and thyroid cancer. In men, leukemia showed the largest proportion at 31.2%of the total detriment, followed by lung cancer at 12.5%, colon cancer at 9.7%, and stomach
cancer at 7.7%. The percentage for leukemia in the detriment was higher than in the DALY. In
women, the detriment of leukemia had the largest proportion at 21.3% of the total detriment,
followed by lung cancer at 20.2% and breast cancer at 14.3%. The percentages of leukemia inthe detriment were higher than in DALY. On the other hand, breast and thyroid cancers in the
detriment were lower than in DALY.
These results supported the concept that DALY can show similar results as the ICRP detriment
without leukemia in men. This could be because of the value of relative life lost (𝑙𝑙𝑇𝑇 ). The

leukemia value of 𝑙𝑙 𝑇𝑇 is largest value in cancer sites in Table.4. Then, 𝐷𝐷𝑇𝑇 of leukemia iseffected by the correction of 𝑙𝑙 𝑇𝑇 . In women, these results suggested that the ICRP detriment

underestimated the weighting fraction of breast and thyroid cancer risk in total if one compared
it with DALY. This may have been because breast and thyroid cancer are non-fatal cancer.
10Figure 3. Comparisons of the attributable fraction of DALY and ICRP detriment for men

Figure 4. Comparisons of the attributable fraction of DALY and ICRP detriment for
women

Fraction of YLL in DALY
We have discussed the fraction of YLL in DALY. In Table.2, the fractions of YLL in DALY of
the cancer sites was almost higher than 70%. Only the fraction for thyroid cancer of women was
smaller than for other cancer sites. These results reflected the survival fraction exceeding 5
years. Table 6 shows the survival fraction exceeding 5 years of each cancer site in Japan and themean years of disability calculated using Eq. (11). With higher survival fractions exceeding 5
years of cancer site, there were smaller fractions of YLL in DALY.

Table 6.

The survival fraction exceeding 5 years and the mean years of disability for each11

cancer site in Japan

A major advantage over the ICRP detriment was that DALY can calculate the risk components
for non-fatal diseases. In DALY, the YLD component can be calculated using DW and YD thatwere defined through public health. Therefore, it is obvious that DALY is a practical tool thatcan compare many types of diseases encountered in common public health
Effects of DW values on DALYIn Table 1, we used DW values in the stages of diagnosis and treatment. DW values that were
established by WHO were 0.75 for the metastatic stage and 0.81 for the terminal stage
depending on the stage of cancer. Here, we calculated the DALY of each cancer with varying
DW values from 0.3 to 0.7 depending on the cancer stage and the DW values based on humansubjects. These results are shown in Figures 5 and 6 with respect to the different DW for both
the diagnosis and treatment stages (DW = WHO).

Figure 5. DALY with different DW values (Japanese Men)
12

Figure 6. DALY with different DW values (Japanese Women)
In men, the DALYs of colon cancer became larger than those of lung cancer with increasing
DW. In women, the DALY of thyroid cancer exceeded that of lung cancer with increasing DW.
These results suggested ways to reduce DALY. In men, it was an effective measure to reduce thelung cancer incident rate. In women, exploring a measure to increase QOL could be effective
because the YLD of breast and thyroid cancer was higher.
DALY in the case of chronic exposure
The preceding DALY indicated an average among the constituent ages of the population
acutely exposed at 1 Gy. Radiation cancer risk was higher at a younger age. Figure 7 shows thedependence of DALY on age-at-exposure at 1 Gy for Japanese population. In Figure 7, thehigher DALY at age 47 were attributed to the age population distribution in Japan (Figure 1).
People are always chronically exposed to natural radiation in their lifetimes, and radiation
workers are exposed in radiation control area. Table 7 shows the results of DALY of all cancers
in the case of a chronic exposure situation.

13

Figure 7. Dependence of DALY on age-at-exposure for Japanese population at an acuteexposure to 1 Gy
Table 7. Calculated results of DALY of all cancers in case of chronic exposure situations

DALY for baseline cancer in Japan
Cancers are caused not only by radiation but also by many factors in a normal lifestyle, forexample, smoking, food, and ultraviolet exposure. We then calculated the DALY of cancer
incidence and mortality for the Japanese baseline to compare with the radiation cancer risk. We
calculated DALY of baseline cancer using Eq. (16) using the cancer incidence baseline λi . Table
8 illustrates the results of DALY per person for each cancer site for the Japanese baseline.
1gg

DALY𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = ∑𝑔𝑔 𝑁𝑁(𝑎𝑎) �∫0 𝜆𝜆i (a)∙RC(a)∙N(a)∙LE(a)da + DW·YD ∫0 𝜆𝜆i (a)·N(𝑎𝑎) da�
0

14

(16)

Table 8. Calculation results of DALY for each cancer site in the Japanese baseline perpersonDALY for all cancers in the Japanese baseline was 4.8 in men and 3.5 in women. Comparing
the DALY of cancer between chronic lifetime exposure cases with 1mGy/year and all cancers in
the Japanese baseline, the ratios of DALY were 1.5% in men and 3.1% in women.
These results may not apply to non-Japanese people. DALY differed from cancer incidence,mortality baseline, and the survival fraction exceeding 5 years as well as the disability weight
and the mean years of disability. These results would depend on the Japanese genetic
background and lifestyle and health care standards. However, these results may be useful if one
considers an alternative measure of radiation risk to the ICRP detriment.
Conclusion
We calculated the DALY of radiation cancer risk as a measure of risk. DALY can be a practical
tool that can compare many types of diseases encountered in common public health, although
DALY for cancer sites was similar to the radiation detriment without leukemia. Moreover, thecalculated results of DALY can provide information to identify the components that should be
reduced in terms of public health. DALY may be a promising risk measure for effective
radiation protection.
Acknowledgement
We would like to thank Masahiro Munakata, Yu Maruyama and Toshimitu Homma of Japan
Atomic Energy Agency for supporting us to conduct this research.

15

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Appendix. A
We find in terms of the 5-years relative survival fraction (SF) the value of the mean years of
disability (YD). For this calculation, we assumed that relative survival rates 𝑅𝑅 depend on timesince diagnosis t as in Eq. (A-1)[10]𝑅𝑅(𝑡𝑡) = 𝑒𝑒𝑒𝑒𝑒𝑒[−𝑡𝑡 ∙ ℎ](A-1)

Here, R (t) is relative survivals rates for each cancer sites, h is mortality rates (death/year) and t
is time since diagnosis (year).
For these calculations, we use SF given in Table.6 and assumed that cancer mortality rate hdepend on age at diagnosis and are equal toℎ = −0.2 × log𝑆𝑆𝑆𝑆(A-2)

Here, log𝑆𝑆𝑆𝑆 is 5 years relative mortality rates, 0.2 is revised coefficient of transformation oflog𝑆𝑆𝑆𝑆 to 1 year relative mortality rate.

Here, to calculate YD, substitute R for 0.5 in Eq (A-1).

Solve equation for YD

0.5 = 𝑒𝑒𝑒𝑒𝑒𝑒[−𝑌𝑌𝑌𝑌 ∙ ℎ]
𝑌𝑌𝑌𝑌 = −log(0.5)ℎSubstitute h for Eq. (A-2) in Eq. (A-4) and express by the sign SF
𝑌𝑌𝑌𝑌 = −𝑙𝑙𝑙𝑙𝑙𝑙2(0.2 × log 𝑆𝑆𝑆𝑆)

17

(A-3)

(A-4)