UNCERTAINTIES IN RADIATION DOSES FOR A CASE-CONTROL STUDY OF THYROID CANCER AMONG PERSONS EXPOSED IN CHILDHOOD TO ¹³¹I FROM CHERNOBYL FALLOUT

Abstract

Uncertainties in thyroid doses due to iodine-131 (¹³¹I) intake were evaluated for 2,239 subjects of a case-control study of thyroid cancer following exposure to Chernobyl fallout during childhood and adolescence carried out in contaminated regions of Belarus and Russia. Using new methodological developments that became available recently, a Monte-Carlo simulation procedure was applied to calculate 1,000 alternative vectors of thyroid doses due to ¹³¹I intake for the study population of 2,239 subjects accounting for sources of shared and unshared errors. An overall arithmetic mean of the stochastic thyroid doses in the study was estimated to be 0.43 Gy and median dose – 0.16 Gy. The arithmetic mean and median of deterministic doses estimated previously for 1,615 from 2,239 study subjects were 0.48 Gy and 0.20 Gy, respectively. The geometric standard deviation of individual stochastic doses varied from 1.59 to 3.61 with an arithmetic mean of 1.94 and a geometric mean of 1.89 over all subjects of the study. These multiple sets of thyroid doses will be used to update radiation-related thyroid cancer risks in the study population exposed to ¹³¹I after the Chernobyl accident.

INTRODUCTION

In the late 1990s, the International Agency for Research on Cancer (IARC) initiated a population-based case-control study of thyroid cancer among people exposed at young age to iodine-131 (¹³¹I) from Chernobyl fallout in the heavily contaminated areas of Belarus and Russia. Detailed description of study methods and estimates of risk of thyroid cancer related to radiation exposure in childhood and adolescence were published by Cardis et al. (2005). Overall, 2,239 subjects, both cases and controls, were included in the study, traced, and interviewed to collect individual behaviour and dietary information. However, only data on 1,615 persons were used by Cardis et al. (2005) for thyroid cancer radiation-associated risk analysis with deterministic (point estimates) thyroid doses calculated in 2004, ‘Thyroid Dosimetry 2004’ (TD04) (Drozdovitch et al. 2010). These point dose estimates are associated with uncertainties that arose from errors in the values of parameters of the dosimetry model. These errors are caused by lack of knowledge on precise values for parameters, incomplete data for exposure assessment, natural variability in parameters’ values between study participants, and the quality of questionnaire data on subject’s behavior and consumptions.

In the last decade, new data on dosimetry model parameters, such as measured deposition of ¹³¹I in Belarusian settlements (Drozdovitch et al. 2013; Khrushchinskii et al. 2014), and region- and age-specific thyroid mass-values derived from thyroid volume measurements (Skryabin et al. 2010), became available, allowing improvement of dose estimates. Also, significant methodological and practical improvements permit proper separation and treatment of sources of shared and unshared errors in dosimetry models (e.g., Drozdovitch et al. 2015; Likhtarev et al. 2014; Simon et al. 2015) and accounting for contribution of shared dosimetry errors in the radiation risk estimates (Kwon et al. 2016; Land et al. 2015).

To incorporate the new available data and new methodology in uncertainty assessment, we evaluated uncertainty and calculated 1,000 alternative vectors of thyroid doses due to ¹³¹I intake for the entire study population of 2,239 subjects. This paper describes the updated methodology and the results of the estimation of radiation doses to the thyroid with associated uncertainties for the subjects of the case-control study, called hereafter ‘Thyroid Dosimetry 2016’ (TD16). It should be noted that thyroid doses only due to ¹³¹I intake are considered in this paper. Contribution to the total dose of other exposure pathways, e.g., intake of short-lived radioiodines (¹³²I, ¹³³I, and ¹³⁵I) and radiotelluriums (^131mTe, ¹³²Te), external irradiation from radionuclides deposited on the ground, and ingestion of ¹³⁴Cs and ¹³⁷Cs, was negligible for most of the study subjects (Drozdovitch et al. 2010).

MATERIALS AND METHODS

Study subjects

The study group included 1,704 persons from Belarus and 535 persons from Russia, both cases and controls, all aged 0-18 y at the time of the accident in 1986. Study subjects and/or their mothers (if the subject was younger than 12 years old at the time of the accident) were interviewed to collect information on places of residence, time spent outdoors, undertaken countermeasures (evacuation, self-relocation, stable iodine administration), and consumption and origin of milk, milk products and leafy green vegetables in the period from 26 April through 20 June 1986. Table 1 shows study subjects’ distribution by age at the time of the accident, i.e., 26 April 1986. Sixty-three percent of the study subjects (1,411 out of 2,239) were younger than 5 years old at exposure. At the time of the accident, study subjects were residents of one of six heavily contaminated oblasts: Gomel or Mogilev Oblast in Belarus, or Bryansk, Kaluga, Orel or Tula Oblast in Russia, except 10 individuals who arrived at the study area sometime after 26 April 1986.

Table 1.

Distribution of study subjects according to age and oblast of residence at the time of the accident.

Age, years	Belarus		Russia				Other	Total
	Gomel	Mogilev	Bryansk	Kaluga	Orel	Tula
0-1.9	631	91	37	7	9	17	8	800
2.0-4.9	444	70	19	14	29	34	1	611
5.0-9.9	257	31	14	28	42	49	-	421
10.0-14.9	102	68	9	19	60	31	1	290
15.0-18.0	-	1	6	2	73	35	-	117
Total	1,434	261	85	70	213	166	10	2,239

Reconstruction of ¹³¹I thyroid doses

To reconstruct thyroid doses due to ¹³¹I intake a ‘semi-empirical model’ was used in this study. The semi-empirical model was based on the correlation between environmental contamination and thyroid doses derived from 130,000 direct thyroid exposure-rate measurements carried out in the territories with different contamination levels among individuals of different ages (Gavrilin et al. 1999). It should be noted that the same approach was used in the previous study by Drozdovitch et al. (2010). The Appendix provides a short description of the model.

Uncertainties in thyroid doses

A Monte-Carlo (MC) simulation procedure that maintains separation of shared and unshared errors was used to calculate stochastic doses. This procedure was similar to the one described by Drozdovitch et al. (2015) and consistent with the 2-dimensional MC method (Simon et al. 2015).

Scheme of calculation of stochastic thyroid doses

For a given dose realization, values of some model parameters were shared among a group of subjects, with the result that any error for these parameters were shared by all subjects within the group. Twenty-eight shared parameters (Table 2) were identified in the dose calculation procedures used in the study. They are coefficients of the semi-empirical model and parameters of the ecological model that describe the temporal variation of ¹³¹I in milk, dairy products and leafy vegetables. Other uncertainties were subject-dependent, or unshared, including errors related to the ratio of the thyroid dose coefficient and ventilation rate for a subject aged i to that for an adult (Table 3), and imprecise responses to questions administered during the personal interview (Table 4).

Table 2.

Parameters of semi-empirical model considered to be shared (subject-independent) in TD16.

Parameter			Central valuea (arithmetic mean (AM))	Distribution	Shared among subjects	Reference
Description	Symbol	Unit
Coefficient of semi-empirical model for combined dry-wet fallout	Ccomb	Gy m2 Bq−1	1.49×10−7	TLN(0.98×AM, 1.2, 0.7×GM, 1.4×GM)	all	(Gavrilin et al. 1999; Balonov et al. 2000)
Coefficient of semi-empirical model for only dry fallout	Cdry	Gy m2 Bq−1	1.44×10−7	TLN(0.98×AM, 1.2, 0.7×GM, 1.4×GM)	all	(Gavrilin et al. 1999; Balonov et al. 2000)
Coefficient of semi-empirical model for combined dry-wet fallout	B	Gy m2 Bq−1	1.6×10−8	TLN(0.94×AMb, 1.4, 0.5×GM, 2.0×GM)c	all	(Gavrilin et al. 1999; Balonov et al. 2000)
137Cs ground deposition density in the settlement:	qCsjx	Bq m−2	DBd	GSD = 1.4 – 1.6	in the same settlement
- Belarus (predominant dry deposition)			DB	TLN(0.94×AM, 1.4, 0.5×GM, 2.0×GM)		Derived from (Drozdovitch et al. 2013)
- Belarus (predominant wet deposition)			DB	TLN(0.9×AM, 1.6, 0.4×GM, 2.6×GM)		Derived from (Drozdovitch et al. 2013)
- Russia				TLN(0.9×AM, 1.6, 0.4×GM, 2.6×GM)		(Stepanenko et al. 2004)
137Cs ground deposition density on territory x for only dry fallout	qCsx,dry	Bq m−2	DB	TLN(0.9×AM, 1.6, 0.4×GM, 2.6×GM)	in the same territory x
The ratio of 131I-to-137Cs on territory x for only dry fallout	Rx,dry	Unitless	45	TLN(0.97×AM, 1.3, 0.6×GM, 1.7×GM)	in the same territory x	(Khrouch et al. 2004)
The ratio of 131I-to-137Cs on territory x for wet fallout	Rx,wet	Unitless	9.2	TLN(0.97×AM, 1.3, 0.6×GM, 1.7×GM)	in the same territory x	(Khrouch et al. 2004)
The exponent of considered power dependence of the ratio Rjx from qjx(137Cs) for territory x	α	Unitless	0.57	TN(0.57, 0.10, 0.37, 0.77)e	in the same territory x	(Khrouch et al. 2004)
The ratio of 131I-to-137Cs in the settlement:	Rjx	Unitless	DB		in the same settlement
- calculated using eqn. 15			calculated	TLN(0.9×AM, 1.6, 0.4×GM, 2.6×GM)		This paper
- measurement of 1 sample			DB	TLN(0.9×AM, 1.6, 0.4×GM, 2.6×GM)		This paper
- measurement of 2 samples			DB	TLN(0.94×AM, 1.4, 0.5×GM, 2.0×GM)		This paper
- measurement of 3+ samples			DB			Observed GSD
Date of single fallout	t0N	d	DB	U(DB-0.5, DB+0.5) f	in the same territory x	(Khrouch et al. 2004)
Fraction of total deposition occurred at day t0N	εN	unitless	DB	TN(AM, 0.15, 0.7×AM, 1.3×AM)	in the same territory x	(Khrouch et al. 2004)
Time when pasture season began	tpasture	d	DB	DU(DB-2, DB-1, DB, DB+1,DB+2) g	in the same territory x	(Khrouch et al. 2004)
The fraction of standard thyroid dose caused by 131I inhalation	kh	unitless	0.05	TLN(0.84×AM, 1.8, 0.3×GM, 3.2×GM)	all	(Khrouch et al. 2004)
The fraction of standard thyroid dose caused by 131I intake with leafy vegetable	kveg	unitless	0.11	TLN(0.9×AM, 1.6, 0.4×GM, 2.6×GM)	all	(Khrouch et al. 2004)
Correction factor for:
– cow’s milk	$K_1^{\mathit{cor}}$	unitless	1.0	-	-
– goat milk	$K_2^{\mathit{cor}}$	unitless	8.0	TLN(6.3, 2, 1.6, 25)	all	(Ilyin et al. 1972)
– milk from local dairy	$K_3^{\mathit{cor}}$	unitless	0.9	U(0.8, 1.0)	all	Expert judgment
– milk from shop	$K_4^{\mathit{cor}}$	unitless	0.8	U(0.7, 0.9)	all	Expert judgment
– breast milk	$K_5^{\mathit{cor}}$	unitless	0.3	TLN(0.28, 1.4, 0.14, 0.55)	all	(Simon et al. 2002)
– milk unknown	$K_6^{\mathit{cor}}$	unitless	0.9	U(0.8, 1.0)	all	(IAEA 1997)
– uncooked milk products	$K_{10}^{\mathit{cor}}$	unitless	0.7	U(0.5, 0.9)	all	(IAEA 1997)
– cooked milk products	$K_{11}^{\mathit{cor}}$	unitless	0.7	U(0.5, 0.9)	all	(IAEA 1997)
– fresh milk products	$K_{12}^{\mathit{cor}}$	unitless	0.9	U(0.8, 1.0)	all	(IAEA 1997)
– kefir	$K_{13}^{\mathit{cor}}$	unitless	0.7	U(0.5, 0.9)	all	(IAEA 1997)
– other milk products	$K_{14}^{\mathit{cor}}$	unitless	0.7	U(0.5, 0.9)	all	(IAEA 1997)
– leafy vegetables	$K_{20}^{\mathit{cor}}$	unitless	0.8	U(0.6, 1.0)	all	(IAEA 1997)
Removal rate of 131I from grass	${\lambda }_{\mathit{grass}}$	d−1	0.0638	TR(0.0438, 0.0638, 0.0838)	all	(Arefieva et al. 1988)
Effective clearance rate of the “indoor” hay from 131I	${\lambda }_f$	d−1	0.0338	TN(0.0338, 0.01, 0.0138, 0.0538)	all	(Koranda et al. 1971)
Rate of 131I elimination from milk	${\lambda }_{\mathit{cow}}$	d−1	0.99	TR(0.5, 0.99, 1.48)	all	(Müller and Pröhl. 1993)

^aOr range of values among study subjects.

^b$\mathit{GM}=\mathit{AM}\cdot {\left(\sqrt{\exp {((\ln \mathit{GSD})}^2)}\right)}^{-1}$ (derived from (Carroll et al 2006))

^cTLN(GM, GSD, min, max): truncated lognormal distribution with the following parameters: geometric mean (GM), geometric standard deviation (GSD), minimal value (min), maximal value (max).

^dDB = Database

^eTN(mean, SD, mode, max): truncated normal distribution with the following parameters: mean, standard deviation (SD), minimal value (min), maximal value (max).

^fU(min, max): uniform distribution with the following parameters: minimal value (min), maximal value (max).

^gDU(a₁, a₂, …, a_n): discrete uniform distribution that returns a₁, a₂, …, a_n with equal probability of n⁻¹.

Table 3.

Parameters of dosimetry model that are considered to be unshared (subject-dependent) in TD16.

Parameter			Central value (arithmetic mean (AM))	Distribution	Reference
Description	Symbol	Unit
Ratios of thyroid dose coefficient due to 131I intake for age i to that for adult	rDC(i)	unitless	Table 5	TLN(0.9×AM, 1.6, 0.4×GM, 2.6×GM)a	(ICRP 1993)
Ratios of ventilation rate for age i to that for adult	rV(i)	unitless		TLN(0.94×AM, 1.4, 0.5×GM, 2×GM)	(ICRP 1994)

^aTLN: truncated lognormal distribution with the following parameters: GM: geometric mean, GSD - geometric standard deviation, min: minimal value, max: maximal value.

Table 4.

Unshared errors associated with the information obtained from personal interviews in TD16.

Parameter			Central value (arithmetic mean (AM))	Distribution
Description	Symbol	Unit
Imprecise date of relocation, change of consumption habits or administration of stable iodine
Answer: “End of April”	-	-	28 April	DU(27, 28, 29, 30 April)a
Answer: “Beginning of May”	-	-	5 May	DU(1, 2, 3, 4, 5, 6, 7, 8, 9, 10 May)
Answer: “Middle of May”	-	-	15 May	DU(11, 12, 13, 14, 15, 16, 17, 18, 19, 20 May)
Answer: “End of May”	-	-	25 May	DU(21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 May)
Answer: “June”	-	-	15 June	DU(1 – 30 June by 1 day)
Consumptions
Consumption of cow milk, milk from shop, milk products (milk in soup, sour milk, sour cream, soft cottage cheese, kefir) reported during personal interview	DB	L d−1	Questionnaire	TN(AM, 0.25×AM, 0.5×AM, 1.5×AM)b
Consumption of leafy vegetables reported during personal interview	DB	kg d−1	Questionnaire	TN(AM, 0.3×AM, 0.4×AM, 1.6×AM)
Imprecise consumptions
Response: ““I did consume (foodstuff), but I do not remember how much (foodstuff) I consumed”	Vimp	L d−1 kg d−1		TLN(GM, GSD, GSD−2×GM, GSD2×GM)c
Response: “I do not remember if I consumed (foodstuff)”	Vimp	L d−1 kg d−1	Pcons×AM	TLN(GM, GSD, GSD−2×GM, GSD2×GM) with probability of B(Pcons)d

^aDU(a₁, a₂, …, a_n): discrete uniform distribution that returns a₁, a₂, …, a_n with equal probability of n⁻¹.

^bTN(mean, SD, mode, max): truncated normal distribution with the following parameters: mean, standard deviation (SD), minimal value (min), maximal value (max).

^cTLN(GM, GSD, min, max): truncated lognormal distribution with the following parameters: geometric mean (GM), geometric standard deviation (GSD), minimal value (min), maximal value (max).

^dB(p): Bernoulli distribution that returns “1” with probability (P_cons) and returns “0” with probability (1-P_cons).

Fig. 1 shows the scheme of calculation of stochastic thyroid doses. At the beginning of the calculation of alternative dose vector for the entire study population, we sampled values for all shared parameters from their probability distributions. To calculate one alternative dose vector, the same value was applied to the group of subjects for which this parameter was considered to be shared. In each simulated alternative dose vector, correlations were intentionally maintained between individual dose estimates of the study subjects with shared parameters’ values. In the process of alternative dose vector simulation, we sampled values of unshared parameters for each study subject from their distributions and calculated one dose realization for the study subject k, D_i,k, (Fig. 1). The one thousand realizations of dose, from D_1,k to D_1000,k, for the study subject k, represent a set of individual stochastic thyroid doses for that study subject (Fig. 1). The set of doses from D_i,1 to D_i,2239 represents the alternative vector of 2.239 thyroid doses number i of the entire study population.

Fig. 1.

Scheme of calculation of stochastic doses for the study population with account of shared and unshared errors.

Updates in dosimetry model parameters to calculate thyroid doses

The main improvements in the new study of thyroid dose estimates (TD16) as compared with the earlier estimated thyroid doses (TD04) are described below.

Ratio of thyroid dose coefficient due to ¹³¹I intake for age i to that for adult

Thyroid dose coefficient, i.e., absorbed dose in the thyroid per unit of ¹³¹I intake via inhalation or ingestion, is proportional to time-integrated activity of ¹³¹I in the thyroid and inversely proportional to the thyroid mass:

$$\mathit{DC}\propto \underset{0}{\overset{\infty }{\int }}A(0)\cdot e^{-({\lambda }_{\mathit{th}}+{\lambda }_r)\cdot t_{\mathit{dt}}}/m_{\mathit{th}}$$ (1)

where A(0) is the activity of ¹³¹I in the thyroid at t=0 (Bq); λ_th is the biological rate of ¹³¹I elimination from the thyroid (d⁻¹) (ICRP 1993); λ_r=0.0862 d⁻¹ is the radioactive decay rate of ¹³¹I.

Ratios of thyroid dose coefficient due to ¹³¹I intake for age i to that for adult, rDC(i), used in TD04, were based on the values of dose coefficients from ICRP Publication 67 (ICRP 1993) and did not account for gender difference in the thyroid mass-values. Since TD04 was developed, region- and sex-specific thyroid mass values for Belarusian children became available (Skryabin et al. 2010). These values were derived from the ultrasound-based estimates of thyroid volume performed by the Sasakawa Memorial Health Foundation (SMHF) in 1991-1996 among children from Gomel and Mogilev oblasts. Thyroid mass values for Russian children were taken from the results of the SMHF thyroid volume measurements’ campaign in Bryansk Oblast (Chernobyl 1997). Ratios of thyroid dose coefficient due to ¹³¹I intake for age i to that for adult were calculated as follows:

$$\begin{gathered} \mathit{rDC}(i)=\underset{0}{\overset{\infty }{\int }}A(0)\cdot e^{-({\lambda }_{\mathit{th},i}+{\lambda }_r)\cdot t_{\mathit{dt}}}/m_{\mathit{th},i}/\underset{0}{\overset{\infty }{\int }}A(0)\cdot e^{-({\lambda }_{\mathit{th},\mathit{adult}}+{\lambda }_r)\cdot t_{\mathit{dt}}}/m_{\mathit{th},\mathit{adult}} \\ =\frac{(\lambda {}_{\mathit{th},\mathit{adult}}+{\lambda }_r)\cdot m_{\mathit{th},\mathit{adult}}}{(\lambda {}_{\mathit{th},i}+{\lambda }_r)\cdot m_{\mathit{th},i}} \end{gathered}$$ (2)

Table 5 provides ratios of thyroid dose coefficient due to ¹³¹I intake for age i to that for adult that were revised based on new available information on thyroid masses and used in TD16. Values of ratios used in TD04 are also shown for comparison.

Table 5.

Ratios of thyroid dose coefficient due to ¹³¹I intake for age i to that for adult used in TD04 and TD16.

Age	TD04	TD16
		Gomel Oblast		Mogilev Oblast		Bryansk Oblasta
		Girls	Boys	Girls	Boys	Girls	Boys
0	8.6	8.5	9.4	8.8	9.7	10.1	10.8
1	8.5	6.1	6.7	5.5	6.0	7.9	8.1
2	7.6	4.6	5.1	4.2	4.6	6.3	6.4
3	6.7	3.8	4.2	3.4	3.8	5.3	5.3
4	5.8	3.2	3.6	2.9	3.2	4.6	4.5
5	5.0	2.9	3.2	2.6	2.8	4.1	4.0
6	4.4	2.6	2.9	2.4	2.7	3.3	3.7
7	3.9	2.4	2.7	2.3	2.5	2.6	2.8
8	3.4	2.2	2.5	2.1	2.4	2.4	2.5
9	2.9	2.1	2.3	2.0	2.2	2.2	2.3
10	2.4	1.8	2.2	1.9	2.1	2.0	2.2
11	2.2	1.6	1.9	1.6	1.8	1.8	2.0
12	2.0	1.5	1.7	1.5	1.6	1.5	1.9
13	1.9	1.4	1.5	1.3	1.5	1.3	1.6
14	1.8	1.3	1.4	1.2	1.3	1.2	1.4
15	1.6	1.2	1.3	1.1	1.2	1.2	1.3
16	1.4	1.1	1.2	1.1	1.2	1.2	1.2
17	1.2	1.0	1.1	1.0	1.1	1.1	1.1
18	1.0	1.0	1.0	1.0	1.0	1.0	1.0

^aThe same values were applied to the study subjects resided in Kaluga, Orel and Tula Oblasts.

Coefficients of semi-empirical model

The model coefficients, C_comb, B and C_dry, were estimated from linear regression between the standard thyroid dose in the settlement and the ¹³¹I deposition in that settlement (Gavrilin et al. 1999). Standard thyroid doses were derived from the results of direct thyroid measurements performed in adults residing in the settlement and were calculated using thyroid mass of 20 g (ICRP 1993) for both males and females. To account for updated thyroid masses, the values of coefficients of the semi-empirical model were adjusted to 1.2. This is a ratio of previously used thyroid mass of 20 g to the mass of 16.7 g, that is the arithmetic mean of thyroid mass-values in adult males and females that were derived from thyroid volumes measured by SMHF (Skryabin et al. 2010).

Variability of ¹³⁷Cs deposition density in the settlement

Parameters of distribution of caesium-137 (¹³⁷Cs) deposition density in settlements used in TD04 were based on expert judgment. Later, data became available to characterize parameters of distribution of settlement-specific ¹³⁷Cs deposition density (Drozdovitch et al. 2013). Table 6 provides characteristics of distribution of ¹³⁷Cs deposition density measured in selected settlements in Belarus. Parameters of distribution of ¹³⁷Cs deposition density in Russian settlements were taken from Stepanenko et al. (2004).

Table 6.

Characteristics of distribution of ¹³⁷Cs deposition density measured in settlements in Belarus where the study subjects resided during 26 April – 20 June 1986.

Oblast	Settlement	N of measured soil samples	137Cs deposition density (kBq m−2)
			Mean	SD	GM	GSD
Predominant dry deposition
Gomel	Burki	274	470	165	460	1.5
	Gden	301	130	40	130	1.4
	Kozeluzhie	284	210	64	210	1.4
	Novoselki	368	670	210	660	1.4
Predominant wet deposition
Gomel	Svetilovichi	573	1,110	540	1,020	1.7
Mogilev	Sidorovka	269	110	55	104	1.7

Ratio of ¹³¹I to ¹³⁷Cs activity in deposition

Since TD04 was developed, the results of measurements of ¹³¹I to ¹³⁷Cs activity in soil samples taken in Belarusian settlements have been collected and systemized (Khrushchinskii et al. 2014). These data made it possible to characterize more precisely the distribution of ¹³¹I to ¹³⁷Cs activity ratio in various Belarusian settlements. Table 7 provides characteristics of the distribution of the ratio of ¹³¹I to ¹³⁷Cs activity in deposition recalculated to 26 April 1986 for selected settlements in Belarus. For most settlements, the ratio of ¹³¹I to ¹³⁷Cs activity in deposition is characterized by GSD 1.3–1.4. Based on the available data, parameters of distribution of the ratio of ¹³¹I to ¹³⁷Cs activity in deposition were assigned and used for dose calculations in TD16 (Table 2).

Table 7.

Characteristics of distribution of measured ratio of ¹³¹I to ¹³⁷Cs activity in deposition recalculated on 26 April 1986 for selected settlements in Belarus where the study subjects resided during 26 April – 20 June 1986.

Oblast	Settlement	N of measured soil samples	Ratio of 131I to 137Cs activity in deposition on 26 April 1986
			Mean	SD	GM	GSD
Gomel	Babchin	19	11.4	2.7	11.0	1.3
	Borisovschina	8	16.9	4.7	16.3	1.3
	Bragin	41	21.6	6.7	20.5	1.4
	Chemerisy	6	29.7	10.1	28.2	1.4
	Chikalovichi	5	15.4	1.8	15.4	1.1
	Korma	8	9.1	3.5	8.6	1.4
	Krugovka	8	7.3	1.8	7.1	1.3
	Ostroglyady	13	15.4	5.9	14.4	1.4
	Popsuevka	8	8.9	2.3	8.6	1.3
	Savichi	9	12.9	1.2	12.9	1.1
	Soboli	12	20.9	6.4	19.9	1.3
	Vyshemir	13	24.3	10.0	22.6	1.5
	Zaspa	6	19.3	4.4	18.9	1.3
Mogilev	Bolshaya Zimnitsa	9	12.0	5.5	10.4	1.6
	Borkolabovo	14	6.2	1.9	5.9	1.3
	Derazhnya	11	6.4	1.9	6.1	1.3
	Malinovka	11	4.2	1.9	3.9	1.5
	Veprin	14	4.9	1.2	4.8	1.3
	Zheleznitsa	5	9.5	2.9	9.2	1.3

Re-definition of sources of shared and unshared errors and their distributions

The following parameters of the dosimetry model, which were considered in TD04 to be unshared errors, are considered to be shared errors in TD16:

• -Reduction factor for different types of milk and milk products, $K_l^{\mathit{eff}}$;
• -Effective rate of ¹³¹I decreasing in cow’s milk, λ_cow.

The type of distribution and its parameters used in TD04 were also reconsidered. For example, uniform distribution was assigned to the values of the reduction factor for different types of milk and milk products, $K_l^{\mathit{eff}}$, according to (Drozdovitch et al. 2015). A major change in parameters’ values was associated with the reduction factor for breast milk that was based on a milk consumption rate for lactating mothers of 0.8 L d⁻¹ and on a transfer coefficient from intake to breast milk for ¹³¹I of 0.37 d L⁻¹ (Simon et al. 2002).

RESULTS AND DISCUSSION

Summary statistics of thyroid doses

One thousand individual stochastic thyroid doses due to ¹³¹I intake were calculated for each person from the study population of 2,239 subjects. Table 8 shows the distribution of arithmetic means of individual stochastic thyroid doses. The overall arithmetic mean of individual mean thyroid doses for the entire study population was 0.43 Gy. More than half of the study subjects (53.8%) received a thyroid dose from ¹³¹I intake which was less than 0.2 Gy. The highest arithmetic mean of individual stochastic thyroid doses among the study subjects was 8.7 Gy. Twelve (0.5% of the total) study subjects were estimated to have received doses of greater than 5 Gy. Among these highly exposed persons, 3 individuals were evacuees from the 30-km zone around the Chernobyl nuclear power plant (NPP), 7 individuals resided in the southern part of Gomel Oblast close to the Chernobyl NPP, one individual resided in Mogilev Oblast in a settlement where ¹³¹I deposition density was 10.3 MBq m⁻², and one individual resided in contaminated settlements in the northern part of Gomel Oblast and consumed 0.4 L d⁻¹ of goat milk with ¹³¹I concentrations 8 times greater than that in cow’s milk (Table 2).

Table 8.

Distribution of arithmetic means of individual stochastic ¹³¹I thyroid doses.

Interval of the means of individual stochastic thyroid doses, Gy	N of subjects	%	Mean dose, Gy
<0.05	712	31.8	0.018
0.05 – 0.19	491	22.0	0.11
0.2 – 0.49	445	19.9	0.33
0.5 – 1.9	502	22.5	0.91
2.0 – 4.9	74	3.3	3.0
≥5.0	12	0.5	6.1
Entire studya	2,236	100.0	0.43

^aThree study subjects received zero thyroid dose due to ¹³¹I intake as they resided outside contaminated areas in April – June 1986.

Table 9 compares age- and gender-specific arithmetic means of individual stochastic thyroid doses estimated for the study subjects from Belarus and Russia. The thyroid dose decreased with increasing age: the arithmetic means in the <2, 2-4, 5-9, 10-14, and 15-18 years age groups were found to be 0.70, 0.51, 0.38, 0.19, 0.20 Gy and 0.43, 0.14, 0.03, 0.02, 0.02 Gy, in Belarus and Russia, respectively. Mean thyroid dose for the study subjects from Belarus was estimated to be more than five times higher than that of the subjects from Russia, i.e., 0.54 vs. 0.10. As can be seen from the table, at all ages (except age group 2-5 y in Russia) thyroid doses for boys were found to be higher than that for girls. It should be noted that in this study there were no gender-specific differences in parameters’ values, except for thyroid mass. Higher doses among boys were realized because of the larger fraction of milk consumers and higher consumption rates of cow’s milk and dairy products compared to the girls.

Table 9.

Distributions of arithmetic means of individual stochastic ¹³¹I thyroid doses between boys and girls at different ages and country of residence.

Age at time of the accident	Belarus						Russia
	Males		Females		All		Males		Females		All
	N	Dose (Gy)	N	Dose (Gy)	N	Dose (Gy)	N	Dose (Gy)	N	Dose (Gy)	N	Dose (Gy)
<2	304	0.80	418	0.63	722	0.70	48	0.53	22	0.22	70	0.43
2-4.9	169	0.64	345	0.45	514	0.51	49	0.063	47	0.22	96	0.14
5-9.9	112	0.49	176	0.30	288	0.38	44	0.048	89	0.026	133	0.033
10-14.9	35	0.38	135	0.14	170	0.19	14	0.037	105	0.019	119	0.021
15-18	-	-	1	0.20	1	0.20	40	0.021	76	0.020	116	0.020
Entire study	620	0.68	1,075	0.32	1,695	0.54	195	0.16	339	0.062	534	0.10

The fitted distribution of 1,000 individual stochastic doses for each subject was found to be approximately lognormal, and the geometric standard deviation (GSD) of that distribution was used to characterize the overall uncertainty for each individual. The GSD varied from 1.59 to 3.61 with an arithmetic mean of 1.94 and a geometric mean of 1.89 over all subjects. Table 10 shows the distribution of the GSDs linked to the subject-specific uncertainties of the stochastic thyroid doses. For almost three-fourths of the study subjects, the GSD was less than 2.0. The largest GSDs were associated with the smallest doses (see Fig. 2) and were defined by uncertainties mainly linked to the parameters of the dosimetry model in low contaminated settlements.

Table 10.

Distribution of the GSDs attached to the individual stochastic thyroid doses.

GSD interval	N of subjects	%	Mean dose, Gy
1.5 – 1.9	1,637	73.2	0.45
2.0 – 2.4	569	25.5	0.39
2.5 – 2.9	16	0.7	0.003
3.0+	14	0.6	0.065
Entire studya	2,236	100.0	0.43

^aThree study subjects received zero thyroid dose due to ¹³¹I intake as they resided outside contaminated areas in April – June 1986.

Fig. 2.

Subject-specific uncertainty (geometric standard deviation [GSD]) of individual stochastic doses as a function of geometric mean of 1,000 individual stochastic doses.

Comparison with deterministic dose estimates

We compared the arithmetic means of 1,000 individual stochastic thyroid doses calculated in this study (TD16) with the deterministic doses (TD04) estimated previously by Drozdovitch et al. (2010) for 1,615 study subjects (Fig. 3). The global arithmetic mean of simulated individual mean doses in this study was slightly lower compared to the mean of deterministic estimates of TD04, 0.43 Gy and 0.48 Gy, respectively. The median of the arithmetic means of stochastic doses among all study subjects was 0.16 Gy compared to that of the deterministic estimates of 0.20 Gy. The differences between the stochastic and the deterministic dose estimates (Fig. 3) are primarily due to the following:

• -The revision of thyroid-mass values;
• -The log-normal nature of distribution of individual stochastic doses;
• -The adjustment of parameters of the semi-empirical model; and
• -The imputation of missed values of consumption (because of imprecise answers obtained during the personal interviews) with substituted values using probability of Bernoulli distribution (Table 4).

Fig. 3.

Comparison of thyroid doses due to ¹³¹I intake estimated in TD04 (as deterministic) and TD16 (as arithmetic mean of 1,000 individual stochastic doses) for 1,615 study subjects.

Contribution of shared errors

Fig. 4 shows the cumulative distribution of 1,000 alternative dose vectors for the study population. Wide distribution (the 95% confidence interval of arithmetic means across alternative dose vectors is 0.274-0.590 Gy) indicates that sources of shared errors are important contributors to the uncertainty, because of number of previously unshared parameters were defined as shared parameters in TD16. Contribution of shared errors to the uncertainty in the thyroid dose estimates is also illustrated in Table 11, which provides information on the distribution of the 1,000-alternative dose realizations.

Fig. 4.

Cumulative percentage of 1,000 alternative dose vectors for the study population.

Table 11.

Parameters of distribution of 1,000 alternative dose vectors for the study population.

Parameter	1,000 alternative dose vectors for the study population, Gy
	2.5%	Median	Mean	97.5%
Minimum	0.0004	0.0634	0.243	1.51
Maximum	0.0046	0.218	0.755	4.94
Median	0.0014	0.122	0.424	2.66
Mean	0.0015	0.125	0.432	2.73
SD	0.0006	0.022	0.079	0.518

Reliability of dose estimates

Among the study subjects, we identified 64 individuals from Belarus with available results of individual measurements of exposure rate against their neck (called ‘direct thyroid measurement’) performed in May – June 1986. The measured exposure rate was corrected to the value of background in the room where measurements were performed and to external and internal contamination of human body to obtain a value of exposure rate that is only due to the ¹³¹I activity in the thyroid (Drozdovitch et al. 2019; Kutsen et al. 2019). Instrumental (i.e., based on direct thyroid measurements) thyroid doses due to ¹³¹I intake were then calculated for these subjects using information on individual behaviour and food consumption collected in our study.

There were 20 more study subjects from Belarus and 18 from Russia who also had direct thyroid measurements. However, the results of these measurements were not available for us, only thyroid doses that were calculated based on these measurements (Drozdovitch et al. 2010). To ensure the quality of the comparison between model-based and measurement-based (instrumental) thyroid doses, we did not include these 38 individuals in our dose validation exercise.

Fig. 5 shows a comparison between the model-based individual thyroid doses and the doses based on individual direct thyroid measurements for the same subjects. A rather wide range of ratios between the two sets of doses can be seen, for 70% individuals the correspondence between the two doses is within a factor of 3 (shown by dashed lines). The mean ± standard deviation of ratios of thyroid dose based on the dosimetry model to the dose based on direct thyroid measurements was found to be 1.2±1.3 (median of 0.8). The observed difference between model- and measurement-based thyroid doses could be explained by relatively large uncertainties in the doses calculated using the ‘semi-empirical’ model and uncertainties associated with recalling the information on relocation history and individual diet of the study subjects collected about 15 years after the Chernobyl accident. It has been reported that if the direct thyroid activity measurements are available for study subjects, individual doses, in general, can be estimated with a high degree of reliability regardless of the quality of questionnaire data (Drozdovitch et al. 2016). However, in our study, the direct thyroid measurements were not available for vast majority of study subjects. Therefore, the quality of questionnaire data could have had an impact on model-based dose estimates in our study. Such impact cannot be quantified as we are not able to check the true validity of the responses provided during the personal interview some 15 years after the accident.

Fig. 5.

Comparison of individual thyroid doses due to ¹³¹I intake for 64 study subjects assessed by the model with instrumental doses derived from direct thyroid measurements. Dashed lines show factor of 3 difference between two sets of doses.

CONCLUDING REMARKS

In summary, 1,000 alternative vectors of thyroid doses due to ¹³¹I intake were calculated for the study population using the most recent methodological developments and applying a Monte-Carlo simulation procedure with accounting for shared and unshared sources of errors in dosimetry model. Dose estimates were improved also by use of more precise information on model parameters, e.g. thyroid mass-values that are specific for population in the study area, detailed characterization of ¹³⁷Cs deposition density in the settlement and ratio of ¹³¹I to ¹³⁷Cs activity in deposition. The results of the study show that uncertainties in estimated thyroid doses are driven by shared errors associated with parameters of semi-empirical model. Quality of questionnaire data also have an impact on model-based dose estimates in our study. These multiple sets of improved doses will be used to update the radiation-related risks of thyroid cancer by accounting for sources of shared errors in the structure of the dosimetry model.