Thyroid doses in Ukraine due to ¹³¹I intake after the Chornobyl accident. Report I: revision of direct thyroid measurements

Abstract

The increased risk of thyroid cancer among individuals exposed during childhood and adolescence to Iodine-131 (¹³¹I) is the main statistically significant long-term effect of the Chornobyl accident. Several radiation epidemiological studies have been carried out or are currently in progress in Ukraine, to assess the risk of radiation-related health effects in exposed populations. About 150,000 measurements of ¹³¹I thyroid activity, so-called ‘direct thyroid measurements’, performed in May–June 1986 in the Ukrainian population served as the main sources of data used to estimate thyroid doses to the individuals of these studies. However, limitations in the direct thyroid measurements have been recently recognized including improper measurement geometry and unknown true values of calibration coefficients for unchecked thyroid detectors. In the present study, a comparative analysis of ¹³¹I thyroid activity measured by calibrated and unchecked devices in residents of the same neighboring settlements was conducted to evaluate the correct measurement geometry and calibration coefficients for measuring devices. As a result, revised values of ¹³¹I thyroid activity were obtained. On average, in Vinnytsia, Kyiv, Lviv and Chernihiv Oblasts and in the city of Kyiv, the revised values of the ¹³¹I thyroid activities were found to be 10–25% higher than previously reported, while in Zhytomyr Oblast, the values of the revised activities were found to be lower by about 50%. New sources of shared and unshared errors associated with estimates of ¹³¹I thyroid activity were identified. The revised estimates of thyroid activity are recommended to be used to develop an updated Thyroid Dosimetry system (TD20) for the entire population of Ukraine as well as to revise the thyroid doses for the individuals included in post-Chornobyl radiation epidemiological studies: the Ukrainian-American cohort of individuals exposed during childhood and adolescence, the Ukrainian in utero cohort and the Chornobyl Tissue Bank.

Appendix. Errors in measured 131I thyroid activities

Estimation of classical measurement errors for ¹³¹I in the thyroid

It is known that at the fixed intensity of emission for a radioactive source, the probability to register $k$ counts using a measuring device for measuring time $t$ is defined by the Poisson distribution (Molina 1973). For a quite large intensity, the Poisson distribution is close to a normal distribution and can be written as:

$${I}_{\mathrm{th}}^{\mathrm{meas}}\sim N\left({I}_{\mathrm{th}}^{\mathrm{tr}},{\sigma }_{\mathrm{th}}^{2}\right),{I}_{\mathrm{bg}}^{\mathrm{meas}}\sim N\left({I}_{\mathrm{bg}}^{\mathrm{tr}},{\sigma }_{\mathrm{bg}}^{2}\right),$$

(A1)

where $N(m,{\sigma }^{2})$ is a normal distribution with expectation value $m$ and variance ${\sigma }^{2}$, ${I}_{\mathrm{th}}^{\mathrm{meas}}$ and ${I}_{\mathrm{bg}}^{\mathrm{meas}}$ are intensities of a radioactive source (providing the reading of a device in terms of pulses per second) registered during the measurement of thyroid and background, respectively, ${\sigma }_{\mathrm{th}}^{2}=\frac{{I}_{\mathrm{th}}^{\mathrm{tr}}}{{t}_{\mathrm{th}}}$ and ${\sigma }_{\mathrm{bg}}^{2}=\frac{{I}_{\mathrm{bg}}^{\mathrm{tr}}}{{t}_{\mathrm{bg}}}$ are the variances of corresponding measurement errors, ${t}_{\mathrm{th}}$ is the duration of a thyroid measurement, and ${t}_{\mathrm{bg}}$ is the duration of a background measurement. Index ‘tr’ denotes the true value, while ‘meas’ denotes the measured value.

In addition to the statistical error of registration, the values ${I}_{\mathrm{th}}^{\mathrm{meas}}$ and ${I}_{\mathrm{bg}}^{\mathrm{meas}}$ include an instrumental error, with variance ${\sigma }_{\mathrm{dev}}^{2}$. The full variances of the measurement errors for both thyroid and background are as follows:

$${\widehat{\sigma }}_{\mathrm{th}}^{2}=\frac{{I}_{\mathrm{th}}^{\mathrm{meas}}}{{t}_{\mathrm{th}}}+{\sigma }_{\mathrm{dev}}^{2}\mathrm{ and }{\widehat{ \sigma }}_{\mathrm{bg}}^{2}=\frac{{I}_{\mathrm{bg}}^{\mathrm{meas}}}{{t}_{\mathrm{bg}}}+{\sigma }_{\mathrm{dev}}^{2}.$$

(A2)

Based on the calibration method used one can write down the approximate relation:

$${C}_{a}^{\mathrm{meas}}\approx {C}_{a}^{\mathrm{tr}}\bullet \left(1+{\delta }_{C}\bullet {\gamma }_{1}\right),\hspace{1em}{\gamma }_{1}\sim N\left(\mathrm{0,1}\right),$$

(A3)

where ${C}_{a}$ is the conversion coefficient (Eq. 2) and ${\delta }_{C}$ is the relative error of the conversion coefficient, which includes the error of the ¹³¹I activity in the bottle source used for the device calibration, the device’s error of the measurement, and the error of the age-dependent factor $G$.

Using Eqs. (A1)‒(A3), ¹³¹I activity in the thyroid estimated from the direct thyroid measurement (see Eq. 1) can be presented as:

$${Q}^{\mathrm{meas}}\approx {C}_{a}^{\mathrm{tr}}\bullet \left(1+{\delta }_{C}\bullet {\gamma }_{1}\right)\bullet \left({I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{tr}}+{\sigma }_{n}\bullet {\gamma }_{2}\right),$$

(A4)

where ${\sigma }_{n}=\sqrt{{\widehat{\sigma }}_{\mathrm{th}}^{2}+{f}_{\mathrm{sh}}^{2}\bullet {\widehat{\sigma }}_{\mathrm{bg}}^{2}}$ and ${\gamma }_{2}\sim N(\mathrm{0,1})$.

Then, Eq. (A4) can be written as:

$${Q}^{\mathrm{meas}}\approx {C}_{a}^{\mathrm{tr}}\left({I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{tr}}+\left({I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{tr}}\right){\delta }_{C}\bullet {\gamma }_{1}+{\sigma }_{n}{\bullet \gamma }_{2}+{\delta }_{C}\bullet {\sigma }_{n}\bullet {\gamma }_{1}\bullet {\gamma }_{2}\right).$$

(A5)

Because ${Q}^{\mathrm{tr}}={C}_{a}^{\mathrm{tr}}\bullet ({I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{tr}})$, Eq. (A5) can be expressed as:

$${Q}^{\mathrm{meas}}\approx {Q}^{\mathrm{tr}}+{C}_{a}^{\mathrm{tr}}\bullet \left({\sigma }_{n}\bullet {\gamma }_{2}+\left({I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{tr}}\right)\bullet {\delta }_{C}{\bullet \gamma }_{1}+{\delta }_{C}\bullet {\sigma }_{n}\bullet {\gamma }_{1}\bullet {\gamma }_{2}\right)\approx {Q}^{\text{tr}}+{\sigma }_{Q}^{\mathrm{tr}}\bullet \gamma ,$$

(A6)

where ${\sigma }_{Q}^{\mathrm{tr}}={C}_{a}^{\mathrm{tr}}\bullet \sqrt{{\sigma }_{n}^{2}+{\sigma }_{n}^{2}\bullet {\delta }_{C}^{2}+({I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{tr}}{)}^{2}\bullet {\delta }_{C}^{2}}$ and $\gamma \sim N(\mathrm{0,1})$.

As ${I}_{\mathrm{th}}^{\mathrm{tr}}$ and ${I}_{\mathrm{bg}}^{\mathrm{tr}}$ are unknown, ${\sigma }_{Q}^{\mathrm{tr}}$ can be written as:

$${\sigma }_{Q}^{\mathrm{meas}}={C}_{a}^{\mathrm{meas}}\bullet \sqrt{{\sigma }_{n}^{2}+{\sigma }_{n}^{2}\bullet {\delta }_{C}^{2}+({I}_{\mathrm{th}}^{\mathrm{meas}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{meas}}{)}^{2}\bullet {\delta }_{C}^{2}}.$$

(A7)

The error factor ${\delta }_{C}$ of the age-dependent conversion coefficient ${C}_{a}$, (Eq. 2) can be calculated as:

$${\delta }_{C}=\sqrt{{\delta }_{b}^{2}+{\delta }_{G}^{2}},$$

(A8)

where ${\delta }_{b}$ is the relative error factor of the device’s calibration using a bottle phantom, and ${\delta }_{G}$ is the relative error factor of the age-dependent factor $G$.

The goal of the calibration of a device using a bottle phantom is to determine its sensitivity, i.e. to find out the values ${I}_{\mathrm{ref}}^{\mathrm{meas}}-{I}_{\mathrm{bg}}^{\mathrm{meas}}$ caused by radioactivity ${Q}_{\mathrm{ref}}$ of a reference radiation source. Therefore, ${\delta }_{b}$ is specified as:

$${\delta }_{b}=\sqrt{{\delta }_{\mathrm{ref}}^{2}+{\left(\frac{{\sigma }_{S}}{{I}_{\mathrm{ref}}-{I}_{\mathrm{bg}}}\right)}^{2}},$$

(A9)

where ${\delta }_{\mathrm{ref}}$ is the relative error factor of activity for the reference radioactive source, which is known from the technical documentation of the provider (Production Association “Isotope”); ${\sigma }_{S}$ is the error factor in measuring the intensity of the reference source.

Because the process of calibration using a bottle phantom is the same as the process of measurement of radioactivity in the thyroid, the error factor ${\sigma }_{S}$ can be calculated as:

$${\sigma }_{S}=\sqrt{{\widehat{\sigma }}_{\mathrm{ref}}^{2}+{\widehat{\sigma }}_{\mathrm{bg}}^{2}},$$

(A10)

where ${\widehat{\sigma }}_{\mathrm{ref}}^{2}=\frac{{I}_{\mathrm{ref}}^{\mathrm{meas}}}{{t}_{\mathrm{ref}}}+{\sigma }_{\mathrm{dev}}^{2}$ is the error variance of measuring the intensity of the reference source during the measurement time ${t}_{\mathrm{ref}}$.

For devices with missing information about the calibration, ${\delta }_{b}$ was, based on expert judgement, estimated to be 30%. The value of the relative error factor ${\delta }_{G}$ for the SRP-68-01 device was estimated from empirical data. According to Kaidanovsky and Dolgirev (1997) this factor depends on thyroid mass and is in the range of 15–18%. Since the scintillation crystals of the gamma-spectrometers were located significantly farther from the thyroid than that for the SRP-68-01 device, the influence of measurement geometry was less and ${\delta }_{G}$ was estimated for spectrometers, again based on expert judgement, to be 5%. This error factor was mainly due to variations in thyroid volume and thyroid position.

Based on Likhtarov et al. (2013c), the following observation model of thyroid radioactivity with classical additive error was selected in the present study:

$${Q}^{\mathrm{meas}}={Q}^{\mathrm{tr}}+{\sigma }_{Q}^{\mathrm{meas}}\bullet \gamma .$$

(A11)

Censoring

Measurements of ¹³¹I thyroid activity were considered reliable if the probability to detect a net signal, which is the difference between thyroid signal and background signal, with the assumption that its true value equals zero, was not more than 25%. This is equivalent to the condition ${I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}{\bullet I}_{\mathrm{bg}}^{\mathrm{tr}}\ge 0.68\bullet {\sigma }_{n}$, where ${\sigma }_{n}$ is defined by Eq. (A4), i.e., the critical limit of ¹³¹I in the thyroid was accepted to be $0.68\bullet {\sigma }_{n}$. The result of a measurement providing less than the critical limit was replaced by half of the critical limit. It was accepted that ${I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{tr}}=0.34\bullet {\sigma }_{n}$ under the condition ${I}_{\mathrm{th}}^{\mathrm{tr}}-{f}_{\mathrm{sh}}\bullet {I}_{\mathrm{bg}}^{\mathrm{tr}}<0.68\bullet {\sigma }_{n}$.

Estimation of Berkson errors due to deviation from the proper measurement geometry

Results of direct thyroid measurements conducted in May–June 1986 were associated with Berkson uncertainties (Masiuk et al. 2013, 2017) arising from deviation of the detector from the proper measurement geometry (where the lower edge of the detector is close to the lower point of the neck). Khrutchinsky et al. (2012) considered deviations from the standard measurement geometry for the SRP-68-01 device without collimator by 0–1 cm shifts in horizontal and vertical direction, and inclinations in horizontal and vertical planes; for such scenarios the relative error was estimated to vary from 0.24 to 0.51 depending on the age of the measured individual.

Following Khrutchinsky et al. (2012), a zero shift of the detector from the neck in horizontal direction was considered to be the proper measurement geometry. It was assumed that with 95% probability the shift of the detector in horizontal direction was in the range 0–2 cm from the neck. It was also assumed to have censored log-normal distributions of the shift with GSD = 2. The impact of a shift in vertical direction along the neck and its inclinations in horizontal and vertical planes were neglected. The uncertainty associated with detector deviation from the proper measurement geometry was considered to be unshared Berkson errors (Drozdovitch et al. 2015; Simon et al. 2015).

Let $G{F}_{j}$ be the factor due to shift of the j-th device’s detector in the horizontal direction away from the neck. For the sake of simplification the detector is calibrated in such way that $G{F}_{j}$ is equal to unity for the proper measurement geometry, i.e., ${\left.G{F}_{j}\right|}_{S=0}=1.$ Then $G{F}_{j}$ can be approximated by a function which is quadratic in the shift S:

$$G{F}_{j}={a}_{j}{\bullet S}^{2}+{b}_{j}\bullet S+1.$$

(A12)

Model of mixed classical and Berkson errors in thyroid measurements

Factors that are characterized by uncertainty of Berkson type are denoted as:

$${F}_{ij}=G{F}_{ij}\bullet {AF}_{j}^{\mathrm{meas}},$$

(A13)

where $G{F}_{ij}$ is the factor due to the shift of the j-th device’s detector in the horizontal direction away from the neck of the i-th individual; ${AF}_{j}^{\mathrm{meas}}$ is the adjustment factor for the j-th device.

The resulting thyroid radioactivity for the i-th individual measured by j-th device can be represented as:

$${A}_{ij}^{\mathrm{meas}}={F}_{ij}^{\mathrm{meas}}{\bullet Q}_{i}^{\mathrm{meas}},$$

(A14)

where ${Q}_{i}^{\mathrm{meas}}$ is the measured ¹³¹I thyroid activity associated with the classical additive error (Eq. (A11)).

The unknown true radioactivity ${A}_{i}^{\mathrm{tr}}$ is expressed as:

$${A}_{ij}^{\mathrm{tr}}={F}_{ij}^{\mathrm{tr}}{\bullet Q}_{i}^{\text{tr}}.$$

(A15)

The connection between ${F}_{ij}^{\mathrm{tr}}$ and ${F}_{ij}^{\mathrm{meas}}$ is determined by a Berkson multiplicative error:

$${F}_{ij}^{\mathrm{tr}}={F}_{ij}^{\mathrm{meas}}\cdot {\delta }_{F,ij},$$

(A16)

where error ${\delta }_{F,ij}$ has a log-normal distribution $\mathrm{log}({\delta }_{F,ij})\sim N(-\frac{{\sigma }_{F,ij}^{2}}{2},{\sigma }_{F,ij}^{2})$ with an expectation value ${\varvec{E}}{\delta }_{F,ij}=1$; ${F}_{ij}^{\mathrm{meas}}$ and ${\delta }_{F,ij}$ are stochastically independent, and ${\sigma }_{F,ij}^{2}$ is the variance of $\mathrm{log}({\delta }_{F,ij})$. Values of ${F}_{ij}^{\mathrm{meas}}$ and ${\sigma }_{F,ij}^{2}$ can be obtained by the two-dimensional Monte Carlo procedure described in (Simon et al. 2015).

According to Eq. (A11), the measured ¹³¹I activity in the thyroid, ${Q}_{i}^{\mathrm{meas}}$, can be expressed as:

$${Q}_{i}^{\mathrm{meas}}={Q}_{i}^{\mathrm{tr}}+{\sigma }_{Q,i}^{\mathrm{meas}}\bullet {\gamma }_{i},\hspace{1em}i=1,...,N,$$

(A17)

where ${\gamma }_{1},...,{\gamma }_{N}$ are the independent standard normal variables; ${\sigma }_{Q,i}^{\mathrm{meas}}$ are the individual standard deviations of errors of direct thyroid measurements that were estimated according to Eq. (10). The values ${\sigma }_{Q,i}^{\mathrm{meas}}\bullet {\gamma }_{i}$ and ${Q}_{i}^{\text{tr}}$ are independent random variables.

Substituting Eqs. (A17)–(A15) and denoting ${\overline{A}}_{ij}^{\mathrm{tr}}={F}_{ij}^{\mathrm{meas}}{\bullet Q}_{i}^{\mathrm{tr}}$ results in:

$${A}_{ij}^{\mathrm{meas}}={F}_{ij}^{\mathrm{meas}}\bullet {Q}_{i}^{\mathrm{meas}}={F}_{ij}^{\mathrm{meas}}\bullet \left({Q}_{i}^{\mathrm{tr}}+{\sigma }_{Q,i}^{\mathrm{meas}}\bullet {\gamma }_{i}\right)={F}_{ij}^{\mathrm{meas}}\cdot {Q}_{i}^{\mathrm{tr}}+{F}_{ij}^{\mathrm{meas}}\bullet {\sigma }_{Q,i}^{\mathrm{meas}}\bullet {\gamma }_{i}.$$

(A18)

Random variables $\{{\delta }_{F,ij},i\ge 1\}$, $\{{\gamma }_{i},i\ge 1\}$ and random vectors $\{({F}_{i}^{\mathrm{meas}},{Q}_{i}^{\mathrm{tr}}),i\ge 1\}$ are jointly independent, but ${F}_{i}^{\mathrm{meas}}$ and ${Q}_{i}^{\mathrm{tr}}$ can be correlated. If the notations ${\sigma }_{ij}={F}_{ij}^{\mathrm{meas}}\bullet {\sigma }_{Q,i}^{\mathrm{meas}}$ and ${\overline{A}}_{ij}^{\mathrm{tr}}={F}_{ij}^{\mathrm{meas}}\cdot {Q}_{i}^{\mathrm{tr}}$ are introduced, Eqs. (A14) – (A18) become the following:

$${A}_{ij}^{\mathrm{meas}}={\overline{A}}_{ij}^{\mathrm{tr}}+{\sigma }_{ij}{\bullet \gamma }_{i},$$

(A19)

$${A}_{ij}^{\mathrm{tr}}={\overline{A}}_{ij}^{\mathrm{tr}}{\bullet \delta }_{F,ij}.$$

(A20)

Equations (A19) and (A20) compose a dose observations model with a classical additive error and a Berkson multiplicative error (Masiuk et al. 2016, 2017).

Finally, the relationship between expectations of true radioactivity and radioactivity measured with Berkson error can be expressed as:

$${\varvec{E}}\left(\left.{\overline{A}}_{ij}^{\mathrm{tr}}\right|{A}_{ij}^{\mathrm{meas}}\right)={\varvec{E}}\left(\left.{A}_{ij}^{\mathrm{tr}}\right|{A}_{ij}^{\mathrm{meas}}\right).$$

(A21)