An Estimation of the Monetary Value of the Person-Sievert Useful for Occupational Radiological Protection within the Healthcare System of Sweden

one of the key principles of radiological protection is the As Low As Reasonably Achievable (ALARA) principle (ICRP 2007): “The likelihood of incurring exposure, the number of people exposed, and the magnitude of their individual doses should all be kept as low as reasonably achievable, taking into account economic and societal factors.” To consider economic and societal factors, decision-aiding techniques such as cost-benefit analysis, cost-effectiveness analysis, and multi-attribute analysis can be used. These techniques have been described by several organizations such as the ICRP (1973, 1977, 1983, 1990, 1991, 2006), the Commission of the European Communities (1991), the International Atomic Energy Agency (2002), the US Department of Energy (2014), and the European ALARA Network (2019). One of the basic concepts in these decision-aiding techniques is the α value, which represents the monetary value assigned to a unit of collective dose for radiological protection purposes (ICRP 1983; US DOE 2014). By multiplying the α value ($ per person-Sv) with the collective dose (person-Sv), the cost of the detriment of ionizing radiation can be expressed in monetary terms (ICRP 1983; IAEA 2002; US DOE 2014). When the cost of achieving the next level of safety in radiological protection is higher than the achieved reduction of the detriment (expressed in monetary terms), an optimal solution has been found considering these two factors (ICRP 1973).

The purpose of balancing costs against radiological protection is that resources available to society are finite (both in terms of natural resources and manpower) and must therefore be prioritized (ICRP 1983). More resources spent in one risk context entails fewer resources spent in other risk contexts (Swedish Civil Contingencies Agency 2012). In this way, the optimal solution in radiological protection is not necessarily the one with the lowest collective dose (ICRP 2006, 2007; US DOE 2014). In general, cost-benefit analyses are now increasingly being required in the U.S. and in Europe (Baker et al. 2008; Hultkrantz and Svensson 2012; OECD 2012; Keller et al. 2021). Looking into the future of the healthcare system of Sweden, the impact of population aging is expected to lead to increasing expenditures (Government Offices of Sweden 2010). Therefore, balancing the resources spent on radiological protection with other needs within the healthcare system will probably be even more urgent in the upcoming decades.

According to ICRP’s recommendations (2006), nuclear utilities are supposed to determine their own α value for radiological protection. Reported by international surveys (ISOE ETC 1998, 2003, 2012, 2018), this circumstance has led to a wide variety of values being used. The most obvious way to determine an α value is to first decide on a value of a statistical life (VSL) (Eged et al. 2001; Katona et al. 2003). VSL can be defined as society’s willingness to pay (WTP) to prevent the death of one statistical person (US NRC 1995; Andresz et al. 2020). To calculate the α value, the VSL value is multiplied by the risk (the detriment-adjusted nominal risk coefficient from ICRP) (ICRP 2007).

In the past, the human capital approach has been the gold standard in estimations of VSL (Hultkrantz and Svensson 2012) and therefore also in determinations of α values (Andresz et al. 2020). The human capital approach is focusing on loss of economic production [gross domestic product (GDP) per capita] and does not include risk aversion and preferences of health (Hultkrantz and Svensson 2012). Several examples of α values based on this approach can be found in the literature (IAEA 1985; Hardeman et al. 1998; Eeckhoudt et al. 1999; Pandey and Nathwani 2003; Na and Kim 2009; Gordon et al. 2011; Lee et al. 2012; Fadul and Na 2016; Perez et al. 2017; Linsheng et al. 2019). In the revealed preference approach of WTP, observational data such as salary differences between occupations of varying risks can be used (Baum 1994). Eeckhoudt et al. (1999) and Linsheng et al. (2019) have reported α values based on the revealed preference approach.

Nowadays, the stated preference approach of WTP is the most preferable one in estimations of VSL (European ALARA Network 2019). In the stated preference approach, surveys are conducted of, for example, people’s WTP to avoid a small risk of death within a given scenario (Swedish Civil Contingencies Agency 2012; Hultkrantz and Svensson 2012). By dividing the respondents’ median WTP with the presented risk reduction, an estimation of their collective VSL within the given scenario can be determined (Olofsson et al. 2016). A so-called “benefit transfer” occurs when VSL values estimated from one risk context are converted into another risk context with appropriate adjustments (OECD 2012). In the literature, examples of benefit transfer can be found where VSL values estimated from the stated preference approach from other risk contexts than radiological protection have been used to determine α values (Bergman 1992; Bengtsson and Moberg 1993; Baum 1994; US NRC 1995; Engström et al. 2021; Andresz et al. 2022). With competing interests for recourses within societies, the strength of benefit transfer is that resources spent on radiological protection would equal other risk contexts throughout society.

However, it has been reported that even when the magnitude of the risk reduction is the same, people value risks differently from different risk contexts (Baum 1994; Itaoka et al. 2006; Swedish Civil Contingencies Agency 2012; Viscusi et al. 2014; Guignet and Alberini 2015; Keller et al. 2021). It is therefore also suitable to determine an α value that has been surveyed from people’s WTP to avoid a small risk of radiation-induced cancer death. Within the nuclear industry, a few examples of studies (Choi et al. 2001; Eged et al. 2001; Katona et al. 2003) can be found that have presented α values based on this approach. To our knowledge, this approach has not previously been used to determine an α value useful for occupational radiological protection within the healthcare system. Therefore, the aim of the present study was to estimate an α value useful for occupational radiological protection within the healthcare system of Sweden. This was achieved by conducting a survey of the stated preference approach focusing on two scenarios: the staff’s WTP for measures against radon exposure at home and their willingness to accept (WTA) getting compensated for x-ray exposure at work. The present study should be seen in the light of ICRP’s recommendation (2006) about stakeholder involvement as an important part of the optimization process.

MATERIALS AND METHODS

The present study was approved by the Swedish Ethical Review Authority (Dnr 2022-04593-01 and Dnr 2023-03506-02). A questionnaire with 16 items was developed using the contingent valuation method of the stated preference approach. Four medical engineers helped with face validity (Tsang et al. 2017), and three medical physicists helped with content validity (Tsang et al. 2017) of the questionnaire. A pilot test was performed on seven nurses, five radiographers and three nuclear technologists; deficiencies in a questionnaire can often be discovered by a small number of respondents (SCB 2004). After completing face validity, content validity, and pilot testing, respectively, some of the items were revised prior to the finalized version of the questionnaire. The questionnaire was sent out by email to staff (physicians, nurses, assistant nurses, radiologic technologists, and nuclear technologists) who are exposed to ionizing radiation at their workplaces in Region Västra Götaland (Sweden), a total of 4,680 employees. To those who had not responded in the first round, two reminding emails were sent out with a 2 wk interval. The questionnaire was distributed with the help of the software Survey & Report (Artologik 2022).

The questionnaire

The questionnaire started off by asking the respondents about informed consent. The first three items were about the respondents’ background information, including age, sex, and occupation. To help respondents put questions into a context, examples and aids are valuable (Hammit and Graham 1999; Boynton et al. 2004). Therefore, the respondents were given general information about mortality rates. For example, “The statistical risk of 40-y-old Swedes to die (from all causes) before they reach the age of 60 is approximately 3,800 out of 100,000 (3.8%)” (SCB 2023a). The respondents were also given information about radon as a radiation-related risk in homes: “Radon emits ionizing radiation that can damage cells in the body, which can lead to cancer. The time between exposure and the risk of dying in radiation-induced cancer is usually one or several decades.”

After these examples and aids, the respondents were presented with a scenario. They were asked to assume that they were living alone, that they had bought a new house with elevated values of radon, and that the protective measures against radon could be costly. The risk of dying in radiation-induced cancer one or several decades after moving into the new house, without taking any protective measures against radon, was presented as 40 out of 100,000 (0.04%) and with protective measures taken the risk would be halved, 20 out of 100,000 (0.02%). These risks are in line with estimated exposures from inhouse radon in Sweden (Swedish Radiation Protection Authority 2007). The respondents were then asked how much they were willing to pay to take protective measures against the radon (item 5). It is difficult for respondents to come up with an answer “out of the blue” to this type of item, which can lead to many zero answers and outliers (DTLR 2002).

To help the respondents, the payment-card method (DTLR 2002) was used. The respondents were given a set of values ($1, $10, $100, $1,000, $10,000, $100,000) and were asked to take a position of their WTP (yes, no, uncertain). Thereafter, the respondents were also asked to give their maximum WTP in an open question (item 6). The open question was then repeated (in item 7 and 8) but focused on other estimations of risk reduction. It has been shown that when respondents are asked about different magnitudes of risks, they are often not logical in their answers, which is referred to as scale-insensitivity (Beattie et al. 1998; Hammit and Graham 1999; Cropper et al. 2011; Olofsson et al. 2016). If the respondents (as a group) are willing to pay less to avoid a smaller risk of radiation-induced cancer death compared to a higher risk, they can be seen to have passed a “weak test” of scale-insensitivity. If the respondents’ estimations of VSL are not significantly different when derived from different magnitudes of risks (that is, their answers of WTP are nearly proportional to the magnitude of risk reduction), the respondents (as a group) have passed a “strong test” of scale-insensitivity (Corso et al. 2001). The problem with scale-insensitivity can be compensated for partly by calculating the median of the respondents’ estimations of VSL derived from different magnitudes of risk reduction (Leblanc et al. 1994; Eged et al. 2001), an approach that was used in the present study.

Item 9 asked the respondents to explain themselves if they had answered the same amount of money in items 6–8 with different risk reductions. The purpose of this item was to help the respondents to avoid scale-insensitivity by making them think about their answers and give them an opportunity to change them if they desired. Item 10 asked the respondents to explain themselves if they had answered $0 in any of the items 6–8. The purpose here was to exclude non-legitimized zero answers from respondents such as, “I would never buy a house with elevated values of radon” or “I think that the government should pay for protective measures against radon.” In this way, some of the respondents’ explanations (given in both items 9 and 10) could be interpreted as so-called protest answers, where the respondents have not accepted the given scenario. The exclusion of protest answers with the help of control items has been proposed by Olofsson et al. (2016). Some of the respondents gave explanations in the control items indicating that they considered protective measures against radon to be an investment that would increase the house price. Respondents with this interpretation of the scenario gave inaccurate estimations of their WTP to avoid a small risk of radiation-induced cancer death, and their answers were therefore also excluded.

In item 11, the respondents were asked about their WTA compensation for being exposed to a small risk of radiation-induced cancer death at their work instead of their WTP to avoid the same risk in their home. In item 11, the scenario was that all of the x-ray machines at their hospital had been replaced. Two new models of x-ray machines had been bought: a low-priced model A and a more costly model B. The staff that would work with model A were going to be exposed to twice as much ionizing radiation compared to the staff that would work with model B. The hospital was offering a compensation as a lump sum for staff that would accept to work only with model A. The risk of dying from radiation-induced cancer (one or several decades) after they started to work with model A was presented as 40 out of 100,000 (0.04%) and for model B as 20 out of 100,000 (0.02%). (These risks are in line with estimated occupational effective doses at our hospitals.) The structure and the presented risks in items 11–14 were identical to items 5–8 about risks with radon exposure. Item 15 was a control item in the same way as item 9 (about scale-insensitivity).

Surveys of the stated preference approach are hypothetical and can overestimate the respondents’ actual WTP in real-life situations (Blumenschein et al. 1998, 2008; Cropper et al. 2011). To reduce hypothetical bias, follow-up certainty items can be used (Blomquist et al. 2009; Svensson 2009; Loomis 2014; Olofsson et al. 2016). Therefore, item 16 asked the respondents (on a scale of 1 to 10) how certain they were that they would actually pay (or actually accept) the amounts of money they have given in the questionnaire in a real-life situation. Loomis (2014) has suggested that answers of less than seven can be seen as uncertain and can therefore be removed in a sensitivity analysis, an approach that also was used in the present study.

To compare the respondents’ estimation of VSL within the given scenarios of radiological protection with the Swedish public’s estimates of VSL from other risk contexts (Hultkrantz and Svensson 2012), a comparison was made between the two populations’ health characteristics by looking into differences in remaining number of quality-adjusted life years (QALYs). The instrument (EQ VAS) was developed by the EuroQol Group (1990) and has been used extensively within health economics (Szende et al. 2014). It contains a visual analogue scale that goes from 0 to 100, where 0 is labeled “the worst health you can imagine” and 100 is labeled “the best health you can imagine”. The respondents’ age distribution (item 1), sex distribution (item 2), and their EQ VAS-score (item 4) were collected in the questionnaire. The respondents’ EQ VAS-score for elderly (70- to 99-y-olds) and their life expectancy (for all age bands) were assumed to be the same as for the Swedish public. In the literature, the Swedish public’s age and sex distribution (SCB 2022a), their average life expectancy for different age bands (SCB 2022b), and their self-rated overall health score on EQ VAS (Teni et al. 2022) were found. In the absence of EQ VAS-scores for 0 to 29-y-olds, this age band was assumed to have the same score as 30 to 39-y-olds.

Analyses

When comparing VSL values and α values from different time periods and countries with the present study, adjustments were made with the help of historical exchange rates (purchasing power parities for actual individual consumption) (OECD 2024a), consumer price index (US BLS 2024), and GDP per capita (constant purchasing power parities) (OECD 2024b) with an income elasticity of 0.8 as described by the Organisation for Economic Co-operation and Development (OECD 2012). In the present study, the respondents’ estimations of VSL from each respective item were determined by dividing the median of their WTP to avoid (or their WTA getting compensated for exposure to) a small risk of radiation-induced cancer death with the risk reduction itself, which is consistent with the contingent valuation method of the stated preference approach (Hultkrantz and Svensson 2012; Olofsson et al. 2016). Respondents WTP and WTA estimations are not usually normally distributed (they are often positively skewed) and, therefore, their median or trimmed mean of WTP and WTA is often used (Jones-Lee and Spackman 2013). The Shapiro-Wilk test was used in the present study to test distributions for normality. A sensitivity analysis was performed of the respondents’ estimations of VSL by excluding:

• Uncertain answers, marked as less than 7 in the certainty item (item 16);

• Protest answers, given by the respondents’ statements in the control items (items 9, 10, or 15;

• Answers of increased house price, given by the respondents’ explanations in the control items (items 9, 10, or 15); and

• Irrational answers, respondents who answered an increasing WTP when the risk reduction was decreasing through items 6–8, or respondents who answered an increasing WTA (an increasing amount of money to be compensated with) when the risk reduction was decreasing through items 12–14.

The “excess burden of taxes” (EBT) describes the efficiency cost that a society suffers from taxes, since they affect labor supply and the price of goods from what would occur in a free market without taxes. The Swedish Transport Administration therefore recommends that, in health economic analyses, investments made with public funds should be inflated with a factor of 1.3 (Swedish Transport Administration 2023). This approach has also been suggested to be used within the healthcare system (Svensson and Hultkrantz 2015). To take this phenomenon into account when hospitals in Sweden use public funds for investments in occupational radiological protection, the recommendation of an α value was divided by the EBT.

ICRP’s radiation detriment-adjusted nominal risk coefficient (RC) for the working age population (18–64 y) of 4.2 × 10⁻² Sv⁻¹ was used (ICRP 2007). The radiation detriment is defined as “a function of several factors, including incidence of radiation-related cancer or heritable effects, lethality of these conditions, quality of life, and years of life lost owing to these conditions” (ICRP 2007). In this way, the α value could be calculated by eqn (1):

$$\mathrm{\alpha }=\left(\mathrm{VSL}\times \mathrm{RC}\right)/\mathrm{EBT}$$ (1)

Recommendations of α values are sometimes made as a single baseline value (α_base) and sometimes as a set of values with an aversion coefficient to allow the monetary value assigned to a unit of collective dose to increase with the level of individual exposure (Lochard et al. 1996; Eged et al. 2002; IAEA 2002; ICRP 2006). To consider economic factors in radiological protection, 80% of nuclear utilities around the world are using the concept of an α value, half of them are using a single α_base value, and the other half are using a set of α values (Andresz et al. 2020). However, when using a set of α values, the aversions coefficient is usually not applied for individual exposures under 1 mSv y⁻¹ (Lochard et al. 1996; IAEA 2002; ICRP 2006), which is the case for most of the staff exposed to ionizing radiation within the healthcare system of Sweden. In this way, the result of the present study should be seen as an α_base value.

For non-normal distributed data in the present study, Mann-Whitney U tests were used to analyse differences between independent groups, Wilcoxon signed rank tests were used to analyse differences between paired samples, and Friedman tests were used for several paired samples.

RESULTS

The questionnaire was returned from 718 respondents out of the 4,680 who received the invitation by email, a response rate of 15%. Of the respondents, 42% worked as physicians, 30% as nurses, 12% as assistant nurses, 13% as radiologic technologists, 1.4% as nuclear technologists, and 2.2% as the remainder “other occupations.” The respondents declared themselves as males (36%), females (64%), and non-binary (0.1%). The respondents’ age distribution was: 20 to 29-y-olds (6%), 30 to 39-y-olds (28%), 40 to 49-y-olds (28%), 50 to 59-y-olds (24%) and 60 to 69-y-olds (14%).

Some respondents did not answer all of the questions. As an example, 622 out of the 718 respondents answered the open question (item 6) about their maximum WTP to take protective measures against radon to decrease their future risk of dying in radiation-induced cancer from 40 out of 100,000 to 20 out of 100,000. In the sensitivity analysis of item 6, a total of 261 answers were included because 316 answers were excluded as uncertain, 13 as protest answers, 16 as answers of interpreted increased house price, and 16 as irrational answers. In Table 1, the respondents’ estimations of VSL from the six open items (items 6–8 and 12–14) are presented as median with interquartile range (IQR) for answers included in the sensitivity analysis, for answers excluded from the sensitivity analysis, and for all answers. A significant difference (Mann-Whitney U test, p < 0.05) could be seen for only one of the six items presented in Table 1 (item 6) between answers included and excluded in the sensitivity analysis. Shapiro-Wilk tests (p < 0.001) showed that the respondents’ answers were non-normally distributed. These distributions were positively skewed between 4.7 and 24.8.

Table 1.

The respondents’ estimations of VSL from the six open items are presented as median (IQR)_, for answers included in the sensitivity analysis, for answers excluded from the sensitivity analysis, and for all answers.^a

	VSL, median (IQR) (millions of USD)
Items	n	Answers included in the sensitivity analysis	n	Answers excluded from the sensitivity analysis	n	All answers
Item 6, WTP for measures against radon exposure at home, decreased risk from 40 to 20 out of 100,000	261	25 (5–50)	361	20 (5–50)	622	25 (5–50)
Item 7, WTP for measures against radon exposure at home, decreased risk from 20 to 10 out of 100,000	271	25 (10–100)	378	20 (5–83)	649	20 (5–100)
Item 8, WTP for measures against radon exposure at home, decreased risk from 4 to 2 out of 100,000	275	50 (5–250)	379	50 (5–250)	654	50 (5–250)
Item 12, WTA getting compensated for x-ray exposure at work, increased risk from 20 to 40 out of 100,000	201	200 (25–500)	286	150 (25–500)	487	150 (25–500)
Item 13, WTA getting compensated for x-ray exposure at work, increased risk from 10 to 20 out of 100,000	214	100 (30–1,000)	312	175 (50–1,000)	526	100 (50–1,000)
Item 14, WTA getting compensated for x-ray exposure at work, increased risk from 2 to 4 out of 100,000	215	500 (50–2,500)	316	500 (50–2,500)	531	500 (50–2,500)

^a The respondents’ answers were converted into millions of USD and rounded off.

For the sensitivity analysis (this time with irrational answers included), Friedman tests (p < 0.001) showed that the respondents were willing to pay less to avoid (and willing to accept less in compensation to be exposed to) a smaller risk of radiation-induced cancer death compared to a higher risk; thus, the respondents (as a group) passed the “weak test” (Corso et al. 2001) of scale-insensitivity. However, Friedman tests also showed significant differences (p < 0.001) of the respondents’ estimations of VSL derived from their answers with different magnitudes of risk, meaning that the respondents’ answers did not pass the “strong test” (Corso et al. 2001) (the near proportional test) of scale-insensitivity.

As can be seen in Table 1, VSL is in general higher for the WTA items (items 12–14) based on the scenario of the respondents’ willingness to accept getting compensated for x-ray exposure at work compared to the WTP items (items 6–8) based on the scenario of the respondents’ willingness to pay for measures against radon exposure at home. For answers included in the sensitivity analysis, the median VSL based on a WTA item was divided by the corresponding median VSL based on a WTP item with the same risk reduction, and these quotients were calculated to be 4, 8, and 10 for the three pairs of items. Of the respondents that were included in the sensitivity analysis, only 126 of them had answered all six items (items 6–8 and 12–14) with amounts of WTP and WTA different from zero. Based on these answers, individual quotients were calculated of VSL for the three pairs of items (WTA/WTP with the same risk reduction), a total of 378 quotients. The median of these individual quotients (WTA/WTP) was calculated to be 10.0 (95% CI 8.0-10.0). Wilcoxon signed rank tests showed significant differences of VSL (p < 0.001) between WTA and WTP for each of the three pairs of items with the same risk reduction (item 6 paired with item 12 and so forth).

For both of the scenarios, the respondents’ WTP for measures against radon exposure at home and their WTA getting compensated for x-ray exposure at work are valid for estimating the respondents’ willingness to avoid a small risk of radiation-induced cancer death. Therefore, all the 1,437 answers in the sensitivity analysis from both the WTP scenario (item 6–8) and the WTA scenario (item 12–14) were used to calculate the respondents’ overall median VSL to be $50 million (IQR $10–363 million). With the help of eqn (1), an α value (useful for occupational radiological protection within the healthcare system of Sweden) was calculated (and rounded off) to be $1,600 (IQR $320–11,700) person-mSv⁻¹. If the excess burden of taxes was not taken into account, the result would instead be $2,100 (IQR 420–15,200) per person-mSv⁻¹. As described in the methods, the result of the present study should be interpreted as an α_base value.

To compare the respondents’ estimations of VSL from the given scenarios of radiological protection with the Swedish public’s estimates of VSL from other risk contexts, a comparison was made between the two populations’ health characteristics. From the present study, the respondents’ mean remaining number of QALYs was calculated to be 31.1. From the literature (SCB 2022a, 2022b; Teni et al. 2022), the Swedish public’s mean remaining number of QALYs was estimated to be 33.2. The difference is thus 6.8%. The outcome of this comparison will be further analyzed in the discussion.

DISCUSSION

The aim of the present study was to estimate an α value useful for occupational radiological protection within the healthcare system of Sweden. In the sensitivity analysis of the survey, the overall median VSL was calculated to be $50 million (IQR $10–363 million) based on both of the given scenarios, the respondents’ WTP for measures against radon exposure at home, and their WTA getting compensated for x-ray exposure at work. The corresponding α value was established at $1,600 person-mSv⁻¹ ($2,100 person-mSv⁻¹ if excess burden of taxes is excluded).

The present study shows a considerably higher estimation of VSL (a factor of 15) compared to a literature review from Hultkrantz and Svensson (2012) of the Swedish public’s estimates with a median VSL of $3.4 million (2024 USD), in which most of the included studies are derived from WTP scenarios of road safety. Five factors were identified as possible explanations for this difference:

1. A factor that actually points in the opposite direction (a lower VSL for radiological protection compared to road safety) is that in health economics, preventing a risk of a consequence in the future is worth less than preventing the same risk at present time (OECD 2012; Swedish Civil Contingencies Agency 2012). Therefore, a social discount rate can be used in a cost-benefit analysis (Pandey and Nathwani 2003; OECD 2012; Swedish Civil Contingencies Agency 2012). For example, in a scenario of radiological protection, Mubayi et al. (1995) used a discount rate of 3% and a latency period between exposure and cancer death of 10 y, which gives a decreased VSL of 26%. In the present study, the expected time between exposure and cancer death (one or several decades) was explained to the respondents in the items and therefore included in their estimations of VSL. This scenario will probably give a lower estimate of VSL compared to another scenario where the respondents would assume to be exposed to the same risk at present time.

2. A factor that could have an effect on the difference in estimates of VSL are dissimilarities in the two populations’ health characteristics. However, the result of the present study showed that these dissimilarities were probably not an important factor, since the difference in the remaining number of QALYs between the two populations was estimated to be only 6.8%. The respondents’ age distribution does not include younger and elderly people, which tend to cancel each other out in comparison with the Swedish public. The respondents scored higher on EQ VAS compared to the corresponding sex and age bands of the Swedish public, which leans toward a higher remaining number of QALYs for the respondents. The respondents’ sex distribution includes more females compared to the Swedish public, and females have a longer life expectancy compared to men. In combination, this circumstance also leans toward a higher remaining number of QALYs for the respondents compared to the Swedish public. However, females tend to score lower on EQ VAS compared to men, which leans toward the opposite direction. Altogether, the difference between the two populations’ health characteristics was considered to be small.

3. A factor that can partly explain the respondents’ higher estimations of VSL compared to the Swedish public’s estimates is differences in income. The respondents’ weighted mean salary can be estimated to be around 50% higher than the mean salary for the Swedish public (SCB 2023b). On top of that, the employment rate of Swedes (15–75 y) is only 67% (SCB 2023c). It is well documented in the literature that there is a positive income elasticity between income and VSL (Viscusi 2014).

4. A factor (also explaining the respondents’ higher estimations of VSL compared to the Swedish public’s estimates) is diversities in given scenarios between studies. Respondents’ WTP are in general higher (80–160%) for risk reductions in a private scenario compared to a public scenario (Johannesson et al. 1996; Hultkrantz et al. 2006). Furthermore, respondents WTA to give up a good is reported to be 550% higher compared to their WTP for the same good (Horowitz and McConnell 2002). This result is similar to the quotients of the three pairs of items (the median VSL based on a WTA item divided with the median VSL based on a WTP item with the same risk reduction) of 4, 8, and 10 in the present study. The VSL estimate in the present study is based on both a private WTP scenario and a public WTA scenario. Most of the studies included in the literature review by Hultkrantz and Svensson (2012) are based on public scenarios of WTP. Together, differences in given scenarios can partly explain the higher VSL estimate in the present study compared to VSL estimates from the Swedish public.

5. A factor (also explaining the reported difference) is that people probably value risks differently from different risk contexts. For example, Fischhoff et al. (1978) have reported that their respondents ranked nuclear power as the riskiest out of 30 activities and technologies in society, 32% riskier than smoking. Several studies have also shown that estimates of VSL do differ between risk contexts (Baum 1994; Itaoka et al. 2006; Swedish Civil Contingencies Agency 2012; Viscusi et al. 2014; Guignet and Alberini 2015; Keller et al. 2021), but in contrast other studies have reported the opposite result (Chilton et al. 2002; Hammitt and Haninger 2010; Adamowicz et al. 2011). Examples have been reported where societies are spending far more resources (up to a factor of 8,000) to avert fatalities within radiation-related activities compared to medical screening and health care (Cohen 1980; Baum 1994).

Opinions differ on whether to use context-specific VSL estimates for different risk contexts compared to using one common VSL estimate for the whole society. The argument for using context-specific VSL estimates obviously rests on the assumption that VSL estimates are just that (context-specific) and therefore would be the best fit for society’s economic demand for improved safety (Graham 2007; Cropper et al. 2011; Robinson and Hammit 2011; Keller et al. 2021). In radiological protection, ICRP recommends stakeholder involvement as an important input in the optimization process (ICRP 2006). The present study should be seen as an attempt to achieve stakeholder involvement, and the result of the survey is a context-specific VSL estimate. The arguments for using one common VSL estimate for the whole society is based on a more rational view, expressing that all lives should be valued equally (Somanathan 2006) and that safety improvements therefore should be valued equally throughout society (Bergman 1992; Svensson and Hultkrantz 2015). For example, the US Department of Transportation recognizes different VSL estimates from different risk contexts but are choosing to use one common VSL estimate in their analyses independently of the nature of the risk (airline safety, road safety and so forth) (US DOT 2021). In this perspective, Carlsson et al. (2012) have shown that up to a third of public administrators would prioritize a project that would increase the public’s sense of safety over other projects that would actually save more lives.

Table 2 presents examples of recommended single α_base values reported in the literature, subdivided into categories, and compared to the result of the present study. As explained in the methods, comparisons of α values from different time periods and countries were made with the help of historical exchange rates (purchasing power parities for actual individual consumption) (OECD 2024a), consumer price index (US BLS 2024), and the GDP per capita (constant purchasing power parities) (OECD 2024b) with an income elasticity of 0.8 as described by OECD (2012). Therefore, α_base values given in Table 2 should be seen as international recommendations for the OECD countries in 2024.

Table 2.

Examples of recommended α_base values, subdivided into categories, and compared to the result of the present study. For comparison, the α values have been adjusted for time period and economic status of country.

Publication	Country	Recommended αbase values, rounded and adjusted for time period and country (USD per person-mSv)
Unclear origin of recommendation
ICRP (1973)	OECD	14–350
US DOE (2014)	U.S.	110–660
International surveys of αbase values used by nuclear utilities
ISOE ETC (1998) a	OECD	190–510
ISOE ETC (2003) a	OECD	450–4,900
ISOE ETC (2012) a	OECD	180–6,400
ISOE ETC (2018) a	OECD	830–9,300
Based on the human capital approach
IAEA (1985)	OECD	14
Hardeman et al. (1998) a	Belgium	83
Eeckhoudt et al. (1999)	France	54
Pandey and Nathwani (2003)	Canada	860
Na and Kim (2009) a	South Korea	41
Gordon et al. (2011)	Ghana	7
Lee et al. (2012)	South Korea	75
Fadul and Na (2016)	South Korea	46
Perez et al. (2017) a	Brazil	36
Linsheng et al. (2019) a	China	25
Based on the revealed preference approach
Eeckhoudt et al. (1999)	France	74
Linsheng et al. (2019) a	China	310
Based on benefit transfer from other risk contexts of the stated preference approach
Bergman (1992)	Sweden	290
Bengtsson and Moberg (1993)	Sweden	120–600
Baum et al. (1994)	USA	220
US NRC (1995)	USA	430
Engström et al. (2021)	Sweden	47–470
Andresz et al. (2022) a	France	140
Based on the stated preference approach within in occupational radiological protection
Choi et al. (2001)	South Korea	880
Eged et al. (2001) a	Hungary	24
Katona et al. (2003) a	Hungary	32
The present study (2024)	Sweden	1,400

^a Recommended α_base values are given a few years earlier compared to the year of publication, which is expressed in Table 2.

Despite adjustments for different time periods, the four international surveys conducted by the Information System on Occupational Exposure–European Technical Centre (ISOE ETC 1998, 2003, 2012, 2018) shows that nuclear utilities have increased the costs they are spending on radiological protection over the years. Publications in Table 2 of recommended α_base values based on the human capital approach have used a wide variety of assumptions and methods in their calculations. However, their difference (when adjusted for time periods and economic status of countries) is only a factor of 12, with the recommendation from Pandey and Nathwani (2003) as an outlier. In general, recommendations of VSL estimates based on the stated preference approach gives higher estimates compared to the human capital approach (US NRC 1995; Hugonnier et al. 2022), which is also reflected in the recommendations of α_base values presented in Table 2. The recommended α value in the present study is higher than the recommendations in studies based on benefit transfer from other risk contexts of the stated preference approach. An explanation for this result is the factors described above in dissimilarities in given scenarios between studies and also by dissimilarities in income between the respondents and the public. Despite adjustments for both different time periods and economic status between countries, the recommended α_base values from the four studies in Table 2 on which all are based on the stated preference approach within occupational radiological protection differ (the present study included) . The present study includes both WTP and WTA scenarios, while the other three studies only include WTP scenarios. Apart from pointing out this dissimilarity, the differences in estimates of α values between these four studies is difficult to explain. Overall, the recommended α value from the present study is in the high end compared to the other studies in Table 2, but inside the interval of values being used by nuclear utilities today reported by ISOE ETC (2018).

There are several limitations of the present study. For example, the response rate was only 15%, which can imply nonresponse bias of the results. In comparison, online surveys in general has been reported to have a mean response rate of 35% (Shih and Fan 2008; Daikeler et al. 2022). Fosnacht et al. (2017) have simulated response rates of surveys and shown that, if sampling size is over 500, estimates from surveys with response rates of 5–10% is often reliable. The 718 respondents in the present study can therefore probably be seen as enough to make general conclusions about the investigated population (staff who are exposed to ionizing radiation at their work in Region Västra Götaland, Sweden). Furthermore, the respondents can most likely be seen as a representative sample of the investigated population, since differences in their proportions of sex (6 percentage points) and in occupations (5 percentage points) were considered to be small. Another limitation of the present study is that around half of the respondents were uncertain of their WTP and WTA in the given scenarios and were therefore excluded in the sensitivity analysis. Some of the respondents gave a protest answer (to one of the control items) with statements indicating that they would not accept any increased risk at all regardless of its magnitude. Another common protest answer was that respondents believed that the employee was obligated to provide the best possible x-ray machines to the hospital and therefore felt that they could not see a purpose with the questionnaire. Also, some respondents interpreted an increased house price in their WTP to take protective measures against radon in their home, which incorrectly increased their estimations of WTP. Furthermore, the respondents were only given short information about radiation-induced cancer risks in the questionnaire. If they had been presented with more information, their answers might have been different. Finally, scale-insensitivity is problematic for most surveys using the stated preference approach (Svensson 2009; OECD 2012), and the present study was no exception. Despite all the drawbacks with surveys of the stated preference approach, the method is often seen as the best available option to estimate a society’s willingness to pay to prevent the death of one statistical person (Mubayi et al. 1995).

CONCLUSION

In the sensitivity analysis of the survey, the overall median VSL was calculated to be $50 million (IQR $10–363 million) based on the two scenarios: the respondents’ WTP for measures against radon exposure at home and their WTA getting compensated for x-ray exposure at work. The corresponding α value was established to $1,600 person-mSv⁻¹ ($2,100 person-mSv⁻¹ if excess burden of taxes is excluded) useful for occupational radiological protection within the healthcare system of Sweden. The recommended α value is in the high end compared to other studies but in the interval of values being used by nuclear utilities today. The present study shows some of the difficulties with and the extensive work necessary to establish an α value that rests on a solid foundation. The given α value should also be seen in the light of ICRP’s recommendation about stakeholder involvement as an important part of the optimization process.