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Economic Considerations for Radiation Protection in Medical Settings—Is It Time for a New Paradigm?

Demeter, Sandor J.1

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doi: 10.1097/HP.0000000000001286
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Abstract

INTRODUCTION

This paper challenges the current classical cost benefit (CB) economic model for assessing radiation protection in medical settings. More specifically, it addresses the costs and benefits of marginal net dose reductions to patients, workers, or the public via expenditures in radiation protection programs (e.g., dose reduction options for imaging equipment, shielding, etc.). Alternate economic options are presented that may be more appropriate in such settings.

The ALARA (as low as reasonably achievable) principle is the foundation for the International Commission on Radiological Protection’s (ICRP) system of radiological protection. ALARA is used worldwide to drive radiation protection policy, guidelines, and regulatory oversight. The full definition of ALARA is, “The principle of optimization of protection: the likelihood of incurring exposures, 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” (bold added; ICRP 2007, p. 89).

The United States Nuclear Regulatory Commission (USNRC, 10CRF20.1300 definitions 2020) has an expanded definition: “…[ALARA] means making every reasonable effort to maintain radiation exposure as far below the dose limits set forth in Part 20 as is practical, taking into account the current state of technology, the economics of improvements in relation to benefits to the public health and safety, and other societal and socioeconomic considerations, and the utilization of nuclear energy in the public interest.”

Relative to the “economic factors,” ICRP has published a suggested cost benefit (CB) methodology. This CB model cost is related to: “The cost of radiation protection encompasses all the efforts made by society to obtain a desired level of radiation protection and is normally expressed in monetary terms” (ICRP 1983, p.16). Benefits are related to monetized years of life saved or averted negative health consequences related to stochastic effects (e.g., cancer).

Given the small incremental radiation dose reductions that may be realized in medical settings for patients, workers, or the general public (i.e., ranges of μSv to mSv), a CB model, which focuses on detriments in stochastic health effects, may not be the optimal methodology for economic analysis. This is due to the associated minimal theoretical benefits of reductions in lifetime cancer incidence or death based on ICRP Publication 103; i.e., a nominal composite risk of both fatal and non-fatal cancers of 5.5% per Sv or 0.0055% per mSv (ICRP 2007).

In addition, ICRP (2007) advises against the use of effective or collective doses for epidemiological evaluation or to assess stochastic risk at the aggregate or individual level. The Health Physics Society (HPS) and the National Council on Radiation Protection and Measurements (NCRP) also advise against such uses for collective dose given that small doses applied to large populations may produce spurious results given large variabilities in individual doses (HPS 2019; NCRP 2012). However, pragmatically, there are limited options in assessing detriment for economic purposes other than theoretically averted stochastic effects in low dose scenarios.

Health care systems are under increasing pressure to manage expenditures, including radiation protection programs. In light of this and in a time of growing health care fiscal restraint and austerity, organizations may focus more on the “economically and socially” acceptable components of the ALARA principle relative to radiation protection program costs.

There is also considerable, and growing, debate in the literature about the linear no-threshold (LNT) model, which is the foundation for the ALARA principle relative to radiation-induced stochastic effects at low doses. Many authors have assessed and challenged the LNT model, especially related to stochastic effects at low doses and significant benefits realized via medical imaging (Ablelquist 2019; Ring et al. 2018; Boyce 2017; Siegel et al. 2017; HPS 2019; Weber and Zanzonico 2016). Some go further to argue that there may be net biological benefit for low dose settings; i.e., hormesis (Costantini and Borremans 2019; Rithidech 2016). Vaiserman et al. (2019) conclude: “Overall, although probably not yet proven to be untrue, LNT has certainly not been proven to be true. At this point, taking into account the high price tag (in both economic and human terms) borne by the LNT-inspired regulation, there is little doubt that the present regulatory burden should be reduced” (abstract).

In concert with this, there is a trend to reduce overall regulatory burden (i.e., red tape reduction). Many jurisdictions are instituting policies to balance new regulations against regulatory reductions to achieve either a “0 sum game” (i.e., one in–one out rule) or a net reduction in regulatory burden (i.e., one in and more than one out). For example, the Canadian Government has a “one-for-one rule” (Government of Canada 2009, 2015), whereas the United Kingdom has a “one in–three out” policy initiative (UK Government Department of Health and Social Care 2016). This may counter increasing radiation regulatory burden related to the cliché of “how low can you go” relative to ALARA-driven dose reduction.

BACKGROUND

Health economics

Health economics is a broad field that assesses both the costs and benefits/risks related to health care services or interventions. Classically, health economics includes cost minimization (CM), cost effectiveness (CE), cost utility (CU), and cost benefit (CB) analyses. Table 1 (adapted from Demeter 2016) outlines the costs and outcomes for these categories noting that costs are always in dollars. For CM, the outcomes are sufficiently equal to choose the lowest cost option. For CE and CU, the outcomes are in years of life gained and quality adjusted years of life gained, respectively. For CB, all outcomes (e.g., a year of additional life, disability-free days, etc.) are all converted to dollar values such that disparate health care interventions and benefits can be compared once normalized to dollar values for outcomes. A “willingness to pay” model is usually used to determine the dollar values of outcomes in CB analysis.

Table 1 - Economic models in health care.
Cost Outcomea Incremental differencea
Cost minimization $ = Lowest cost
Cost effectiveness $ Natural units $/year of life gained
Cost utility $ QALY units $/QALY
Cost benefit $ $ $/$
aQALY = quality adjusted life years.

ICRP publication 103 (ICRP 2007) reiterates its ICRP publication 37 guidelines (ICRP 1983) on using a traditional CB approach to address the economic aspect of ALARA; i.e.: “The basic notion in the application of cost-benefit techniques to decision-making is very simple: an option is selected if the resulting net benefit exceeds that of the next best alternative and not otherwise. In the case of the introduction of a practice involving radiation exposures, the net benefit to society can be ideally expressed as B = V−(P + X + Y), where B is the net benefit from the introduction of the practice, V is the gross benefit, P is all production costs excluding radiation protection costs, X is the cost of achieving a selected level of radiation protection, and Y is the cost of detriment associated with that level of radiation protection… Although quantification of costs and benefits in this context will sometimes present difficulties in practice, the principles are crucial and are recommended by the Commission” (ICRP 1983, pp. 5 and 12).

For most medical radiation protection professionals, this approach is complex, not intuitive, and would generally require input by a health economist. It may involve significant subjectivity in assessing costs and benefits, which can be societally driven.

It should also be noted that in an era of “scarce health resources,” every dollar spent on radiation protection cannot be spent elsewhere. In other words, you lose the “opportunity” to direct these resources to other patient care services (i.e., the economic concept of “opportunity costs”).

Case study examples will be used to challenge a conventional CB approach and to present and compare various alternate approaches for the economic evaluation of radiation dose reduction in medical settings.

Case Study #1—CT dose reduction

A hospital is deciding on dose reduction options for a CT scanner purchase. The range in cost between the base model (with standard dose reduction options) and the full dose reduction optimized model is $300,000 (e.g., addition of iterative reconstruction software to base dose reduction options). For the sake of the example, the average dose reduction for a single body CT scan is ~ 5 mSv. The following economic analysis assumptions are simplified for the purpose of illustration.

Economic analysis assumptions and inputs

All studies are clinically justified, and protocols have been optimized to achieve the lowest possible radiation dose while still producing equally clinically acceptable images. There is no change in diagnostic accuracy between images acquired between the two options and, subsequently, no expected change in patient management or clinical outcomes based on the reduction in radiation dose. It is noted that there are no “dose limits” for patients akin to occupational or public dose limits. Diagnostic reference levels (ICRP 2017) can be used to optimize patient doses within jurisdictions.

The economic perspective will be limited to the incremental cost of the CT upgrade and the potential years of life saved or the anticipated dollar equivalent of the derived benefit relative to theoretically averted oncological stochastic effects. Table 2 outlines the baseline assumptions for costs and benefits. For simplicity, the only cost considered is the incremental one-time net cost of $300,000 at the time of purchase.

Table 2 - Economic assumptions.
Cost ($)a Benefits
Incremental one-time net cost of $300,000 at time of purchase. For simplicity this is the only cost considered.
Annual net increased costs in licensing or service contract related to the dose reduction option are not considered.
Lifetime of equipment 10 y. No depreciation costs or potential revenue are assigned at end of life.
The cost of the CT procedures themselves is not considered as alternate examinations are not being compared. It is assumed that the CT scan would be the ideal, optimized and justified examination.
No discounting or opportunity cost adjustments made.
$50,000 y−1 life year saved (not quality adjusted).b
Background 50% lifetime chance of getting cancer and an approximate 25% chance of dying of cancer (i.e., patients with cancer have an approximately 50% chance of dying of their cancer) (Canadian Cancer Society 2017).
Radiation composite detriment risk = 5.5% probability of lifetime fatal and non-fatal cancer per Sv (ICRP 2007).
To avoid the complexities of unpackaging the composite detriment risk, and to be conservative, all cancers are assumed to be fatal.
CT Case Study: The theoretical incremental cancer mortality benefitc of a net 5 mSv reduction = 0.0275% or a reduction of lifetime risk of dying of cancer by ~ 28/100,000 people.
Public Case Study: The theoretical incremental cancer incidence benefitc of a net 50 μSv reduction = 0.000275% or a reduction of lifetime risk of dying of cancer by ~ 28/10,000,000 people.
aUnited States dollars.
bMid-range of NICE proposed thresholds (NICE 2017).
cAs per ICRP 103 (ICRP 2007), these theoretical risk estimates are generally not to be used for prospective or retrospective epidemiological population risk analysis but are used to guide radiation protection programs/systems and are used for illustrative purposes in the case studies.

In the context of a heterogeneous CT population case mix, the “net benefit” is estimated simply, and conservatively, based on theoretical reduction in stochastic effects, focusing on cancer, and using ICRP 103 stochastic risk estimates (ICRP 2007). To be conservative, all cancer cases are assumed to be fatal.

The cost equivalent (benefit) per cancer fatality averted is unknown and variable depending on age at diagnosis and age at death relative to life expectancy. A value of ~$50,000 (USD) per quality adjusted life year (QALY) saved is commonly quoted and will be used as the estimated “willingness to pay” value per expected year of life gained (NICE 2017; Neumann et al. 2014). Given the complexity of assigning health utility indices, “quality” adjusted years of life saved will not be used.

Lung cancer is the chosen index solid tissue cancer given its high relative mortality burden. It is assumed that the average age of onset is 60 y in a population with a life expectancy of 80 y, resulting in a potential net benefit of 20 y per case of lung cancer. Lung cancer case fatality rates are assumed to be 100%. Overall, this is a conservative approach as it overestimates the risk of radiation-induced cancer mortality and does not consider competing causes of mortality and morbidity. The economic analysis, considering the above assumptions, is summarized in Table 3.

Table 3 - Economic analysis for a net reduction of 5 mSv per person.
Cost (one time) Benefit (y)a Benefit ($)b Cost benefit ratio ($)c Cost effectiveness ($) ratio (ICER)d
$300,000 0.0028 280 1,071 >50,000,000
aLife years saved per person = (estimated cancer related fatalities) × 20 y per life saved per 5 mSv averted = 28/100,000 × 20 y = 0.0056 y.
b$50,000 per year of life saved × 0.0056 years per person = $280.
cΔ cost ($)/Δ benefit ($) = CB = $300,000/$280 = $1,071 (i.e., cost > benefit, i.e., need to spend $1,071 for every $1 of benefit per person).
dΔ cost ($)/Δ benefit (y of life) = CE = $300,000/(0.0056 y) = $53,571,429 per additional year of life saved, ICER = incremental cost effectiveness ratio.

As illustrated in Table 3, a conventional CB approach results in a ratio factor of 1,071, which means that you must spend $1,071 for every $1 of benefit. The CE analysis results in an incremental cost effectiveness ratio (ICER) > $50,000,000 per additional year of life gained. It should be noted that CE ICER ratios ~ >$100,000 are generally declared to be cost ineffective (NICE 2017; Neumann et al. 2014). Based on these results, it is difficult, using conventional CB and CE economic analyses, to justify the $300,000 expenditure.

In addition, given the myriad of indications for CT scanning determining a “gross health benefit,” other than theoretical reductions in stochastic effects, would be difficult to compute. As discussed earlier, the “benefit” of potential lifetime reductions in stochastic effects is theoretical and is generally used for radiation protection monitoring and not epidemiological or economic analysis.

Case #2—Non-radiation/non-nuclear energy worker exposure

Non-radiation/non-nuclear energy worker dose limits are generally equivalent to public dose limits, i.e., 1 mSv, under the US Nuclear Regulatory Commission (NRC) 10CFR20.1301 a.1 guidance and the Canadian Nuclear Safety Commission (CNSC) Radiation Protection Regulations 13(1) (CNSC 2000). However, the NRC will allow a maximum public dose limit of 5 mSv with justification (USNRC, 10CRF20.1301 d.1-3 2020).

When designing a hospital-based nuclear waste storage room, posting/restricted access is required if the hourly dose rates exceed 20 μSv h−1 (USNRC, 10 CFR20.1301 a.2 2020) to 25 μSv h−1 [CNSC, Radiation Protection Regulations 21(b)]. Dose rates and conservative occupancy factors are used to estimate doses.

For the purpose of this case study and under the ALARA principle, the presumption is that the license applicant will demonstrate a maximum annual dose to members of the public and/or non-radiation/non-nuclear energy workers of 50 μSv (i.e., 1/20th annual dose limit), unless economic hardship can be demonstrated (CNSC 2010). The unanswered question is, how should “economic hardship” be considered in relation to potential risks?

For the sake of exploring this question, it is assumed that the hospital designed a Nuclear Medicine waste storage facility with shielding resulting in an estimated 100 μSv y−1 maximum dose (i.e., 1/10th annual dose limit) taking conservative occupancy factors into consideration (e.g., an adjacent secretary office). What would be the ALARA-based economic argument to increase renovation/construction funding to result in a 50 μSv y−1 dose?

Using the same conservative assumptions of the previous case study as outlined in Table 3, a CB approach would be: $50,000 per year of life saved × 0.000056 years per person = $2.80 per person.

The CB breakeven point would be that the cost of additional shielding should not exceed $1.40, which is impossible and demonstrates why the conventional ALARA-driven CB approach is not appropriate.

Alternate approaches

Alternate economic approaches include a cost-benefit approach that sets a threshold based on cost per unit of dose averted vs. years of life gained (i.e., $/unit of dose reduced), setting thresholds based on reducing theoretical incremental radiation-induced lifetime cancer risks to a fixed rate (e.g., below 1/100,000, one order of magnitude below background, etc.) or setting thresholds at a fraction of background radiation dose. These will be discussed in turn below.

Cost per unit of dose averted

Although this approach avoids converting dose into stochastic effects, it still has the same problem of what dose reduction is considered reasonable and at what cost. Similar to setting a cost effectiveness threshold of $50,000 per additional year of life saved, a societally driven value judgement will have to be made on what is a reasonable cost per mSv or μSv averted in public or occupational settings.

For the first case study, this would equate to $300,000 per 5 mSv averted = $60,000 per mSv averted per patient scanned. The cost would drop significantly if collective effective doses averted were used as the denominator.

For example, at a rate of 3,000–5,000 scans mo−1 (36,000–60,000 y−1) per CT scanner, this would result in a collective dose reduction of 180,000–300,000 person mSv y−1 at a cost of $1.70 to $1.00 per person mSv averted. Holding utilization constant and assuming a camera life of 10 y, this would reduce the cost per mSv averted by a factor of 10, noting that such projections are unreliable as technologies will evolve and new CT scans may deliver lower doses for less additional cost. This is noting recommendations to not use collective dose for such modeling by the Health Physics Society (HPS 2019).

The second case study is more difficult to conceptualize given the almost negligible averted stochastic event benefits of a net 50 μSv y−1 reduction in dose. The economic justification to expend or forgo resources for additional shielding depends on the cost of additional shielding. However, as stated earlier, a reasonable threshold for cost per dose averted is more societally than scientifically driven and remains a topic for discussion and clarification.

Probabilistic approach

A risk avoidance probabilistic approach is used for other environmental hazards. For example, the US Environmental Protection Agency (EPA) uses values of 1/10,000 to 1/1,000,000 lifetime risk for environmental carcinogens to trigger remediation actions (USEPA 2000). Setting the thresholds equal to averting a 1/10,000, 1/100,000, or 1/1,000,000 lifetime cancer risk from ionizing radiation, and using ICRP Publication 103 data (i.e., 5.5% lifetime risk of cancer risk Sv−1) would result in 1,818 μSv, 181 μSv, and 18 μSv thresholds, respectively. This approach would dictate that if the proposed threshold is met, no additional resources would be required to reduce the dose any lower.

These figures need to be put into the context of natural background radiation exposures of 2 to 3 mSv y−1 in North America (USNRC 2017), which equates to ~1/9,000 to 1/6,000 lifetime risk of cancer. In addition, it needs to be noted that the background lifetime risk of cancer is ~50% (Canadian Cancer Society 2017), which speaks to factors other than radiation for causation.

Again, like the cost per unit of dose averted option, setting a reasonable “risk threshold” is also societally driven.

Thresholding relative to background radiation dose

Current NRC and CNSC public dose limits are generally an order of magnitude less than occupational dose limits. Given a North American annual background radiation dose of 2 to 3 mSv (USNRC 2017), this would equate to 0.2 to 0.3 mSv y−1 (i.e., 200 μSv to 300 μSv y−1) or a 1/18,000 to 1/12,000 lifetime risk of cancer using ICRP publication 103 estimates. As in the previous example, no additional resources would be required to reduce the dose any lower once a threshold is set and deemed to be societally acceptable.

This is noting that the NCRP (1993) sets the “negligible individual radiation dose” at 0.01 mSv y−1. Arguments have been made that the negligible individual dose threshold should be raised to 0.1 mSv y−1 as “…radiation protection should not include trying to protect people from radiation doses that are consistent with variations in background radiation” (Abelquist 2019, abstract).

DISCUSSION

Given small potential dose reductions to patients, workers, or the public in medical settings, combined with small incremental theoretical benefits in averted stochastic effects, it is difficult to justify dose reduction expenditures using the ICRP recommended conventional CB economic model.

Zanzonico (2016) makes the argument that baseline clinical benefits of diagnostic imaging studies significantly outweigh the theoretical stochastic risks associated with ionizing radiation. Zanzonico (2016) also argues that the LNT model should not be applied at the individual level and that effective dose is best suited to guide population-based radiation safety programs, a sentiment that is echoed by the ICRP (2007). This would also speak against using LNT and effective dose to conduct conventional CB or CE economic studies, as it may be a misapplication of original intent.

Brenner (2012) also argues against the use of effective dose as a surrogate for individual risk as too “generic” and proposes the use of “effective risk,” which can be better tailored to the age and gender of an individual.

Using an LNT model, Cipriano et al. (2011) published a CE/CU study comparing thresholds blends of MRI and CT to monitor a young cohort (i.e., starting at the age of 20 y) of Crohn’s patients. The assumption was that the dose per CT would be 16 mSv. As expected, the cost effectiveness varied by the frequency of CT scans (e.g., 2 scans every year vs. 1 scan every 10 y) titrated against the age at which MRI was introduced. They found that CT monitoring was the “dominant” economic choice if the dose could be reduced to 6 mSv. Uncertainties about cancer risks were discussed related to risk estimate uncertainties at low radiation doses and the possibility that non-LNT models could significantly change the results.

In addition, in patient cohorts there is a correlation between cumulative radiation dose and degree of underlying morbidities (e.g., cancer staging and follow up). The mortality risks of these underlying competing morbidities may far exceed any theoretical risk related to medical imaging radiation doses (Stopsack 2019). Table 4 outlines challenges in using conventional CB or CE approaches to dose reduction.

Table 4 - Challenges in using conventional economic approaches to assess dose reduction strategies in low-dose medical settings.a
Minimal reduction in stochastic events, relative to nominal net dose reductions, translates into unsupportable conventional CB ratios and ICERS.
Assuming the examination is justified, and fully optimized, there is no additional change in clinical outcomes (i.e., benefits) assuming images are equally diagnostic between regular and low dose protocols (i.e., the only patient benefit is reduction in stochastic events).
Patients receiving higher cumulative diagnostic radiation doses tend to be those who are sicker with significant competing co-morbidities such that the relative impact of nominally reduced radiation induced stochastic events is diminished.
Heterogeneous set of diagnostic imaging indications resulting in highly variable dose profiles and effective dose estimates between patients and between institutes and over time as medicine and imaging technologies evolve.
Effective dose calculations based on CT phantoms/modeling are not generalizable to all patients due to differences between phantoms and individual body habitus making assessment of dose reduction difficult at the individual patient level.
ICRP (2007) advices against using estimated stochastic event rates for prospective or retrospective epidemiological analysis, especially in relation to the expected number of cancer cases. Calculating CB ratios and ICER require such an analysis rendering the technique inappropriate by ICRP guidelines.
Conventional CB and CE economic analysis requires expertise which may not be readily available in many DI settings.
aCB = cost benefit, CE = cost effectiveness, DI = diagnostic imaging, ICER = incremental cost effectiveness ratio, ICRP = International Commission on Radiological Protection.

Thaker et al. (2015) published a systematic review of the effectiveness of policies to reduce radiation exposure in medical settings. It is interesting to note that comments on ALARA, LNT, risk vs. benefit, or economics were not included in the analysis. In other words, the relative costs vs. benefits between policies for lowering radiation dose were not considered.

It is also interesting to note that the ALARA model provides a “relative” framework for proposed dose limits based on what is “reasonable.” To put this in perspective, public dose limits are generally set at 1 mSv y−1 and occupational does limits at 20 mSv to 50 mSv y−1 (CNSC Radiation Protection Regulations, USNRC 10 CRF20.1301 2020). These dose limits can be modified for non-occupational caregivers and responders to planned or unplanned special exposures. This is deemed to be what is “reasonable” in most settings. However, the proposed annual and career dose limits for astronauts of 500 mSv y−1 and 1,000 mSv to 4,000 mSv, respectively, demonstrate how “relative” ALARA-based dose limits can be based on what is determined to be “reasonable” (NASA 2008). This dose limit range demonstrates significant flexibility, and one may extrapolate for medical settings that significant resource expenditure to achieve relatively small dose reductions may not be reasonable.

At the end of the day, decisions on expending scarce health resources are driven by many factors and are generally guided by societal values that vary between jurisdictions. What society is willing to pay for dose reductions in patients, staff, and others is becoming a practical question given evolving austere health care funding policies and academic challenges to LNT. Fig. 1 (adapted from Demeter 2016) illustrates that decision makers consider many factors, depicted as “lenses,” to shape the “image” of their policy decisions. Guideline setting organizations, such as the ICRP, and regulators, such as the International Atomic Energy Agency (IAEA), focus most heavily on the first three “lenses” (i.e., epidemiology, efficacy, and effectiveness) and to a growing extent on the ethics lens (ICRP 2018; IAEA 2002; Shrader-Frechette and Persson 1997), but decisions can be heavily weighted by the other lenses.

Fig. 1
Fig. 1:
Decision makers consider many factors, depicted as “lenses,” to shape the “image” of their policy decisions.

This paper argues that conventional CB and CE approaches are not ideal to assess what is economically reasonable in the domain of radiation protection, especially in medical settings where dose reductions are in the order of μSv to mSv. A number of alternate options have been presented.

It is by design that no one alternate approach or “threshold” has been recommended. Broader consultation with stakeholders, including scientists, ethicists, patients, and the general public is required to move the agenda forward. The decision of how much to spend to reduce radiation doses in patient care, occupational, and public settings is truly driven by societal values, especially in an era of fiscal austerity and increased attention to opportunity costs.

CONCLUSION

The full ALARA principle is defined as “as low as reasonably achievable, taking social and economic factors into consideration.” Given small incremental radiation dose reductions that may be realized in medical settings and corresponding small changes to theoretical stochastic effects, a conventional CB approach (i.e., cost per averted stochastic effects or years of life saved) is less than ideal.

Alternate approaches, such as cost per unit of radiation averted (e.g., $/μSv averted), cancer induction/fatality probabilistic thresholds, or thresholds relative to natural background radiation are options. However, deciding on what is reasonable should be driven by a multi-stakeholder consultative process. The decision on what is a “safe” level of radiation and what are reasonable costs to make it “safer” are driven by society values and may vary from jurisdiction to jurisdiction.

Acknowledgments

International Commission on Radiological Protection (ICRP) Committee Member (Committee 3), Commission Member of the Canadian Nuclear Safety Commission (CNSC), and a core member of the Health Technology Expert Review Panel (HTERP) of the Canadian Agency for Dugs and Technologies in Health (CADTH). The opinions I express are my own and do not necessarily reflect those of these or other organizations.

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Keywords:

analysis, cost benefit; linear hypothesis; radiation protection; radiation, medical

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