Lifetime Risk Definition

There are various definitions for excess lifetime risks (10, 15). All considered definitions emerge from the difference between risk under exposure and the baseline risk without exposure. Here we focus on the lifetime excess absolute risk (LEAR), sometimes also referred to as lifetime attributable risk (LAR), e.g. (9). The LEAR is defined as

with lifetime risk of dying from a specific disease of interest (here: lung cancer) under exposure LR_E(a) = ^∫ _a ¹ r_E(t)S(t∣a) dt, baseline lifetime risk LR₀(a) = ^∫ _a ¹ r_E(t)S(t∣a) dt, minimum age at risk a, baseline lung cancer mortality rates r₀(t) and lung cancer mortality rates under exposure r_E(t) at age t. S(t ∣ a) is the conditional survival function with S(t ∣ a): = P(T ≥ t ∣ T ≥ a) and T ≥ 0 the unknown random retention time until death. S(t ∣ a) describes the probability to survive until age t given the survival to age a. We set S(t): = S(t ∣ 0) = P(T ≥ t) and model the survival function as S(t) = e with baseline mortality rates for all causes of death q₀(t). ERR(t) denotes the excess relative risk at age t. In Eq. (1), the following risk projection model is assumed:

Established risk models for lung cancer from radon exposure follow such an ERR structure (8, 18). The ERR(t) depends not only on age t but on further variables such as cumulative lagged exposure to radon progeny, time since exposure or exposure rate. The exact composition and complexity of the ERR(t) depends on the specific risk model.

Lifetime Risk Calculation and Choice of Components

In the computation of LEAR, we distinguish between major and minor components. Minor components are defined with limited freedom of choice or possess minimal influence on the resulting LEAR. Major components, on the other hand, necessitate further decision-making because they are less constrained, and their choice is consequential.

The LEAR_E(a) relies on three major components: mortality rates, risk models, and exposure scenarios. The first component encompasses mortality rates for lung cancer r₀(t) and all-cause mortality rates q₀(t), at each age t. The relative risk projection model shapes ERR(t) at each age. The exposure scenario involves yearly exposure to radon progeny in working level months (WLM) and has an impact on ERR(t) for every age t. Minor components include minimum age at risk a, maximum age a_max, minimum latency time L between exposure and risk amplification, and the chosen approximation approach for the survival function S(t).

The LEAR is subsequently estimated and calculated through the following approximation:

where the approximation is utilized for the survival function S(t ∣ a). This approximation is based on the Nelson-Aalen estimator of the cumulative hazard rate (19).

The minimum age at risk a was set to a = 0 to account for the full lifetime of an individual. The maximum age a_max was set to a_max = 94 for comparability to previous studies (20). For readability, we write LEAR = LEAR_E(0). For the latency period L between exposure to radon progeny and death from lung cancer, the cumulative exposures were lagged by L = 5 years since all considered risk projection models also assume L = 5. LEAR estimates were computed and compared for different combinations of major calculation components: three sex-averaged reference populations, seven risk models and four exposure scenarios, resulting in 3 × 7 × 4 = 84 distinct LEAR estimates. Besides the total LEAR, the LEAR per WLM (LEAR/WLM) is considered, defined as the LEAR divided by total cumulative exposure accrued over the entire exposure scenario in WLM. All statistical or numerical analyses were conducted with the statistical software R (21).

Mortality Rates

The following sex-averaged mortality rates were chosen: ICRP reference rates reflecting a mixed Euro-American-Asian population derived from population data from the years 1993–1997 (3, 22); rates from Greece 2018, the Netherlands 2018 and Norway 2016 based on population data provided by the WHO Mortality Database (23) reflecting a heavy smoker reference population; and rates from Costa Rica 2019, USA 2019 and Sweden 2016 reflecting a light smoker population. The country selection was based on smoking behavior following the OECD Health Statistics (24) on tobacco consumption (percentage of the population aged 15+ who are daily smokers) from the year 2000 to account for a latency of around 20 years between smoking and the development of lung cancer. This latency time was chosen based on several studies (25–27). The three countries with the highest percentage of daily smokers aged 15 and older (32–35%) were chosen to represent the heavy smoker population, while the three countries with the lowest percentage of daily smokers (12–19%) were chosen to represent the light smoker population. Further, the countries were chosen with the objective to employ complete and recent data.

The rates of heavy and light smokers were constructed by aggregating death cases d_i and population sizes n_i from different countries and sexes, where i = 1; . . .; N indexes both the country and sex for every age:

If d corresponds to lung cancer deaths at age t, this yields the baseline rate m = r₀(t), and if d denotes all-cause death counts at age t, m = q₀(t). The full derivation of Eq. (4) is shown in the  Supplementary Materials, Section A (10.1667_RADE-24-00060.1.S1.pdf) ( https://doi.org/10.1667/RADE-24-00060.1.S1).²

Figure 1 shows the difference in lung cancer deaths (panel A) and all-cause deaths (panel B) per 100,000 persons for all three sex-averaged reference populations (exact numerical values in the  Supplementary Table S1 (10.1667_RADE-24-00060.1.S1.pdf);  https://doi.org/10.1667/RADE-24-00060.1.S1). Population data is given in 5-year age intervals. Light smoker and heavy smoker populations are similar in all-cause deaths per 100,000, with visible differences only at ages 85+. The ICRP reference population shows considerably more all-cause deaths per 100,000 compared to the smoker populations until age 85. There are notably more lung cancer deaths per 100,000 for heavy smokers than for light smokers (as expected). However, at ages 85+ heavy smoker lung cancer deaths per 100,000 decreased whereas for light smokers, they stayed approximately constant. The ICRP reference population yields relatively many lung cancer deaths, comparable to the heavy smoker population.

FIG. 1

Lung cancer deaths (panel A) and all-cause deaths (panel B) per 100,000 persons by age in the sex-averaged ICRP reference population (3) and in the constructed reference populations for heavy and light smokers.

Unless explicitly stated otherwise, all lifetime risk estimates are calculated with mean mortality rates for males and females (sex-averaged mortality rates). Lifetime risks with male-specific mortality rates are analyzed in  Supplementary Materials, Section B (10.1667_RADE-24-00060.1.S1.pdf) ( https://doi.org/10.1667/RADE-24-00060.1.S1).

Risk Models and Cohorts

The LEAR calculation is based on a risk projection model and data from a cohort study, on which the risk model was fitted. Established risk models for lung cancer due to radon exposure in uranium miners cohort studies are based on the general structure in Eq. (2) and are fitted with internal (or sometimes also external) Poisson regression on grouped data. The preferred risk model contains a linear relationship between cumulative occupational radon exposure in WLM and excess relative risk of lung cancer, which is additionally modified by time since exposure, attained age or age at exposure, and in some cases also exposure rate (8). Recently, more focus has been given to more recent periods with low-radon exposures or exposure rates (“sub-cohorts 1960+”) (28–30).

Here, the considered risk models are the categorical BEIR VI exposure-age-concentration model fitted on the pooled 11 miners cohort (BEIR VI model) (6) as well as on the Pooled Uranium Miners Analysis (PUMA) cohort (PUMA model) (18, 28), the adjusted Jacobi model fitted on six cohort studies (2, 31), and parametric risk models fitted on the German Wismut cohort (7) as well as on the Joint Czech and French miners cohort (32).

These models were selected for the following reasons. The initial factors for radon dose conversion were computed using the Jacobi model (2). The Joint Czech and French risk model, along with the BEIR VI model fitted to the pooled 11 miners cohort, contributed to a novel radon dose conversion proposal by ICRP (4). The German Wismut cohort is the world's largest single cohort of uranium miners. Notably, this extensive cohort was not included for the BEIR VI risk model (as the cohort was only established later). Suitable parametric models are used for both the Wismut 1960+ sub-cohort and full cohort, containing a continuous exposure rate effect for the full cohort that contrasts with the categorical exposure rate considerations in the BEIR VI and PUMA models. Note that we deliberately included Wismut models from the follow-up period 1946–2013 (7) rather than from the latest follow-up 1946–2018 (29) to ensure a broader variety of risk model structures for sensitivity analyses. While the more recent models offer slightly more precise estimates, such as by additionally stratifying the baseline by duration of employment, they are structurally similar to the other models compared here and do not contribute to the diversity of our model selection. The PUMA study is the largest uranium miners cohort worldwide, encompassing twice as many uranium miners and roughly three times as many lung cancer deaths (33) as the pooled 11 miners cohort (6). In particular, it includes the German Wismut cohort.

The generic categorical BEIR VI exposure-age-concentration model at age t reads

where W_5-14; W_15-24; W₂₅₊ is the cumulative radon exposure in the windows 5–14, 15–24 or 25+ years before age t with corresponding parameters θ_15-24; θ₂₅₊ and ϕ_age and γ_z are factors for attained age and exposure rate, respectively. We refer to Eq. (5) as the “BEIR VI” model when fitted to the pooled 11 miners cohort, and as “PUMA full” or “PUMA sub” when fitted to the full PUMA cohort or to the 1960+ sub-cohort, respectively, the latter comprising miners hired in 1960 or later. Note that in PUMA models the exposure rate factor γ_z accounts for the annual exposure rate, whereas in the classical BEIR VI model γ_z corresponds to the cumulative exposure rate.

The adjusted Jacobi model is the classical Jacobi model in (31) adjusted by the factor 0.83 to account for overestimation (2). It reads with time since exposure TE, age at exposure AE = t - TE, and cumulative exposure W(t) in WLM at age t in years,

with AE-specific parameters α(AE) and TE-specific parameters θ(TE). Note that although this model is based on six cohorts, the modifying effect structure of time since exposure and age at exposure was estimated solely from the Czech cohort. The parameter estimates in α(AE) are adjusted to match the meta-estimate for ERR per WLM derived from all six cohorts (31).

The generic parametric risk models for ERR at age t read,

with cumulative exposure W(t) in WLM and continuous effect modifiers age at median exposure AME(t) in years, time since median exposure TME(t) in years and cumulative exposure rate ER(t) in WL with corresponding parameters β; α; e and ψ. We consider Eq. (7) fitted on two different cohorts, namely the joint Czech and French and the German uranium miners sub-cohort with miners hired in 1960 or later (Wismut 1960+ sub-cohort). Equation (7) fitted on the joint Czech and French cohort is referred to as the “Joint CZ+F” risk model. We call Eq. (7) fitted on the Wismut 1960+ sub-cohort with follow-up 2013 “Wismut sub”, whereas Eq. (8) was fitted to the full German uranium miners cohort and is referred to as ‘Wismut full”. The parameter estimates differ between cohorts and only Wismut full incorporates an exposure rate effect with ψ ≠ 0.

All considered risk models include unknown parameters (indicated by Greek letters) which are estimated using Maximum-Likelihood methods based on miners cohort data. In total, we consider four categorical risk models (BEIR VI, PUMA full, PUMA sub, adjusted Jacobi) and three parametric continuous risk models (Joint CZ+F, Wismut full, Wismut sub) (Table 1). Here, the terms “categorical” and “parametric/continuous” refer to the categorical or continuous nature of the effect-modifying variables. Among all seven considered models, three categorical models (BEIR VI, PUMA full, PUMA sub) and one parametric model (Wismut full), account for an exposure rate effect. The explicit parameter estimates for all risk models can be found in  Supplementary Materials, Section C (10.1667_RADE-24-00060.1.S1.pdf) ( https://doi.org/10.1667/RADE-24-00060.1.S1) or the corresponding references. For the actual calculation of lifetime risk estimates, parameter estimates are plugged into the corresponding risk model structure.

TABLE 1

Overview of all Considered Risk Models and Associated Cohort Data

Exposure Scenario

As exposure scenarios, we consider the internationally well-accepted default choice for LEAR calculation with occupational exposure of 2 WLM from age 18–64 (94 WLM total cumulative exposure over lifetime (WLM/life), moderate exposure) as used in (11). Furthermore, we use three scenarios calculated from mean exposures during employment of miners from the Wismut cohort depending on the period of begin of employment (1946–1954: 1,750 WLM/life, “very high exposure”; 1955–1970: 352 WLM/life, “high exposure”; and 1971–1989: 54 WLM/life, “low exposure”). The mean exposure was determined by averaging the annual exposures of miners (with WLM > 0) by age. The constructed exposure scenarios differ considerably in shape and yearly exposure (Fig. 2).

FIG. 2

Exposure to radon progeny in WLM per year by age for the four considered exposure scenarios with total cumulative exposure in parentheses (panel A). Panel B differs in the scale of the y-axis only and gives a more focused view on lower exposures per year.

Comparison of Lifetime Risk Measures

Three additional lifetime risk measures were calculated: The risk of exposure-induced death REID [first introduced in (34) and employed in (13, 35)], the excess lifetime risk ELR (36) and the radiation attributable decrease of survival RADS (15). The central difference of the additionally considered lifetime risk measures compared to the LEAR is the explicit accounting for radon exposure in the survival function. The LEAR approach assumes that radon exposure affects only the explicit lung cancer risk but not the survival function. Survival under exposure shall be denoted by S_E(t ∣ a) and baseline survival by S₀(t ∣ a) = S(t ∣ a), emphasizing that S₀(t ∣ a) does not depend on exposure. It holds,

As for the LEAR, we investigate a = 0 and write REID = REID_E(0); ELR = ELR_E(0) and RADS = RADS_E(0). To calculate these additional lifetime risk measures, assumptions on the survival function affected by exposure are necessary. Analogously to we set where q_E(u) describes the all-cause mortality rate at age u affected by exposure. For computation of S_E(t) we employ the approximation and assume that radon exposure only influences the risk for lung cancer mortality. Therewith, q_E(u) differs from q₀(u) by an increased lung cancer mortality rate. Hence, q_E(u) = q₀(u) + r₀(u)ERR(u) and

Employing the same approximation as for the LEAR, the final approximated formulas for all considered lifetime risk measures are

Effects of Reference Populations

The LEAR per WLM estimates for the population of heavy smokers closely align with those of the ICRP reference population, whereas light smokers consistently yield lower estimates. The heavy smoker population (baseline lifetime risk of 5.27%), exhibits higher LEAR per WLM estimates than light smokers (baseline lifetime risk of 4.12%). For comparison, the baseline lifetime risk of the ICRP reference population is 4.83%. The differences between reference populations can be explained when the factors r₀(t) and S(t) are interpreted as weighting factors r₀(t)S(t) for the ERR(t) in the LEAR calculation [Eq. (3)] since these weights completely depend on mortality rates (Fig. 4). The weights r₀(t)S(t) are notably lower for light smokers than for heavy smokers and ICRP reference at all ages except for ages 80+. This characteristic roughly translates to the age-specific contributions r₀(t)S(t)ERR(t) to the final LEAR estimate. Thus, the population of light smokers produces lower LEAR per WLM estimates because lung cancer rates are lower among light smokers, whereas the results for the ICRP reference population and the heavy smoker population are almost similar. Using male-specific compared to sex-averaged mortality rates results in higher lifetime risk estimates across all reference populations, risk models, exposure scenarios, and lifetime risk measures ( Supplementary Materials, Section B (10.1667_RADE-24-00060.1.S1.pdf);  https://doi.org/10.1667/RADE-24-00060.1.S1).

FIG. 4

Illustration of the influence of the three reference populations on LEAR calculation. Panel A: Product of baseline lung cancer mortality rates r₀(t) and survival S(t) × 10³; panel B: age-specific contribution to the LEAR, r₀(t)ERR(t)S(t) × 10³; both for every age t with the BEIR VI risk model and the moderate exposure scenario of 2 WLM from age 18–64 years.

Effects of Risk Models and Exposure Scenarios

Despite large differences in the four considered exposure scenarios, the resulting respective LEAR per WLM is notably constant (reading Fig. 3 horizontally). Only estimates with BEIR VI deviate considerably and exhibit an increasing trend with decreasing exposure. Notably, this does not apply to PUMA models, although they have a very similar model structure. Generally, the risk models influence LEAR estimates essentially (Fig. 5). There are large differences in age-at-exposure effects and the magnitude and shape of ERR(t); depending on the chosen risk model. All risk models peak at different ages at exposure. The Joint CZ+F and Wismut sub model exhibit distinct ERR(t) patterns, despite originating from an identical risk model structure [Eq. (7)]. This affects the age-specific contribution r₀(t)ERR(t)S(t) to the LEAR (Fig. 5B). Multiplying the ERR(t) (Fig. 5A) with r₀(t)S(t) at every age t yields the curves from Fig. 5B. Integrating these curves over all ages t yields the LEAR estimate for each risk model.

FIG. 5

Excess relative risks of different risk models (panel A: categorical models, panel B: parametric models) and their age-specific contribution to the LEAR, r₀(t)ERR(t)S(t) × 10³ (panels C and D, respectively) for the moderate exposure scenario of 2 WLM from 18–64 years and the ICRP reference population. For readability, data points are displayed only for every third age.

In the  Supplementary Materials, Section D (10.1667_RADE-24-00060.1.S1.pdf) ( https://doi.org/10.1667/RADE-24-00060.1.S1), further sensitivity analysis on the effects of varying annual exposure and differences between single acute and protracted homogeneous exposure across age are shown for all lifetime risk measures and risk models. Results show stable or slightly declining lifetime risk estimates per WLM for varying annual exposure for all risk models, except for the BEIR VI risk model. Comparing acute exposure at different ages to protracted homogeneous exposure across age reveals substantial differences in lifetime risk estimates especially influenced by the consideration of exposure rate in risk models. Depending on age at acute exposure, the excess lifetime risks (per WLM) differ roughly by a factor of two for all risk models and all lifetime risk measures.

Comparison of Lifetime Risk Measures

Excess lifetime risks were calculated for three additional lifetime risk measures for all combinations of reference populations, risk models and exposure scenarios (Fig. 6 and Table 3 for moderate exposure). There are only slight differences in results for ELR, REID and LEAR, except for very high exposures. RADS estimates are larger than results for the other three measures. We observe the monotonicity ELR ≤ REID ≤ LEAR ≤ RADS (per WLM) for all combinations except for the very high-exposure scenario. At this very high exposure, the monotonicity between lifetime risk measures is ELR ≤ REID ≤ RADS ≤ LEAR (per WLM) for all reference populations and risk models.

FIG. 6

Excess lifetime risk estimates per WLM × 10⁴ for different lifetime risk measures and the four considered exposure scenarios (panels A–D) were calculated with the ICRP reference population.

TABLE 3

Results for Excess Lifetime Risks per WLM × 10⁴ for Different Lifetime Risk Measures, Reference Populations and Risk Models for the Moderate Exposure Scenario of 2 WLM from Age 18–64 Years

Effect of Mortality Rates and Reference Populations

Smoking is the greatest risk factor for lung cancer (37, 38) and the interaction effect of smoking and radon on lung cancer is not yet fully understood (8). We investigated whether strong differences in the smoking behavior of reference populations are reflected in the corresponding LEAR estimates by constructing a sex-averaged light and heavy smoker reference population. For comparison, the widely accepted ICRP sex-averaged reference population from (3) was also considered. In the  Supplementary Materials (Section B (10.1667_RADE-24-00060.1.S1.pdf);  https://doi.org/10.1667/RADE-24-00060.1.S1), lifetime risk sensitivities with male-specific mortality rates are additionally investigated.

This analysis clearly showed that employing a smoking reference population results in elevated LEAR per WLM estimates. This confirms the results published in the literature (39) that smoking behavior in a reference population influences lifetime risk estimates heavily. This can be explained by acknowledging that smoking amplifies baseline lung cancer risk r₀(∙), which enters the LEAR calculation linearly. In particular, the risk models used are not adjusted for smoking, resulting in the implicit assumption of a multiplicative interaction between smoking and radon on the lung cancer risk here, in line with the findings (8, 40). However, other epidemiological studies suggest a sub-multiplicative (6, 7, 30)41) or additive interaction (42). While we retain the multiplicative model due to the heterogeneous nature of smoking adjustments in the existing literature and compatibility issues with our heavy- and light-smoker reference rates, exploring lifetime risk estimates with smoking-adjusted risk models could offer interesting insights.

In that manner, if a LEAR for a smoker is of interest, it may be reasonable to compute smoking-specific LEAR estimates with mortality rates from smoker populations and risk models fitted on suitable cohorts of smoking persons with comparable smoking behavior. Especially between countries heavy differences in lung cancer mortality rates may occur not only due to smoking behavior, but also because of variable health care and medical standards (43, 44). Likewise, if a LEAR for a specific country and sex is of interest, country- and sex-specific lifetime risk estimates with corresponding sex-specific mortality rates should be calculated, as similarly recommended for detriment calculations (45). Additional analyses ( Supplementary Materials, Section B (10.1667_RADE-24-00060.1.S1.pdf);  https://doi.org/10.1667/RADE-24-00060.1.S1) showed an overall increased lifetime risk when calculated with male-specific baseline mortality rates, with lifetime risk variability closely aligning with results obtained using sex-averaged rates. It is expected that lifetime risks calculated with female-specific mortality rates would be lower correspondingly. However, calculating lifetime risks with female-specific rates and risk models derived from male uranium miners amplifies the risk transfer issue, which is why we excluded female-specific analyses in this study.

This analysis further revealed that the ICRP reference population results in remarkably similar LEAR estimates as when using the heavy smoker population and produces generally high LEAR and LEAR per WLM estimates, too. The same result was observed for male-specific reference populations ( Supplementary Materials, Section B (10.1667_RADE-24-00060.1.S1.pdf);  https://doi.org/10.1667/RADE-24-00060.1.S1). This indicates that ICRP reference rates rather represent smokers than non-smokers. In particular, LEAR estimates with the ICRP reference population overestimate absolute risks for non-smokers and underestimate (but to a lesser extent) risks for smokers, compare (2). However, smoking behavior has evolved over the years and the smoking population rates in this analysis are derived from population data from more recent years (2016–2019) compared to the ICRP reference rates (1993–1997). This may contribute to explaining the results obtained for the ICRP population. Hence results incorporating ICRP rates must be interpreted with care.

Effect of Risk Models

Varying risk models lead to a large variability in LEAR estimates. This becomes clear when interpreting the LEAR as a weighted average of the ERR(∙) term (which depends on risk models) with weights r₀(∙₎S(∙). Even risk models with identical ERR(∙) term structures (Joint CZ+F and Wismut sub) inherit different parameter estimates and result in distinct LEAR estimates. The BEIR VI model imposes high variation of the LEAR per WLM for different exposure scenarios due to its strong inverse exposure rate effect. The PUMA models use fewer categories for exposure rate and annual exposure rate instead of cumulative mean exposure rate compared to the BEIR VI model. This explains the lower variability of results from PUMA models for different exposure scenarios despite the structural model similarity to BEIR VI. Although Wismut full also incorporates an inverse exposure rate effect, the impact on LEAR per WLM is considerably weaker because of the continuous nature of the model. In considered risk models without exposure rate effect modifiers, the ERR(t) (and therefore the LEAR) increases linearly when the exposure is increased. This results in remarkably stable LEAR per WLM estimates (Fig. 3).

The Wismut full risk model results in remarkably small lifetime risk estimates, particularly compared to the PUMA full model. This is a direct consequence of the fact that parameter estimates of Wismut full are also comparatively small. Compared to other cohorts in PUMA, the Wismut full cohort is characterized by longer duration of employment combined with rather high-cumulative radon exposure at low-exposure rates [(20) see table 1]. These structural differences might result in the substantial differences between parameter and lifetime risk estimates from PUMA full and Wismut full risk models, despite the fact that the Wismut cohort makes up over half of the PUMA study data (2.3 out of 4.1 million person-years at risk) (33). In models from the 1960+ sub-cohorts (Wismut sub, PUMA sub), differences between parameter and lifetime risk estimates are less pronounced, which supports that uncertainties in exposure assessment in the early years of the Wismut cohort might also play an important role.

Exposure assessment in the early years of uranium mining relied on expert ratings rather than on direct measurements, increasing the potential for measurement error (20). Inconsistencies in exposure assessment across different periods can lead to differences in risk estimates. Improved exposure assessment quality, such as in the 1960+ sub-cohorts of PUMA and Wismut, reduces measurement error and yields more accurate risk estimates at low exposures and exposure rates. Ongoing research explores the effects of measurement error in the early years within the Wismut cohort (46, 47). Measurement errors are one of many possible explanations for the differences in risk estimates at low exposures and exposure rates between the full and the 1960 + sub-cohort (29).

Note that the inverse exposure-rate effect, also known as the protraction enhancement effect, plays a critical role in the observed LEAR variability. This effect describes a decrease in (excess) relative risk for higher exposure rates and was demonstrated in many miners studies (6, 8). However, this effect diminished when the analyses were limited to miners with low levels of cumulative exposure in WLM or those employed in more recent times (30, 32), but it was shown to be statistically significant for the first time at such exposure levels in the PUMA 1960+ sub-cohort (28).

Generally, variations in LEAR and LEAR per WLM depending on the choice of risk model emerge from differences in underlying cohorts, risk model structures and assumptions for the fitting process of risk model and cohort. Especially decisions in the necessary data grouping process prior to applying Poisson regression on cohort data are highly susceptible to influencing risk model estimates (48). Also, the design of baseline stratification, e.g. with the statistical software Epicure (49), influences risk model parameter estimates and corresponding lifetime risk estimates (50). In categorical risk models, ERR(t) curves might exhibit abrupt changes at specific ages, times since exposure, and exposure rates as given by the model. This raises concerns about the discontinuity of these models. On the other hand, parametric risk models, which also incorporate effect modifiers, provide a smoother and more intuitive transition over age. Therefore, it seems more reasonable and plausible to use parametric risk models (or generally models with a continuous structure), such as those fitted on a representative cohort (cf. (28)), for calculating LEAR estimates. Especially for the BEIR VI model, there were attempts to use a smooth version of this categorical risk model by employing spline functions, see e.g. (51).

While our analyses focus on established excess relative risk (ERR) models, we acknowledge that lifetime risk estimates incorporating excess absolute risk (EAR) results for lung cancer related to occupational radon exposure are available, as in the electronic attachment of (8). The EAR approach offers an alternative perspective on lifetime risk assessment, although comprehensive application across all our studied cohorts is technically constrained. Future research may explore further EAR models, where possible, potentially enriching the interpretation of radon-related risks.

Effect of Exposure Scenario

In the early years of uranium mining at Wismut after 1945, miners were exposed to high levels of radon and its progeny, and had very different exposure situations than miners later. Due to improved measures for occupational safety like air ventilation, the mean exposure at the Wismut reduced constantly from 1955 and reached levels of international radiation protection standards in the 1970s (52). The large size of the Wismut cohort study enabled us to construct realistic occupational exposure scenarios with heterogeneous exposure rates over age (low, high, and very high exposure) additional to the default choice of 2 WLM from age 18–64 years (moderate exposure). In particular, the exposure scenario reflecting begin of employment in 1946–1954 (very high exposure) shows very high exposures at early ages due to missing protective measures in the mines. Likewise, but to a considerably lesser extent, this holds for the exposure scenario with begin of employment 1955–1970 (high exposure). On the other hand, the scenarios for begin of employment 1970–1989 (low exposure) and the ICRP default (moderate exposure) show homogeneous exposure over age without clear peaks.

Despite substantial differences in exposure scenarios, the LEAR per WLM remains relatively constant for all risk models except for BEIR VI with a threefold increase from highest to lowest exposure scenario.

The LEAR per WLM tends to slightly increase (except for the PUMA sub-model) for the two exposure scenarios with moderate and low cumulative exposure compared to the other two exposure scenarios. Regarding risk models without an exposure rate effect modifier (Adj. Jacobi, Wismut sub and Joint CZ+F), this is because of the more homogeneous exposure in age in these two scenarios – in contrast to the other two scenarios with high and very high-cumulative exposure where the majority of exposure is at earlier ages. At these earlier ages, LEAR and LEAR per WLM are less affected by exposure (see Fig. 4). However, the effect is small. On the other hand, risk models with an exposure rate modifier (BEIR VI, Wismut full, PUMA full and PUMA sub) are additionally affected by variable cumulative exposure. LEAR estimates with the BEIR VI model are heavily affected by this categorical-inverse-exposure rate effect as mentioned before. PUMA sub behaves differently because of its unique feature of an increasing factor for time since exposure 25–34 years ago  Supplementary Materials, Section C (10.1667_RADE-24-00060.1.S1.pdf);  https://doi.org/10.1667/RADE-24-00060.1.S1). This parameter estimate is likely an artifact stemming from the reduced statistical power of the PUMA sub-cohort compared to the PUMA full cohort.

Note that stable LEAR per WLM estimates translate to a roughly linear relationship between LEAR and exposure, e.g. a doubling in yearly exposure roughly doubles the LEAR as well. The LEAR measure is technically unbounded and may result in unreasonable large values for extreme exposure scenarios. LEAR estimates exceeding 100% are to be interpreted cautiously.

Combining risk models derived from low-exposure cohorts with extreme exposures may not seem reasonable at first glance. Risk models without an exposure rate effect modifier tend to be suitable only for low-exposure scenarios (7, 53). However, the goal of this sensitivity analysis was to particularly investigate and combine extreme cases for a better understanding of LEAR drivers.

In summary, the stability of LEAR per WLM for changing exposure scenarios implies no benefit from employing complex over simple exposure scenarios when calculating lifetime risks for realistic exposures. This confirms the default exposure scenario of 2 WLM from age 18–64 years for a working population as a suitable and reasonable choice.

Effect of Lifetime Risk Measures

Comparisons between the different lifetime risk measures ELR, REID, LEAR and RADS, provide valuable insights. The monotonicity observed for all combinations of major components except for the very high-exposure scenario, i.e. ELR ≤ REID ≤ LEAR ≤ RADS (per WLM), underscores the relationship between these measures.

All four measures preserve mostly the behavior as seen for the LEAR regarding risk model and reference population effects. RADS is the only measure where estimates with ICRP mortality rates are higher than estimates with the heavy smoker reference population. This is because RADS estimates are independent of all-cause mortality rates in contrast to ELR, REID and LEAR.

The three measures ELR, REID and RADS (per WLM) are more severely affected by the very high-exposure scenario than the LEAR because these measures account for excess risk in the survival function.

This can be observed by comparing LEAR to, for example, RADS (per WLM) across varying exposure scenarios, moving from lower to higher levels (Fig. 6). For the very high-exposure scenario, LEAR per WLM stands out as it is barely affected by exposure. RADS per WLM decreases considerably for higher levels of exposure. This confirms the stability of LEAR per WLM in capturing the exposure-response relationship for varying exposure scenarios.

The observed relation ELR ≤ REID ≤ LEAR (per WLM) can be mathematically proven to hold for all combinations of calculation components. Assuming a harmful effect of radon exposure, it holds r_E(t) ≥ r₀(t) and S_E(t∣a) ≤ S₀(t ∣ a) for all t; a ≥ 0. Evidence shown in  Supplementary Materials, Section E (10.1667_RADE-24-00060.1.S1.pdf) ( https://doi.org/10.1667/RADE-24-00060.1.S1),

For moderate excess absolute risks, it even holds ELR ≤ REID ≤ LEAR ≤ RADS (per WLM). At higher exposures the indefinite growth of LEAR exceeds RADS, breaking the inequality.

A critical aspect in estimating ELR, REID, and RADS is the modeling choice of S_E(t): Since there is currently no reliable evidence that radon can cause diseases other than lung cancer (54, 55), we assume that radon exposure affects solely the lung cancer risk, i.e. q_E(u) = q₀(u) + r₀(u)ERR(u) for all ages u.

LEAR exhibits linear growth for increase in lung cancer mortality rates r₀ or yearly exposure whereas the other three measures grow sublinear due to the additional exponential term in the survival function. This mathematical elegance makes the LEAR particularly appealing ( Supplementary Materials, Section D (10.1667_RADE-24-00060.1.S1.pdf);  https://doi.org/10.1667/RADE-24-00060.1.S1). Further, for low lung cancer mortality rates r₀ or yearly exposure, values for LEAR, REID and ELR (per WLM) are similar, while RADS values deviate. The similarity of REID, ELR and LEAR is also observed in detriment calculations (45).

We conclude that LEAR and REID are the most practicable lifetime risk measures, in accordance with previous findings (9, 10). Both quantities behave very similar for low to moderate exposures and the LEAR is easier to compute since it avoids the ambiguous radiation-affected survival S_E(t). The ELR has a convenient statistical interpretation but is not linear in increase in lung cancer mortality rates r₀ or yearly exposure and may even turn negative. We recommend sticking with the LEAR approach for its broad applicability across most exposure scenarios encountered today. However, for notably higher exposures, the linearity of LEAR and its indefinite growth is unrealistic, and we recommend employing the REID for such situations. RADS serves well as a comparative tool between risk models, by being less influenced by external baseline mortality rates compared to the other lifetime risk measures (15).

Calculation Components with Minor Influence

Prior analyses showed that latency time L, minimum age at risk a, the choice of approximation formula for the survival curve S(t) and maximum age a_max have negligible impact on lifetime risk estimates similar to results of sensitivity analyses on radiation detriment (45). However, in our lifetime risk calculations for lung cancer related to radon exposure the choices of the lag time L = 5 and minimum age at risk a = 0 are predetermined by the risk model and to not discard early years of life, respectively.

Strengths and Limitations

For the first time in a sensitivity analysis on excess lifetime risks for lung cancer related to radon, new reference populations mirroring smoking behavior were constructed from WHO data. Further, realistic exposure scenarios derived from the Wismut cohort study were employed in the calculation. This provides a more accurate representation of the actual conditions and radon concentrations that individuals experience in their working environments, and enhances the reliability of risk assessments.

Since no confidence intervals are presented, it is difficult to evaluate whether the presented lifetime risk estimates are statistically compatible. Further, variations in risk models emerge from differences in the underlying cohort and model structure. Smoking is not accounted for in the risk models and thus, any effects of smoking behavior come from amplified baseline lung cancer risks r₀. In that manner, also the risk transfer from miners cohorts to reference populations stays ambiguous [multiplicative risk transfer (56)].

Likewise, it is not accounted for sex-specific risks or further individual characteristics. Data for radon effects on females are sparse. Based on the published literature (57) we assumed the same ERR for females and males.

Future Perspectives

The results on the large impact of reference lung cancer mortality rates on the LEAR encourage to calculate country-specific lifetime risk estimates in future work. Moreover, quantitative estimates for the underlying uncertainty of lifetime risk estimates will sharpen the understanding of variability in lifetime risk estimates.