Introduction

One of the most important questions in radiation research relates to the shape of the dose–response for different detrimental health outcomes at low exposures levels. Various international radiation protection organizations use the linear no-threshold (LNT) model to predict risks of cancer after ionizing radiation (IR) exposures (NCRP 2018; Shore et al. 2018, 2019; ICRP 2005; UNSCEAR 2000). However, the most recent analysis of the Life Span Study (LSS) data suggests a significant quadratic upward curvature, especially for the incidence of all solid cancers in males (Grant et al. 2017). For cardiovascular diseases (CVD), doses above 5 Gy IR have been shown to be associated with a significantly elevated risk (HPA 2010). At doses between 0.5 and 5 Gy, there is clear evidence for an increased risk (HPA 2010; Kreuzer et al. 2015; Azizova et al. 2015a, 2015b; Moseeva et al. 2014). Radiation risks at low (< 0.1 Gy) and low-to-moderate (0.1–0.5 Gy) doses have been examined only in a few studies with considerable discrepancies in findings and require further research (for example, Shimizu et al. 2010; Mitchel et al. 2011, 2013; Little et al. 2012; Ozasa et al. 2012, 2017; Schöllnberger et al. 2012, 2018; Simonetto et al. 2014, 2015; Takahashi et al. 2017; Gillies et al. 2017). In this context, the question whether even smallest doses of IR may increase the risk of CVD or whether nonlinear dose–response curves may be better suited to describe the health risk is of special interest. There could also be a threshold for the dose below which radiation may have no effect, or lead to either a strongly elevated risk or a protective effect. Such questions are of great importance for radiation protection, especially against the rising worldwide use of IR in medical applications. They are also relevant for occupationally exposed groups of individuals. For CVD, the question of the shape of the dose–response is as important as it is for cancer because even though relative radiation risks of CVD are smaller than radiation risks of cancer (Ozasa et al. 2012), the overall burden of disease is much larger due to high background rates of CVD in Western populations (World Health Organization 2013).

Recently, significantly elevated risks of death from ischemic heart diseases (IHD) in a cohort of tuberculosis patients from Canada exposed to low-to-moderate doses of highly fractionated X-ray radiation from repeated chest fluoroscopies were reported (Zablotska et al. 2014). The reported dose–response was strictly linear, and researchers described a novel finding of a significant inverse dose-fractionation association in IHD mortality (Zablotska et al. 2014). The aim of the present study is to investigate radiation-associated risk of IHD in the Canadian fluoroscopy cohort study (CFCS) with a larger set of radio-biologically motivated dose–response models and to comprehensively characterize model uncertainties using multi-model inference (MMI, Burnham and Anderson 2002; Claeskens and Hjort 2008; Walsh and Kaiser 2011).

Materials and methods

Data sources

The CFCS data have been described in detail elsewhere (Zablotska et al. 2014). The cohort includes 63,707 tuberculosis patients from Canada who were first treated for tuberculosis between 1930 and 1952 and could have received multiple fluoroscopic X-ray examinations to maintain therapeutic pneumothorax, one of the preferred treatments in the pre-antibiotic era. Most individuals in the cohort were born between 1920 and 1929 (see Table 2 in Zablotska et al. 2014). Absorbed lung doses from fluoroscopic examinations were estimated for each patient for each year since first admission for treatment of tuberculosis (Zablotska et al. 2014). For each lung dose to be estimated 100,000 simulations were carried out and an arithmetic mean of all simulations was used for dose–response analyses. The lung dose was used because it should be a reasonable surrogate for doses to the heart and associated major blood vessels (Zablotska et al. 2014). There could be substantial uncertainties in dose estimates. These are partially accounted for in the dose-estimation methods, where doses were estimated using Monte Carlo simulation techniques, which are sampled from probability distributions of various data sources and should provide a reasonable estimate of radiation doses to the lung and heart. As stated by Zablotska et al. (2014), the impact of errors in exposure estimates in dosimetry was estimated in previous studies and shown to be relatively small and primarily of Berkson type (Howe and McLaughlin 1996) and therefore unlikely to introduce a substantial bias in risk estimates (Carroll et al. 2006).

Thirty-nine percent of the cohort (24,932 patients) were exposed to at least one fluoroscopy while the remaining 38,775 are considered unexposed to radiation from fluoroscopy. On average, exposed patients were treated 64 times with a typical fluoroscopic examination delivering a mean lung dose of 0.0125 Gy at a dose rate of approximately 0.6 mGy s−1. The mean cumulative person-year-weighted lagged lung dose among exposed was 0.79 Gy (range, 0–11.6 Gy). Doses were lagged by 10 years, a minimal latent period that has been used in several studies of long-term risks of radiation exposure on cancer and non-cancer mortality risk (Zablotska et al. 2014; Little et al. 2012; Darby et al. 2010).

Study participants had to be alive at the start of follow-up in 1950 and were followed-up for mortality until the end of 1987 with 1,902,251.68 person-years. During this time, 5818 deaths from IHD (ICD-9 codes 410–414 und 429.2) were identified through a linkage with the Canadian Mortality Database. The cohort was evenly split between men and women. Patient age at first admission for tuberculosis treatment ranged from 1 to 81 years. Additional characteristics of the CFCS are provided in Table S1 of the Online Resource.

Statistical methods

The present analysis applied the same dataset cross-classified by sex, Canadian province of most admissions (Nova Scotia, other), type of tuberculosis diagnosis (pulmonary, nonpulmonary), stage of tuberculosis (minimal, moderate, advanced, or not specified), smoking status (unknown, non-smoker, smoker), age at first exposure (0–4, 5–9, 10–19, or 20–87 years), attained age (0–24, 25–29, … 80–84, or 85–100 years), calendar year at risk (1950–1954, 1955–1959,… 1980–1984, or 1985–1987), duration of fluoroscopy screenings, and 10-year cumulative lagged lung dose as (Zablotska et al. 2014). Poisson regression was based on time-dependent person-year–weighted mean cumulative dose in cross-classified cells, using excess relative risk (ERR) models in combination with a parametric baseline model.Footnote 1 The general form of an ERR model is h = h0 × (1 + ERR(D, Z)), where h is the total hazard function and h0 is the parametric baseline model. ERR(D, Z) describes the change of the hazard function with cumulative lagged lung dose D allowing for dose–effect modification by co-factor(s) Z, such as sex, age at first exposure or dose fractionation so that ERR(D, Z) = err(D) × ε(Z). Here, err(D) represents the dose–response and ε(Z) contains the dose–effect modifiersFootnote 2 (DEMs). A parametric baseline model had been developed to analyze the risk for IHD in the Mayak Workers Cohort (Simonetto et al. 2014). It was taken as guidance for developing a parametric baseline model for the CFCS data. Both models for cohorts Mayak and CFCS are provided on pages 4–6 of the Online Resource. The baseline model in equation (S4) of the Online Resource was combined with the LNT model and adjusted for dose fractionation (Zablotska et al. 2014):

$$ h = h_{0} \{ 1 { } + \upbeta_{ 1} \times D \times { \exp }{\mkern 1mu} [\upbeta_{ 2} ({{drate}} - \, 0. 2)]\} , $$
(1)

where β1 denotes the slope of the linear dose–response and β2 is the parameter associated with the DEM drate − 0.2. Parameter drate represents the dose fractionation, a surrogate for dose rate, defined as drate: = D × time−1 where time is the overall duration of fluoroscopic procedures.Footnote 3 The unit of drate is Gy year−1. By centering drate parameter β1 corresponds to the risk for a patient with radiation exposures at 0.2 Gy year−1, i.e., approximately 16 fluoroscopic procedures per year (Zablotska et al. 2014).

Subsequently, the dose–response model from Eq. (1) (i.e., β1 × D) was substituted by the models in Fig. 1 (Q-model–Gompertz model). They were chosen with care to reflect as many biologically plausible shapes for dose–responses as possible, including supralinear and sublinear models. Motivations for these models from the biological scientific literature are provided in Table 1 and in the “Discussion” section. The mathematical forms and names of the functions illustrated in Fig. 1 are given in columns 1 and 2 of Table 1, respectively. Columns 3 and 4 of Table 1 state which types of radiation biological experiments have previously provided evidence for applying these functions in the present analysis, and the relevant citations of the biology papers, respectively. Mathematical details of all models in Fig. 1 are also given on page 7 of the Online Resource; that also includes the categorical model. The threshold-dose parameter (Dth) contained in some models (LTH, smooth-step, sigmoid, hormesis, two-line spline) was optimized during the model fits. The smooth-step model was implemented as a modified hyperbolic tangent function, which can accommodate various different shapes. With this function, a step is not imposed a priori but results from fitting that model to data.

Fig. 1
figure 1

Typical shapes of the functions that were used to analyze the dose–response for IHD mortality in the Canadian Fluoroscopy Cohort Study (follow-up 1950–1987). 1st row: linear no-threshold (LNT) model, quadratic (Q), linear-quadratic (LQ); 2nd row: linear-exponential (LE) model, linear-threshold (LTH), smooth-step model; 3rd row: sigmoid model, hormesis model, two-line spline model; 4th row: Gompertz model, categorical model. Additional dashed lines show the flexibility of some of the models

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Table 1 Dose–response models used for MMI and related biological studies that motivate the use of these specific models in the present study; Canadian Fluoroscopy Cohort Study, 1950-1987
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Multi-model inference (MMI) method

The term MMI was coined to describe a frequentist approach to model averaging (Burnham and Anderson 2002) and has been applied to model selection in radiobiology. In contrast to Bayesian model averaging (BMA) (Hoeting et al. 1999), which is based on the evaluation of model-specific marginal likelihood functions to determine a model average, MMI relies on the Akaike Information Criterion (AIC; Akaike 1973, 1974) and AIC-based model weights for model building. BMA is computationally more demanding and only a few radiation epidemiological studies have used it to account for uncertainties in dose estimation (Little et al. 2014, 2015, Land et al. 2015, Hoffmann et al. 2017). Both BMA and MMI apply the concept of Occam’s group (Madigan and Raftery 1994, Hoeting et al. 1999, Noble et al. 2009, Kaiser and Walsh 2013), where a group of models deemed adequate for averaging is selected from a larger group of candidate models (see Fig. 1). The methods of picking models for Occam’s group can vary. For example, Walsh and Kaiser (2011) selected all published models, which have been applied to the same LSS dataset for the same endpoint, whereas Kaiser and Walsh (2013) developed a rigorous selection process based on likelihood ratio tests (LRTs).

The shape of the MMI-derived dose–response is more reliably determined than the shape for any individual dose–response because the MMI dose–response shape accounts for strengths of evidence for each of the contributing dose–response shapes. MMI also provides a more comprehensive characterization of model uncertainties by accounting for possible bias from model selection. It is a statistical method of superposing different models that all describe a certain data set about equally well (Burnham and Anderson 2002, Claeskens and Hjort 2008). In the present study, the MMI approach aims to detect nonlinearities in the dose–response by combining biologically plausible dose–responses based on goodness-of-fit.

Model selection

To assess the influence of model-selection criteria on the risk estimates, we used two approaches. In the “sparse model approach”, candidate dose–response models from Fig. 1 are compared using the LRT at a 95% confidence level. With this method, a small set of final non-nested models with highly significant dose–responses was identified for Occam’s group. Specifically, for each final non-nested model we calculated the AIC using the formula:

$$ {\text{AIC}}{\mkern 1mu} = {\mkern 1mu} {\text{dev}}{\mkern 1mu} + {\mkern 1mu} 2{\mkern 1mu} \times {\mkern 1mu} N_{{par}} , $$

where dev is the final deviance and Npar is the number of model parameters. Models with smaller AIC are favored based on fit (via dev) and parameter parsimony (models with more parameters get punished by the factor 2 × Npar) (Walsh 2007). For a set of final non-nested models, AIC-weights are calculated; models with smaller AIC are assigned a larger weight (see page 9 of the Online Resource). The resulting weights, multiplied by a factor of 104, gave a number of samples for risk estimates to be generated by uncertainty distribution simulations. We then combined model-specific probability density functions into one dataset. The resulting probability density distribution represents all uncertainties arising from the different models and their superposition. Central risk estimates from MMI were calculated from AIC-weighted maximum likelihood estimates (MLE) for single risk models. 95% confidence intervals (CI) were derived from the final merged MMI probability density distributions.

In the second, “rich model approach”, an LRT-based reduction of dose–response parameters of the candidate models was not performed. The AIC was calculated for each different model fit together with the AIC-weights. Models with bilateral AIC-weights smaller than 5% did not survive the selection process; all others were included into the set of final non-nested models. This approach leads to a larger number of models deemed suitable for MMI. The calculation of AIC-weights for the two sets (or Occam’s groups) of dose–response models based on both approaches (“sparse” versus “rich”) is detailed on page 9 of the Online Resource. The software used to perform all analyses is briefly introduced on page 10 of the Online Resource.

Results

Similar to the previously published results (Zablotska et al. 2014), the slope parameter β1 was not significant without adjustment for dose fractionation (β1 = − 0.046 Gy−1, Table 2). Adjustment led to a significant ERR per dose = 0.182 Gy−1 with 95% CI (0.049, 0.325) (Table 2) (ERR per dose = 0.176 Gy−1 in Zablotska et al. 2014). Subsequently, the LNT model from Eq. (1) was substituted by all other models from Fig. 1, keeping the DEM drate − 0.2.

Table 2 Maximum likelihood estimates of model parameters, related 95% confidence intervals and final deviances of fitting ERR-LNT models to the mortality data for ischemic heart diseases (Zablotska et al. 2014); Canadian Fluoroscopy Cohort Study, 1950-1987
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Considering the relations in Figure S1 of the Online Resource and a sparse model approach, four final non-nested models survived the selection process and were included into Occam’s group: LNT, Q, two-line splineFootnote 4 and the Gompertz models. For these four models, the model parameters (baseline and radiation-associated), their MLE and symmetric, Wald-type standard errors are provided in Table S2 of the Online Resource. Details related to model selection according to the sparse model approach are provided in the Online Resource (see pages 9, 15, 16, and Table S3).

According to the rich model approach, 10 models survived the selection process and contributed to MMI with normalized weights provided in Table 3. Figure 2 shows the ERR plotted against the cumulative lagged lung dose for the four final non-nested models and for the simulated dose–response curve from MMI, calculated with the sparse and the rich model approaches. Figures 3 and 4 show the best models and MMI for doses < 2 and 0.1 Gy, respectively. Table 4 provides risk predictions based on MMI (sparse) and the LNT, Q, two-line spline and Gompertz models. The radiation-associated excess cases according to the four final non-nested models and MMI (sparse) are presented in Table 5.

Table 3 Results of fitting the dose–response models from Fig. 1 as ERR models to the mortality data for ischemic heart diseases (Zablotska et al. 2014); Canadian Fluoroscopy Cohort Study, 1950–1987
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Fig. 2
figure 2

ERR for IHD mortality in the Canadian Fluoroscopy Cohort Study (follow-up 1950–1987) versus cumulative lagged lung dose for the four final non-nested ERR models (Table 3) and the simulated dose–response curves from MMI, calculated with the sparse model approach and the rich model approach. The shaded area represents the 95% CI region for the MMI (sparse model approach). For AIC-weights see the insert. The dotted-straight line shows the risk prediction from (Zablotska et al. 2014). The ERR-LNT model from the present study and the LNT model from Zablotska et al. (2014) give almost identical risk predictions. The figure is valid for males and females. A dose fractionation of 0.2 Gy year−1 was assumed. Point estimates and related 95% CI from the fit of an ERR-categorical model that divides the dose range into the following categories (D < 10−6 Gy, 10−6 Gy ≤ D < 1 Gy; 1 Gy ≤ D < 2 Gy, 2 Gy ≤ D < 6 Gy, and D ≥ 6 Gy) are as follows: ERR = 0.0089 (– 0.0173, 0.0348), ERR = 0.1820 (– 0.0652, 0.428), ERR = 1.002 (– 0.225, 2.23), ERR = 10.3 (– 17.8, 38.1). In the categorical fit, zero risk was assigned to the dose range D < 10−6 Gy. The point estimates and their 95% CI are not shown in the figure because of the very large 95% CI for the highest dose category. Online version contains color

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Fig. 3
figure 3

ERR for IHD mortality in the Canadian Fluoroscopy Cohort Study (follow-up 1950–1987) versus cumulative lagged lung dose up to 2 Gy for the four final non-nested ERR models (Table 3) and the simulated dose–response curves from MMI, calculated with the sparse model approach and the rich model approach. Vertical-dotted lines represent the 95% CI region for the MMI (sparse model approach). For AIC-weights see the insert. The dotted-straight line shows the risk prediction from (Zablotska et al. 2014). The figure is valid for males and females. A dose fractionation of 0.2 Gy year−1 was assumed. Online version contains color

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Fig. 4
figure 4

ERR for IHD mortality in the Canadian Fluoroscopy Cohort Study (follow-up 1950–1987) versus cumulative lagged lung dose up to 0.1 Gy for the four final non-nested ERR models (Table 3) and the simulated dose–response curves from MMI, calculated with the sparse model approach and the rich model approach. Vertical-dotted lines represent the 95% CI region for the MMI (sparse model approach). For AIC-weights see the insert. The dotted-straight line shows the risk prediction from (Zablotska et al. 2014). The figure is valid for males and females. A dose fractionation of 0.2 Gy year−1 was assumed. Online version contains color

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Table 4 Values for ERR for mortality from ischemic heart diseases (Zablotska et al. 2014) at various cumulative lung doses calculated with MMI (sparse model approach) and the four final non-nested models; Canadian Fluoroscopy Cohort Study, 1950–1987
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Table 5 Radiation-associated excess cases for the mortality data for ischemic heart diseases (Zablotska et al. 2014) according to the four final non-nested models and MMI (sparse model approach); Canadian Fluoroscopy Cohort Study, 1950–1987
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The Gompertz model had the best fit to the data (Table 3). Both Q and Gompertz models predicted no increase in risk below 0.05 Gy (Fig. 4). While both models predicted a sublinear dose–response at low and medium doses up to ~ 1 Gy, the two-line spline model predicted a risk higher than all other models (Figs. 2 and 3). The ERR predictions from MMI and LNT model at 0.1 Gy and 1 Gy are identical within their 95% CI (Table 4) and the dose–response from MMI is roughly linear at low doses (Fig. 4). At low and medium doses up to ~ 1 Gy, MMI and the LNT model predict similar risk values (Fig. 3). Consequently, up to 1 Gy both models (LNT and MMI) predict very similar excess cases (Table 5). At doses > 1.5 Gy, the dose–response from MMI predicted a higher risk compared to the LNT model (Figs. 2 and 3, Table 4). For the entire dose range, the dose–responses from MMI calculated using both the sparse and the rich model approaches were similar to each other (Figs. 2 to 4). For example, at 1 Gy, MMI predicted an ERR of 0.216 with 95% CI (0.062, 0.48) and ERR = 0.218 with 95% CI (0.058, 0.473), for rich and sparse model approaches, respectively.

Figure S2 of the Online Resource shows the baseline cases as predicted by the ERR-LNT model versus attained age with the secular trend together with crude rates.

Discussion

CFCS is the largest cohort of patients exposed to fractionated low-to-moderate doses of IR via fluoroscopic X-rays. About 15.5% of exposed CFCS patients were exposed to doses < 0.1 Gy and thus provide direct evidence of possible risks from low-dose exposures such as CT scans (like fluoroscopic examinations, CT scans in their most commonly known form apply X-rays). We examined ten biologically plausible dose–response models together with a categorical model. At low and medium doses the MMI technique predicted an almost linear dose–response.

While the sparse model selection approach led to a set of four final non-nested models, the rich model approach yielded an Occam’s group that contained ten out of the eleven dose–response models that were fitted to the data. Both sets of dose–response models describe the data approximately equally well (see values of ΔAIC in Table 3).

The reason for MMI-predicted risks being significantly higher compared to the LNT model at doses > 1.5 Gy is the relatively strong contributions of the Q, two-line spline and Gompertz models to the MMI (88% of the total, Table 3). At 5 Gy, MMI predicted an approximately fivefold risk compared to the LNT model, at 10 Gy a sixfold risk.

To better understand predicted radiation risks at higher doses, we used a restriction analysis based on cohort data with restricted dose-ranges and observed that the second slope of the two-line spline model (β2) was driven by high doses (> 2 Gy). When restricting the data to doses smaller than 2 Gy, the first slope (β1) of this model became very similar to the slope of the LNT model (results not shown). The LNT model was influenced mostly by doses < 2 Gy. The higher doses hardly influence the slope of the LNT model due to the lower number of cases in this dose range (212 cases out of 5818). Thus, the fit of the two-line spline model, which predicts a more than two times higher number of excess cases than the LNT model (Table 5), is consistent with the fit of the latter model.

The present study applied a larger range of biologically realistic smooth dose–response models (Fig. 1). Exploring a larger range of different dose–response models is motivated by the following biological findings, which are summarized in Table 1. The use of the LNT model finds support from the study of Stewart et al. (2006). These researchers investigated the effects of a high-dose (14 Gy) exposure on the development of atherosclerotic plaques (number of lesions, plaque area and plaque composition) in ApoE–/– mice. They found that after the high-dose exposure the mean number of atherosclerotic lesions (initial plus advanced) in carotid arteries of irradiated mice was significantly larger than in age- and sex-matched controls. Their study also revealed a significantly enhanced inflammatory content and plaque hemorrhage of irradiated carotid artery lesions compared to controls (Stewart et al. 2006). Because only one high-dose exposure was investigated, these findings infer an LNT-like dose–response. Analyses with a quadratic or linear-quadratic model are supported by the work of Hoving et al. (2008). They found that the number of initial atherosclerotic lesions and the plaque area in female mice 30 weeks after exposure to 0, 8 or 14 Gy clearly exhibit a dose–response consistent with a quadratic or linear-quadratic response (see panels B and E in their Fig. 3). In addition, some of the findings reported by Hoving et al. (2008) support the use of an LNT model. The specific feature of the linear-quadratic model that it can exhibit a U-shape at low doses is supported by the findings of Mitchel et al. (2011, 2013) and Ebrahimian et al. (2018). The findings of these three studies will be briefly described below in the context of the hormesis model. The application of the linear-exponential model is justified because of the findings by Mancuso et al. (2015) related to atherogenesis in ApoE–/– mice. Although the pattern of radiation-induced aortic alterations and their severity increased at 6 Gy compared with a 20-fold lower dose of 0.3 Gy, their results tend to be far from linearity and suggest that lower doses may be more damaging than predicted by a linear dose–response (Mancuso et al. 2015). The LTH model is another realistic possibility for a dose–response related to radio-epidemiological cohorts given the findings from animal studies on protective anti-inflammatory effects induced by low doses of radiation (Mitchel et al. 2011, 2013; Mathias et al. 2015; Le Gallic et al. 2015; Ebrahimian et al. 2018). Investigating the expression of various inflammatory and thrombotic markers in the heart of ApoE–/– mice, Mathias et al. (2015) provided evidence for anti-inflammatory effects after 0.025–0.5 Gy exposures: they found slight decreases of ICAM-1 levels and reduction of Thy 1 expression at these doses. In contrast, an enhancement of MCP-1, TNFα and fibrinogen at 0.05–2 Gy indicated a proinflammatory and prothrombotic systemic response (Mathias et al. 2015). In such a situation, a LTH model may describe the data better than the LNT model. Interestingly, Mitchel et al. (2007) reported that their dermatitis data from C57BL/6 J mice indicate that low doses may generally produce either no effect or protective effects with respect to this autoimmune-type and age-related non-cancer disease that has been linked to inflammation (Williams et al. 2012). The findings of anti-inflammatory protective effects at low doses (Mitchel et al. 2007, 2011, 2013, Mathias et al. 2015, Le Gallic et al. 2015, Ebrahimian et al. 2018) and detrimental effects at moderate (0.3 Gy) and higher doses (6 Gy) (Mancuso et al. 2015) provide a biological context for applying the smooth-step model (Fig. 1). A step-type response (with a steep slope) may reflect the distinct dose at which protective mechanisms are lost. Different tissues and different individuals can be expected to have different threshold-doses, leading to an overall smooth transition. While at low doses it is feasible that risk increase may be balanced by a protective decrease as in the LTH model, a smooth transition zone may exist where risk increases steadily, followed by a plateau. The sigmoid model can exhibit similar shapes as the smooth-step model. Therefore, the same references are relevant as for the smooth-step model (Mitchel et al. 2007, 2011, 2013; Mathias et al. 2015; Le Gallic et al. 2015; Mancuso et al. 2015; Ebrahimian et al. 2018). The empirical hormesis model applied in the current study has been introduced to describe stimulation of plant growth after low-dose herbicide exposures (Brain and Cousens 1989). Dose–responses which allow for protective effects at low doses, such as LQ, hormesis and two-line spline models, can be justified from mouse studies (Mitchel et al. 2011, 2013). Mitchel et al. (2011) exposed ApoE–/– mice to 0.025, 0.05, 0.10 or 0.50 Gy 60Co γ-irradiation at either low dose rate (1.0 mGy min−1) or high dose rate (approximately 0.15 Gy min−1) and investigated biological endpoints associated with atherosclerosis (aortic lesion frequency, size and severity, total serum cholesterol levels and the uptake of lesion lipids by lesion-associated macrophages). In general, low doses given at low dose rate during either early- or late-stage disease were protective, slowing the progression of the disease by one or more of these measures (Mitchel et al. 2011). The influence of low doses (0.025, 0.05, 0.10 or 0.50 Gy) of 60Co γ-irradiation at low dose rate (1.0 mGy min−1) or high dose rate (approximately 0.15 Gy min−1) on atherosclerosis in ApoE–/– mice with reduced p53 function was investigated by Mitchel et al. (2013). Radiation exposure to doses as low as 25 mGy at early-stage disease, at either the high or the low dose rate, inhibited lesion growth, decreased lesion frequency and slowed the progression of lesion severity in the aortic root. In contrast, exposure at late-stage disease produced generally detrimental effects. Both low- and high-dose-rate exposures accelerated lesion growth and high-dose-rate exposures also increased serum cholesterol levels. All effects were highly nonlinear with dose (Mitchel et al. 2013). An increase in anti-inflammatory and anti-oxidative parameters resulting in atherosclerotic plaque size reduction in ApoE–/– mice after chronic exposure to external low-dose γ-radiation was reported by Ebrahimian et al. (2018). Their results suggest that chronic low-dose gamma irradiation induces an upregulation of organism defenses leading to a decrease in inflammation and plaque size. Low-dose induced anti-inflammatory effects which play an important role in that context are currently intensely studied (see for example the reviews by Rödel et al. 2012a, 2012b, Frey et al. 2015) and have also been reported by Le Gallic et al. (2015) and Mathias et al. (2015). Earlier, low doses of γ-radiation delivered at low dose rates exhibited a protective effect related to chronic ulcerative dermatitis, an inflammatory skin reaction, in C57BL/6 mice, decreasing both disease frequency and severity and extending the lifespan of older animals (Mitchel et al. 2007). The two-line spline model can describe supralinear or sublinear dose–responses (Fig. 1) but also linear dependencies. Therefore, its application in the present study finds support from the same studies referenced in the context of the LNT model, the linear-exponential, LTH and hormesis models (refer to Table 1). The Gompertz model can exhibit linear, sublinear and smooth-step dose–responses but also supralinear responses. Therefore, its use in the present study is motivated by the same biological findings referenced in the context of the LNT model, the linear-quadratic, LTH, smooth-step and linear-exponential models, see Table 1.

Interpretation of our findings is limited by the absence of information on important independent risk factors for CVD in the CFCS data (Zablotska et al. 2014), particularly socioeconomic status and smoking. Only a limited amount of information is available on smoking for approximately 20% of the cohort (smoking was therefore not included in the baseline model, in accordance with Zablotska et al. 2014). Some studies suggest that these factors account for a substantial proportion of observed increase in CVD (see for example Yusuf et al. 2004). However, smoking was not associated with radiation (Zablotska et al. 2014), so could not be considered as a confounding variable in the current analyses. Furthermore, numerous recent studies found weak evidence for interaction between radiation and smoking (for example, Kreuzer et al. 2018). The CFCS data also lack information on other important CVD risk factors, such as family history of heart disease, diabetes, high blood pressure, obesity, and cholesterol plasma levels. However, because these factors are unlikely to be associated with radiation dose, they are unlikely to have biased the observed association between exposure and IHD mortality (Zablotska et al. 2014).

Another limitation is that all study participants had tuberculosis. We are aware that the precise relationship of radiation dose to IHD risk in immunocompromised, chronically ill tuberculosis patients may well differ from that in healthy individuals.

Our study findings are also limited by the end of follow-up in 1987 (Zablotska et al. 2014). It is noted that out of the 63,707 tuberculosis patients 34,717 individuals were still alive at the end of follow-up. CFCS study investigators are in the process of extending mortality follow-up by 30 years (1988–2017). In addition, they will also conduct, for the first time, cancer incidence follow-up of the cohort during 1969–2017. New doses to all organs within and outside the field of fluoroscopic irradiation will be estimated using computerized phantoms specific to the CFCS population.

Within the approach of the present study, the dose fractionation proportionally affects the magnitude of the dose–response function but not the shape of the dose–response. Given evidence of a significant inverse dose-fractionation association in the primary analysis (Zablotska et al. 2014), it seems to be a hypothesis of interest that the dose–response shape might differ by the dose rate, i.e., dose fractionation (while the person-year-weighted mean dose fractionation within the whole cohort is 0.109 Gy year−1, for mean cumulative person-year-weighted lagged lung doses  ≤ 0.1 Gy and > 0.1 Gy that quantity is 0.008 Gy year−1 and 0.101 Gy year−1, respectively). To investigate whether there may be any difference in the shape of the dose–responses at low- and high-dose fractionations the analyses of the present study could in principle be repeated within several strata of dose rate. Zablotska et al. (2014) performed such an analysis and calculated the ERR for three categories of dose fractionation. For IHD an inverse dose-fractionation association was found using the LNT dose–response model (see Table 6 in the publication by Zablotska et al. 2014). While such an effort is beyond the scope of the present study, there is also concern that such an in-depth analysis performed in the context of MMI may outstrip the CFCS data in terms of their ability to characterize risk of subsequent IHD in meaningful populations due to the above mentioned absence of information on classical modifiable cardiovascular risk factors such as lipids, hypertension, diabetes, abdominal obesity, diet, psychosocial factors, etc., as well as family history of IHD.

Generally, inference based on a set of multiple plausible models is a sound alternative to inference relying only on a single “best” model when the uncertainty in the model selection is large. The pitfall of using the MMI approach is, however, related to that specific aspect: the subjectivity of the model selection. In the present study, this problem is addressed with a two-tiered strategy. On the one hand, as already stated above, the models in Fig. 1 are carefully chosen to reflect as many biologically plausible shapes for dose–responses as possible. On the other hand MMI was applied in two different approaches, sparse and rich, as described in the “Materials and methods”. In the center of the case-weighted means (case-weighted mean age, case-weighted mean dose, etc.) all models yield similar risks. Only at the borders of the data space where only a few cases are located the calculated risks will differ strongly. Here, MMI helps with the comprehensive characterization of uncertainties.

In the context of subjectivity of model selection the following aspect is noted. It would be generally possible to choose a larger number of non-nested plausible models (of the same or similar number of parameters) that could lead to fits of similar shapes. That way one could end up with a situation of having a very large number of models in the set of final non-nested models, each of which with a very small AIC-weight. This situation is prevented by only including into Occam’s group those non-nested models with a bilateral AIC-weight larger than 5% (see Table S3 of the Online Resource including the related footnote e).

At low and medium doses our results are in agreement with the earlier findings (Zablotska et al. 2014) and based on a more comprehensive analysis with a larger series of biologically plausible dose–responses. An essential difference with the primary analysis (Zablotska et al. 2014) is the use of a different baseline model. The present study applied the parametric baseline model given in equation (S4) of the Online Resource with 21 baseline parameters while in (Zablotska et al. 2014) a stratified baseline model with one free parameter for each possible combination of available categories in the data was used. Their baseline model contained several thousand free parameters and was not suitable for AIC-based MMI analysis for which parsimony in parameters is essential (Walsh and Kaiser 2011).

In a recent MMI-based analysis of the LSS mortality data for heart diseases observed during 1950-2003 an ERR of 0.08 at 1 Gy with 95% CI (0, 0.20) was reported (Schöllnberger et al. 2018). Shimizu et al. (2010) reported an ERR per dose of 0.14 Gy−1 with 95% CI (0.06, 0.23). Within the error bars these values are consistent with our estimate of 0.216 at 1 Gy with 95% CI (0.062, 0.48). For IHD, however, these authors did not find a significant association between radiation exposure and IHD (refer to Web Table B in Shimizu et al. 2010). The latest analysis of the LSS mortality data with extended follow-up from 1950 to 2008 found no significant association between radiation exposure and IHD either (Takahashi et al. 2017). For IHD mortality in male Mayak workers, an ERR per dose of 0.09 Gy−1 with 95% CI (0.02, 0.16) was reported (Simonetto et al. 2014). This value is consistent with the risk prediction from the present study. For females, no significant elevation in risk was found (Simonetto et al. 2014). Azizova et al. (2015a) did not find a significant association of total dose from external γ-rays with IHD mortality in Mayak workers. A population-based case–control study of major coronary events (i.e., myocardial infarction, coronary revascularization, or death from IHD) in 2168 women who underwent radiotherapy for breast cancer between 1958 and 2001 in Sweden and Denmark was conducted by Darby et al. (2013). The study included 963 women with major coronary events and 1205 controls. Rates of major coronary events increased linearly with the mean dose to the heart by 7.4% per gray (95% confidence interval, 2.9 to 14.5; P < 0.001), with no apparent threshold (this corresponds to an ERR per dose of 0.074 with 95% CI (0.029, 0.145)). Darby and colleagues had applied a linear dose–response model. In that context it is noted that Schneider et al. (2017) put forward arguments that the dose–response may not necessarily be linear. It follows from Darby et al. (2013) that for a mean heart dose of 5 Gy ERR = 0.37 with 95% CI (0.15, 0.73). The value of ERR = 0.37 is considerably lower than our MMI estimate for 5 Gy (see Table 4: ERR = 4.70 at 5 Gy with 95% CI (0.60, 10)). Ghobadi et al. (2012) report results from rodent experiments showing that irradiation of heart, lung, or both independently induces specific cardiac dysfunction and pulmonary vascular damage, mutually enhancing each other. Their findings suggest that irradiation of an already diseased lung can indirectly increase the IHD risk, compared to irradiation of a healthy lung. We may hypothesize that this biological effect increases the IHD risk significantly compared to LNT behavior at doses above 2 Gy, which are concomitantly associated with long duration of tuberculosis.

There remains considerable controversy over the effects of dose-protraction on long-term health outcomes. In fact, the ICRP is putting a major effort into evaluating the many modern studies with dose-protraction (Shore et al. 2017). Survivors of atomic bombings in Hiroshima and Nagasaki were exposed to acute exposure and could not provide useful information on the effects of dose fractionation. Limited data exist on the dose rate effects in Mayak workers, primarily in the form of annual absorbed doses. In contrast, the CFCS has detailed exposure information on the dose and dose rate of a typical fluoroscopic examination and number of fluoroscopic procedures for each patient per year. Altogether, the CFCS is the largest study of patients exposed to moderately fractionated low-to-moderate doses of IR and presents one of the most valuable cohorts worldwide to derive information related to radiation effects at low, moderate and high doses of IR.

For IHD mortality among 308,297 nuclear industry workers from France, United Kingdom and United States, as part of the International Nuclear Workers Study (INWORKS), an ERR per dose of 0.18 Sv−1 with 90% CI (0.004, 0.36) was reported (Gillies et al. 2017). Recently, the CFCS data for IHD (Zablotska et al. 2014) were combined with a cohort of tuberculosis fluoroscopy patients from Massachusetts and analyzed with a linear dose–response model applying two different dose regimes with a fixed cut-point at 0.5 Gy (Tran et al. 2017). The authors reported increasing trends for doses < 0.5 Gy; over the entire dose range a negative dose trend was observed (Tran et al. 2017). This is probably due to the inability to adjust for dose fractionation effects in the Massachusetts data where only cumulative doses to the lung have been estimated. The present study used a more comprehensive and flexible approach by analyzing the data with a variety of different linear and nonlinear models including those that exhibit flexible threshold-doses without applying artificial cut-points at certain doses and without relying on LNT as a foregone conclusion (Little et al. 2012, Little 2016).

Conclusions

The present study confirms previous findings in a number of studies of essentially linear dose–response for death from IHD at low and moderate doses (0–1 Gy). Our analyses suggest that different biological mechanisms may operate at low and medium doses compared to high doses and that at higher doses, the LNT model may underestimate the risk compared to the dose–response from MMI by a factor of 5. Our results should be of particular interest to international radiation protection organizations, which largely rely on analyses of radio-epidemiological cohorts using the LNT model. We conclude that our findings have important implications for risk assessment of IR in the context of medical applications (such as CT scans and radiotherapy), nuclear energy production and accident related long-term risks.