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Exposure–lag–response associations between lung cancer mortality and radon exposure in German uranium miners

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Exposure–lag–response associations shed light on the duration of pathogenesis for radiation-induced diseases. To investigate such relations for lung cancer mortality in the German uranium miners of the Wismut company, we apply distributed lag non-linear models (DLNMs) which offer a flexible description of the lagged risk response to protracted radon exposure. Exposure–lag functions are implemented with B-Splines in Cox models of proportional hazards. The DLNM approach yielded good agreement of exposure–lag–response surfaces for the German cohort and for the previously studied cohort of American Colorado miners. For both cohorts, a minimum lag of about 2 year for the onset of risk after first exposure explained the data well, but possibly with large uncertainty. Risk estimates from DLNMs were directly compared with estimates from both standard radio-epidemiological models and biologically based mechanistic models. For age > 45 year, all models predict decreasing estimates of the Excess Relative Risk (ERR). However, at younger age, marked differences appear as DLNMs exhibit ERR peaks, which are not detected by the other models. After comparing exposure–responses for biological processes in mechanistic risk models with exposure–responses for hazard ratios in DLNMs, we propose a typical period of 15 year for radon-related lung carcinogenesis. The period covers the onset of radiation-induced inflammation of lung tissue until cancer death. The DLNM framework provides a view on age-risk patterns supplemental to the standard radio-epidemiological approach and to biologically based modeling.

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  1. In the standard radio-epidemiological approach, exposure–response is related to cumulative exposure, whereas exposure–response in the DLNM framework is related to exposure rate.

  2. \(\otimes\) denotes the Kronecker product, while \(\odot\) denotes the Hadamard product


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Dr. Gasparrini was supported by the Medical Research Council UK (Grant IDs: MR/M022625/1 and MR/R013349/1). The authors would like to thank Dr. Kreuzer and Dr. Sobotzki (Federal Office for Radiation Protection) for the excellent cooperation in providing the data and for their comments. We also thank two anonymous referees for their helpful comments.

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Results of DLM analysis

For all models, the maximum time lag L was fixed to 40 year as in Gasparrini (2014). Each model is adjusted for age at begin of employment (abe) and the calendar year (cal) (Eq. (1)).

Models L1 and L3 apply constant and piecewise constant functions for \(w_x(\ell )\), respectively. Piecewise constant functions possess three cut-off points at time since exposure 10 year, 20 year, and 30 year (See Tables 2, 3).

Models L2 and L4 correspond to models L1 and L3 albeit with additional adjustment for silica dust. The corresponding exposure–response \(f(z_{t-\ell })\) is specified as a linear threshold function. Response to silica exposure is restrained to zero below a threshold of 0.92 mg/\(m ^3\)/yr; above threshold \(f(z_{t-\ell })\) increases linearly. The threshold value is motivated in ref. (Zaballa and Eidemüller 2016) as break point for the capability of silica dust removal. The lag–response \(w_z(\ell )\) for silica dust is defined as a piecewise constant function with two cut-off points at equally spaced quantiles of the distribution of the lags. There is no evidence of departure from of multiplicative joint effect for exposure to radon and silica dust. This choice yields an acceptable flexibility under the condition of not spending too many model parameters df on a complicated modeling of silica dust. In this way, all models of the present study consume five parameters df on controlling for the confounders of silica dust, age at begin of employment, and the calendar year (Figs. 6, 7, 8, 9, 10, 11).

Comparing models with adjustment for silica dust L2 and L4 with their counterparts L1 and L3 without adjustment reveals improvement in the AIC of at least 50 points and likewise improvements in the BIC (Table 2). These findings justify the inclusion of silica dust adjustment in the main analysis of the present study. Figure 6 depicts lag–responses for models L1–L4 with more pronounced shapes for increasing radon exposure rates. In terms of goodness-of-fit, the introduction of more complex shapes for the lag–response yields moderate improvements (Table 2).

Fig. 6
figure 6

Comparison of lag–response curves for the hazard ratio (HR) of DLMs L1–L4 for four different radon exposure rates 50 WLM/yr, 100 WLM/yr, 150 WLM/yr, and 200 WLM/yr, in models L2 and L4 (red lines) silica dust is a confounder but not in models L1 and L3 (blue lines); for models L1 and L2 (solid lines), the lag–response is constant; for models L3 and L4 (dashed lines), the lag–response is piecewise constant with cut-off points at 10 year, 20 year, and 30 year

Table 2 Properties and goodness-of-fit for DLMs L1–L5 with a linear exposure–response \(f(x_{t-\ell })\) to annual radon exposure rates and varying shapes of lag–responses \(w_x(\ell )\); for piecewise constant, lag–response cut-offs are located 10 year, 20 year, and 30 year; df denotes the number of model parameters, lowest values for AIC and BIC in bold; L5 is the preferred DLM

The next phase of model development was concerned with improvements of the lag–response \(w_x(\ell )\) of DLMs. To determine the shape of \(w_x(\ell )\), we tested models with B-Splines of degrees one to six with zero up to five knots on equally spaced quantiles of the weighted lag distribution. The intercept of the hazard ratio (HR) on the y axis was determined in the fits. For most of the curves, the intercepting HR was estimated < 1, and the HR exceeded 1 only after a lag of 3 years. This observation strengthens the argument that no risk occurs in the early years after exposure. In our models, we set the minimum lag to 2 year. However, we do not allow hormetic effects in the lag–response and fix HRs smaller than one at early lags to zero. For the preferred DLM L5, the shape of the lag–response is shown in Fig. 7 for various radon exposure rates. Modeled with a quadratic B-spline and one knot, lag–response curves for model L5 exhibit a maximum at about 9 year after first exposure followed by a steady decline. Properties of model L5 are given in Table 2.

Fig. 7
figure 7

Lag–response curves for the hazard ratio (HR) of the preferred DLM L5 for five radon exposure rates between 30 WLM/yr and 200 WLM/yr

DLNM NL3 with right-constrained lag–response at 40 year

Fig. 8
figure 8

Selected lag–response curves of the hazard ratio (HR) for exposure rates between 30 and 200 WLM/yr (left panel) and exposure–response curves for time since exposure between 10 and 30 year (right panel) for DLNM NL3 with right-constrained lag–response function at 40 year

Fig. 9
figure 9

The exposure–lag–response surface for the hazard ratio (HR) of DLNM NL3 with right-constrained lag–response function at 40 year

Estimates for confounders age at begin of employment, calendar year, and silica dust exposure for the preferred DLNM NL4

Fig. 10
figure 10

Selected lag–response curves of the hazard ratio (HR) for exposure rates between 1 and 5 \(\frac{\mathrm{mg}/\mathrm{m}^3}{\mathrm{yr}}\) (left panel) and exposure–response curves for time since exposure between 10 and 30 year (right panel) for silica dust for the preferred DLNM NL4

Table 3 Estimates of cal and abe from DLNM NL4
Table 4 Estimates of cross-basis coefficients for the preferred DLNM NL4

Baseline rates \(\lambda _0\) of lung cancer mortality from the preferred DLNM NL4

Fig. 11
figure 11

Baseline rates of lung cancer mortality from the preferred DLNM NL4 are averaged among age groups of 5 years and calculated separately for six calendar periods between 1946 and 2003

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Aßenmacher, M., Kaiser, J.C., Zaballa, I. et al. Exposure–lag–response associations between lung cancer mortality and radon exposure in German uranium miners. Radiat Environ Biophys 58, 321–336 (2019).

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