The association between radon gas exposure and lung cancer has been well-documented in cohorts of underground Uranium Miners.1–7 However, traditional regression analysis techniques used in these studies focus on quantifying cumulative exposure-response functions that do not directly address the types of questions that concern regulators. The public health impacts of different policy options regarding radon concentrations in the workplace may be more useful to regulators than the estimated change in the excess relative rate of lung cancer per unit increase in cumulative exposure to radon.
Using data from an important cohort study of underground miners, we apply the extended parametric g-formula8,9 to estimate the risk of lung cancer death had several historical radon exposure standards been in place throughout follow-up. The policy interventions that we consider are specified in terms of caps on monthly occupational radon exposure rather than limits on cumulative exposure (ie “limit radon exposure to X working-level months per month while at work, and set monthly radon exposure to 0 working-level months when not at work”). The interventions we consider are “threshold interventions”10 in which the intervention on radon exposure for a given month depends on the observed exposure for that month.
The extended parametric g-formula has been used to estimate cumulative risk under threshold interventions in diverse substantive areas.11–15 This approach was described by Robins et al9 to extend the standard parametric g-formula estimator to allow interventions to depend on the natural value of exposure. A formal discussion of the identifying conditions under which the extended parametric g-formula estimator can have a causal interpretation can be found in recent work by Richardson and Robins16 and by Young et al.17 Our implementation of the parametric g-formula also accommodates competing risks, as outlined by Taubman et al11 and by Cole et al.15
Here, we use the g-formula to estimate cumulative incidence of lung cancer mortality under various intervention scenarios and compute risk difference and risk ratio measures, which are often the most relevant estimates to present to the lay public and policy makers. These effect measures have intuitive interpretations as the estimated difference (or ratio) in cumulative incidence that would have been seen had the same population of miners been exposed to different dynamic exposure regimes corresponding to hypothetical industry guidelines.
Estimates of attributable risk due to lung cancer derived in previous reports, such as the Biological Effects of Ionizing Radiation IV and VI reports, and life table calculations also aim to facilitate communication of the public health impact of radon exposure. However, these previous reports estimate the attributable fraction of radon-related excess lung cancer deaths, which conforms to change in risk given complete elimination of radon; we instead focus on public health impacts of plausible policy interventions (ie reduction in radon exposure to specific limits, rather than elimination of radon exposure).
In this work, we use the extended parametric g-formula to compare observed lung cancer mortality in the Colorado Plateau Uranium Miners cohort to estimated lung cancer mortality if radon exposure had been limited to 3 historical radon exposure standards in the United States.
The Colorado Plateau Uranium Miners’ cohort includes 4137 men who worked in an underground uranium mine on the Colorado Plateau for at least 1 month prior to 1 January 1964 and agreed to a health screening between 1950 and 1960. Miners began follow-up at the midpoint of the year of age in which their first health screening occurred or, if the miner was younger than 18 years at their first health screening, age 18. Miners were followed until death or December 31, 2005, as described in a previous report.7 Age, calendar year at cohort entry, and race were ascertained during the health screening. In the current study, we administratively censor workers at 90 years of age to avoid imprecise estimates at older ages when few miners were alive and at risk for lung cancer mortality (n = 84; 5 lung cancer deaths). Three miners whose estimated cumulative radon exposure exceeded an implausible level of 10,000 working-level months were excluded.
As an analysis of existing deidentified data, this study was granted an exemption by the University of North Carolina’s Institutional Review Board.
Vital status was ascertained using Social Security Administration, Internal Revenue Service, National Death Index, and Health Care Financing Administration records.3,7 For follow-up through 1990, death certificates were reviewed by a nosologist and underlying cause of death was coded using the International Classification of Diseases (ICD) codes in use at the time of death.3,4 Additional follow-up through 2005 was performed through linkage to the National Death Index and the Social Security Administration mortality file.7 Miners who were confirmed alive in 1979 (when the National Death Index began) and not found in these databases were presumed to be alive at the end of follow-up. Fourteen miners were lost to follow-up prior to 1979, and no cause of death was reported for 22 miners. Lung cancer mortality was defined as an ICD code for malignant neoplasm of trachea, bronchus, and lung: ICD-6 codes 162–163; ICD-7 codes 162.0, 162.1, 162.8, and 163; ICD-8 code 162; ICD-9 code 162; and ICD-10-CM codes C33-C34.
Radon Exposure Assessment
Details of radon exposure assessment in this cohort have been described previously.3,4,7 Radon levels in Colorado plateau uranium mines were measured between 1951 and 1968. During this time period, 43,000 measurements were made in 2500 mines. These measurements were used to estimate annual average radon concentrations in each mine; if multiple measurements were available in the same year for a mine, those measurements were averaged to produce a summary measurement.18
The cumulative radon exposure for each miner was estimated based on the mine-specific annual radon concentration estimates and the miner’s employment history. Cumulative exposure to radon progeny was expressed in units of the working-level month, which is equivalent to experiencing one “working-level” for 170 hours. A working-level is the combination of radon decay products in 1 liter of air that would result in emission of 20.8 microjoules of potential alpha energy exposure per cubic meter of air. Occupational radon exposure was assumed to be 0 after cessation of employment. Cumulative radon exposure prior to study entry was assigned to the day prior to study entry.
We use the parametric g-formula to estimate the proportion of miners experiencing lung cancer mortality under 4 exposure scenarios: (1) no intervention on exposure; (2) monthly radon exposure capped at the radiation protection guideline recommended by the first report of the Federal Radiation Council in 1960 (3 rems per 13 weeks = 2 working-level months)19; (3) monthly radon exposure limited to the Federal Radiation Council’s 1967 recommendation, which was the basis for the US Environmental Protection Agency’s 1971 guidance on radiation protection for underground uranium mining (12 working-level months per year/12 months = 1 working-level month)20,21; and (4) monthly radon exposure capped at the US Mine Safety and Health Administration exposure standard adopted in the 1970s and still used in 2014 (4 working-level months per year/12 months = 0.33 working-level months).22 Using the g-formula, we estimate the lung cancer mortality under the following dynamic treatment regime: if at work, radon exposure level is not allowed to exceed the intervention level, and if not at work, radon exposure level is set to 0.
The steps to implement the extended parametric g-formula have been described in detail elsewhere.11–15 First, we parametrically model the conditional probabilities of the exposure, outcomes, and work status using the observed data (see the eAppendix, http://links.lww.com/EDE/A821, for details). We use the estimated conditional probabilities to predict work status, exposure, other death, and lung cancer mortality under the “natural course,” an intervention that prevents censoring due to drop out but does not intervene on exposure status, in a Monte Carlo sample of 50,000 miners drawn with replacement from the existing cohort. The large Monte Carlo sample is used to minimize simulation error. We estimate the distributions of baseline covariates nonparametrically using the empirical distribution in the Monte Carlo sample. We compare these predicted values with the observed data to assess the fit of the parametric models.23
Next, in the same Monte Carlo sample of miners, we estimate the cumulative incidence of lung cancer had each of the 3 historical radon exposure guidelines described above been in place from cohort entry through the end of employment. Note that exposure accrued prior to entry is not influenced by the policy interventions under study. For each of these scenarios, if a miner’s estimated monthly exposure exceeds the monthly exposure limit, the miner’s exposure for that month is set to the intervention exposure limit. If the miner’s estimated monthly exposure is below the monthly limit, no intervention occurs for that miner in that month. This might be conceptualized as an intervention under which the miner is removed from the mine when the limit is reached for the month and allowing him to return to work the following month.
The parametric g-formula uses the following process to estimate lung cancer mortality under each intervention scenario. (1) Exposure and work status are assigned using the conditional probabilities estimated from the parametric models above; (2) If the miner is not at work during that month, exposure is set to 0. If the miner is at work, exposure is estimated using the conditional probabilities estimated from the parametric models discussed above. If the predicted dose for any month exceeds the intervention level, it is set to the intervention level; otherwise, the miner’s exposure is not intervened on for that month; (3) The probability of lung cancer mortality is estimated based on the joint distribution of covariates; (4) An indicator of lung cancer death is drawn from a Bernoulli distribution with the probability estimated from step 3; and (5) The cumulative incidence of lung cancer mortality is estimated in the simulated cohort.
We estimate cumulative lung cancer mortality for each intervention scenario using an extension of the Kaplan-Meier approach that accommodates competing risks and yields an estimate of the cumulative subdistribution of lung cancer mortality.11,24 Lung cancer mortality is compared between each intervention scenario and the natural course using risk differences (RDs) and risk ratios (RRs), and 95% confidence intervals (CIs) are computed using standard errors estimated by the standard deviation from results of the procedure conducted using 200 nonparametric bootstrap resamples. SAS version 9.3 (SAS Institute, Inc., Cary, NC) was used for all analyses.
In total, 4134 male miners entered follow-up between 1950 and 1964. Table 1 describes the characteristics of the study population at baseline. Most (94%) of the cohort had been occupationally exposed to radon prior to study entry, with a median cumulative radon exposure of 154 working-level months. The median time between hire and cohort entry was 1.5 years (interquartile range = 0.3–3.9). The cohort was followed for 135,275 person-years and experienced 617 lung cancer deaths and 14 losses to follow-up. The median age at lung cancer death was 71 (interquartile range = 63–90) years, with the youngest death occurring at age 33 years (Figure 1).
The natural course replicates the observed data closely. Differences in the distribution of person-months by age, calendar year, race, smoking status, employment, and radon exposure between the natural course and the observed data were negligible (Table 2). Figure 2 illustrates the similarity in predicted lung cancer mortality between the observed data and the model estimates from the natural course.
Radon exposure was reduced from a median of 3.47 working-level months per month under the natural course to 1.34, 0.81, and 0.31 working-level months per month, under the intervention limits of 2, 1, and 0.33 working-level months, respectively. Because the interventions caused miners to live longer, the distribution of person-months shifted toward older ages, later calendar years, and a smaller proportion of months employed (Table 2).
With no intervention on radon exposure, estimated lung cancer mortality by age 90 was approximately 16%. Interventions limiting radon exposure to historical radon exposure guidelines resulted in lower cumulative lung cancer mortality by age 90. With incremental decreases in radon exposure limits, there was a corresponding reduction in lung cancer mortality under the 3 interventions (Figure 3). The risk of lung cancer death by age 90 decreased by 23% (risk ratio = 0.77 [95% CI = 0.72 to 0.81]), 28% (0.72 [0.68 to 0.77]), and 33% (0.67 [0.61 to 0.73]), when each miner’s monthly radon exposure was capped at 2, 1, and 0.33 working-level months, respectively (Table 3). In the simulated cohort, we estimate that capping exposure at the Federal Radiation Council guidelines of 2 and 1 working-level months would have prevented 149 and 187 lung cancer deaths by age 90, respectively, whereas capping exposure at the Mine Safety and Health Administration standard of 0.33 working-level months would have prevented 216 lung cancer deaths over the study period.
We applied the parametric g-formula to estimate the effect of radon exposure interventions on lung cancer mortality in the Colorado Plateau Uranium Miners cohort. By limiting monthly radon exposure to 2, 1, and 0.33 working-level months, we estimated that lung cancer mortality would have been reduced by 23%, 28%, and 33%, respectively. These reductions are notable given that 77% of the cohort was classified as ever-smokers. Had the most stringent of the guidelines, the Mine Safety and Health Administration standard of 0.33 working-level months, been in place (and followed) throughout the study period, we estimate that 216 fewer lung cancer deaths would have occurred than were observed under the actual history of regulation. Our findings support historical recommendations to lower radon exposure limits and suggest that the Mine Safety and Health Administration standard prevents a substantial number of lung cancer deaths among people who are occupationally exposed to radon.
The parametric g-formula provides estimates of the cumulative incidence of lung cancer death for exposure scenarios under several assumptions. The first assumption, sometimes called the consistency assumption, requires that exposure levels set by investigators in the counterfactual scenarios correspond to well-defined interventions. For our study interventions, we capped monthly radon exposure at a specified number of working-level months. This scenario could be achieved by using personal radon monitoring devices and removing the worker from the mine when the limit is reached and then returning him to work the following month. One could imagine other scenarios, such as job sharing/switching, respirator use, improving ventilation with ambient monitoring, or gradually reducing exposure by limiting the number of hours worked when a miner’s exposure approaches the intervention level. Our analysis assumes that these methods of capping exposure would produce equivalent results.
We also assumed that miners’ potential outcomes were independent of the exposure they received, conditional on observed variables. This assumption, known as the exchangeability assumption, implies no unmeasured confounding or selection bias, and means that experiences of participants receiving low exposures represent the potential outcomes of participants receiving high exposures, had they received low exposures. Because we did not have information on time-varying smoking status, we included smoking as a fixed variable at study entry under the assumption that most workers started smoking prior to their employment in the mine. The exchangeability assumption may have been violated if there were differences in smoking status over time between miners with high and low radon exposure. It is also possible that an unobserved variable such as health status or exposure to silica may have been associated with mine exposure intensity or duration and lung cancer mortality. In addition, the estimates presented here are conditional on miners surviving exposure between the date of hire and cohort entry. Although this could result in selection bias, it is unlikely that radon exposure would have caused lung cancer deaths during this brief period.
This version of the parametric g-formula assumes that the parametric models used to predict relevant variables are correctly specified. To obtain a consistent point estimate, we must correctly specify 4 parametric models (for work status, exposure, death, and lung cancer death). We used monthly linear models to predict the natural log of radon dose and pooled logistic regression models for work status, non-lung cancer deaths, and lung cancer deaths. We assume that there is no interaction between radon and smoking, that the effects of radon persist over time, and that there is no variation in the effect of radon on lung cancer mortality with time since exposure or exposure rate. Relaxing this assumption to allow interaction between cumulative radon exposure and exposure rate in the model to predict lung cancer mortality (as discussed in the BEIR VI report)1 did not alter the results. Covariate distributions and cumulative incidence functions in the observed data closely matched our predicted natural course, suggesting that the models may be adequately specified, but the modeling assumptions are not testable. Confidence intervals are narrow partly because this method is fully parametric, and the additional modeling assumptions reduce the variance of the estimate.
Estimates of lung cancer mortality in the intervention scenarios may be subject to error from at least 2 sources. First, lung cancer mortality under the intervention scenarios is predicted based on observed lung cancer mortality for miners who were exposed to low doses of radon. There was a substantial proportion of exposed person-time with radon exposures below the intervention levels (31% of exposed miners had radon levels ≤2 working-level months). However, results may be biased if miners who received low doses of radon exposure were systematically different from miners who received higher doses, in ways other than measured variables. Second, larger exposure measurement error at low doses of exposure could imply that the dose-response relation between radon exposure and lung cancer mortality is incorrectly specified.
Studies of the health effects of occupational exposures are subject to the healthy worker survivor bias, in which work status is both a time-varying confounder and a mediator of the relationship between exposure and outcome. In addition, traditional analyses of occupational data are often subject to bias due to nonpositivity or zero probability of exposure within strata of a confounder (here, when participants are not at work). Naimi et al25 demonstrated that Cox proportional hazards models with or without adjustment for work status and marginal structural Cox proportional hazards models fit using inverse-probability weights produced biased estimates in situations characterized by the healthy worker survivor effect.
The g-formula appropriately accounts for time-varying confounding by work status by allowing investigators to set exposure at each time point. In addition, the g-formula allows estimation of the effects of interventions that avoid violations of the positivity assumption. The positivity assumption is violated if (1) radon exposure is impossible when the miner is not working; (2) time-varying work status is a confounder; and (3) the interventions under consideration require that a person have nonzero exposure when not at work. The interventions considered here did not require the miners to be exposed when they were not at work and therefore did not induce bias due to nonpositivity.26
The parametric g-formula is subject to the g-null paradox, in which it will reject the null hypothesis (of no causal effect of exposure on outcome) even when true if the sample is sufficiently large. However, because the existing literature provides strong evidence that the causal null hypothesis is false (ie, that radon does affect lung cancer mortality),2–4,6,7,27–31 use of the parametric g-formula is justified in this setting.
This analysis estimates the effect of reducing occupational radon exposure to specific monthly doses on lung cancer mortality. Instead of estimating the reduction in mortality per unit of cumulative radon exposure (as in standard regression models) or the reduction in mortality if no miners had been exposed to radon (as in attributable fraction calculations), we used the g-formula to compare mortality under interventions on radon exposure that correspond to potential (and, in this case, historical) regulatory limits. The estimated reduction in mortality associated with applying various policy guidelines demonstrates the ability of the parametric g-formula to estimate intervention effects and provide intuitive results for policy makers.
We thank Alex Keil for helpful comments on an earlier version of this manuscript. The findings and conclusions in this report are those of the authors and do not necessarily represent the views of the National Institute for Occupational Safety and Health.
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