Study of occupational exposure to human carcinogens is key to a better understanding of public and worker health. However, a key barrier to understanding health effects of occupational exposures is healthy worker survivor bias.^1–3 Healthy worker survivor bias is a phenomenon in which healthier workers persist longer in jobs than less healthy workers, thus potentially accruing more exposure.⁴ Employment status often predicts health outcomes under study, which can bias estimates of association between exposure and health if employment status is not considered in analysis.^5,6 Further, when exposure can influence employment status (eg, if latent disease caused by exposure leads to impaired ability to work), this bias is not amenable to control through covariate adjustment in standard regression models of exposure-disease relationships.¹

Healthy worker survivor bias was an initial motivation behind the parametric g-formula, an approach that utilizes regression models within the framework of g-computation to estimate causal effects of occupational exposures under assumptions that allow for control of healthy worker survivor bias.⁷ The parametric g-formula can be used to directly assess impacts of exposure limits on worker health, which aids in decision-making around personal exposure limits in the workplace. Briefly, this approach utilizes multiple regression models (exposure, employment, and outcomes) and a Monte Carlo simulation to estimate cumulative risk under hypothetical interventions. The parametric g-formula has been used to assess impacts of hypothetical exposure limits for a number of occupational hazards such as asbestos, arsenic, diesel exhaust, particulate matter, and radon.^8–13 However, estimators of the parametric g-formula are highly modeling and simulation intensive, which creates 2 practical issues: (1) heavy reliance on modeling assumptions for validity and (2) heavy computational burden.¹⁴ G-estimation of structural nested models is another feasible approach, but it is difficult to interpret¹⁵ or may not estimate cumulative risk,¹⁶ which is often the target of risk assessment. Inverse probability-of-exposure weighted estimation of marginal structural models has been recommended against because the probability of exposure is zero among those who have left work, violating a key assumption of the approach.¹⁷

To address healthy worker survivor bias and assess impacts of exposure limits on worker health, we propose use of inverse probability of censoring weighting for dynamic regimes.^18–20 This approach uses the observed data as a pseudo-trial in which individuals are artificially censored from the observed data when they are observed to be inconsistent with the “treatment arm” (eg, monthly exposure above an occupational limit), and inverse probability weighting is used to correct for the bias introduced by censoring. Here, we demonstrate this approach in a reanalysis of the Colorado Plateau Uranium Miners (CPUM) cohort.²¹ We demonstrate strengths of this approach for reducing modeling assumptions while estimating impacts of hypothetical occupational exposure limits.

Worker and person-time characteristics are given in Table 1. Fifteen percent of the workers had deaths attributed to lung cancer. Workers had high cumulative exposure to radon (median across follow-up = 280 WLM, respectively, 5-year lag). Cumulative employment was 6 years (1-year lag), averaged over all follow-up time.

Estimated weights for a limit of 0.33 WLM yielded a mean, stabilized weight of 1.71, indicating substantial concerns for bias. Thus, we did not use censored data from regimes with limits below 0.75 WLM.³⁴ For other regimes, the mean inverse probability weight was close to 1.0 (Table 2). Most censoring occurred in the first observation rather than later in follow-up. Sparsity was not apparent in tabular analyses, supporting findings from the weights (Web Table 1) (available at https://doi.org/10.1093/aje/kwae299).

Semiparametric estimates of the hazard ratio were very similar to estimates from the fitted marginal structural model (Figure 2, Table 3). Estimates of cumulative mortality incidence derived under the marginal structural Cox model (along with a similar model for competing risks) yielded cumulative incidence estimates that also tracked well with nonparametric estimates, suggesting that the fitted model produced accurate risk estimates (Figure S3). Notably, extrapolating from this model to estimate lung cancer cumulative incidence by age 90 years at a limit of 0.33 WLM yields an estimate (95% CI) of 0.06 (0.03–0.09). Under no exposure, cumulative mortality incidence was negligibly lower (at the levels of rounding we used) than the estimate at 0.33 WLM. Nonparametric cumulative mortality incidence estimates from ages 16 to 90 years at 1 and 2 WLM are lower but less precise than prior estimates from the parametric g-formula (Figure 3).¹³

Sensitivity analyses suggested that further control for employment or exposure histories did not substantially change our estimates of lung cancer risk under the dynamic regimes we examined down to 0.75 WLM (Web Tables 1–6).

Personal exposure limits in the occupational setting have a natural interpretation as dynamic exposure regimes. We estimated that, among 4127 workers in the CPUM cohort, elimination of exposure would have cut lung cancer risk through age 90 years from over 16% to just under 6%, a stark demonstration of the hazardously high exposures experienced by this cohort. Our approach to contrasting exposure limits in worker cohorts reduces strong parametric assumptions of existing approaches. Crucially for using occupational data to assess risk from occupational exposures, our approach can reduce concerns about healthy worker survivor bias.

The CPUM cohort makes a compelling example for this approach. First, this cohort has previously been used to estimate effects of dynamic exposure regimes similar to ones we assessed. Second, this cohort has played a role in determining the personal exposure limits that workers experience today.⁴¹ Third, this cohort is highly exposed, which helps to highlight some challenges of assessing risk at low exposure, including the role of model specification. Edwards et al¹³ used the parametric g-formula to estimate that, under a dynamic regime that capped all worker exposures at 0.33 WLM, risk through age 90 years would have been reduced from 16% to 11%. In contrast, we estimated a reduction to 6%. There are subtle differences between the dynamic regimes examined. Edwards et al¹³ “capped” exposures at a limit by reducing high exposures to exactly the limit, whereas in our analysis, the worker exposures followed the empirical distribution of exposures under the limit.²⁰ We estimated a risk of 11% at a limit of 7 WLM, in which the weighted mean monthly exposure at work was 1.9 WLM. Thus, it is not likely the differences in regimes fully explain the different results. Differences between approaches likely also relate to model misspecification at low exposures. The parametric g-formula is known to be sensitive to model specification issues, and most of the cases (and hence information for model fitting) occur among highly exposed workers.^42,43 With radon, “inverse dose-rate” effects suggest that the exposure-response for cumulative exposure is higher with protracted (lower dose-rate) vs acute exposure; in the parametric g-formula, that phenomenon must be explicitly modeled and thus subject to misspecification, or effects will be underestimated at low exposure limits.⁴⁴ In contrast, our nonpooled approaches do not utilize a model to pool information about the exposure-response between low and high exposures, and our MSM agreed broadly with results from the nonpooled approaches.

Our estimated lung cancer risk through age 90 years of nearly 6% is consistent with estimates from other occupational populations from a similar era. In prior analyses of other US-based occupational cohorts, we estimated a respiratory mortality risk through age 90 years among unexposed workers of 7% among copper smelters with an average birth year of 1912¹² and a lung cancer mortality risk at age 80 of 6% among a pooled cohort of silica-exposed workers with an average birth year of 1926 (unpublished sensitivity analysis among 15 158 US-based workers¹¹). Published smoking prevalence among one of the US-based cohorts was > 80% among workers exposed above the median cumulative exposure value,⁴⁵ which was similar to the prevalence of ever-smoking in our cohort (77%). However, applying estimates of lifetime risk among current, former, and never smokers (14.5%, 7.5%, and 1.5%, respectively) from a Swiss population directly to the CPUM, a smoking prevalence (55%, 32%, 23%) weighted estimate of lifetime lung cancer is approximately 9%, which is closer to the estimate of Edwards et al.¹³ Notwithstanding the crudeness of these calculations, we intuit that the true risk through age 90 years, had workers been unexposed to radon, is likely to be somewhere between our estimate and that of Edwards et al.¹³

A strength of using approaches like our weighting approach or other g-methods like the parametric g-formula and structural nested models is that they allow control of confounding by time-varying factors that are affected by prior exposures (eg, Naimi et al⁴⁶). Confounding by employment status has been proposed to explain healthy worker survivor bias.^1,2,7 Cumulative radon exposure has been associated with the subsequent hazard of leaving work among these miners.¹⁵ Thus, adjusting for employment status by including it in a regression model for lung cancer is not appropriate for controlling for confounding, although the magnitude and direction of bias from such adjustment are unknown.^1,2,7 In our approach, confounding control is gained by inverse probability weights that account for employment status by fitting censoring models to actively employed person-time.

Previously, Robins et al¹⁷ cautioned against the use of marginal structural models in occupational studies because the probability of occupational exposure among those off work is zero, which violates the positivity assumption. Notably, those authors were referring to an approach to inverse probability weighting in which one directly models the probability density of exposure, which is zero in the stratum of unemployed person-time. We avoided the positivity problem by using an alternative strategy to inverse probability weighting, which was similar to that proposed by Joffe.²⁸ We modeled the probability of having exposure that is consistent with a specific dynamic exposure regime via inverse probability of censoring weights.

However, we note that we were still potentially sensitive to practical violations of positivity. Workers exposed in the earliest years of the cohort, when no protections were in place, may have had high enough exposures such that none of them followed the low-exposure regimes of interest. While basic tabular analysis did not suggest sparsity was an issue, the mean estimated inverse probability weights deviated from 1.0 at the lowest exposures, nonetheless suggesting bias.^34,35 Consequently, for dynamic regime limits below 0.75 WLM, we extrapolated risk estimates from the marginal structural model. Because the CPUM is one of the highest exposed miner cohorts, nonparametric estimates of radon’s effect in the workplace would benefit from the use of data from lower-exposed cohorts (eg, Rage et al⁴⁷ and Kreuzer et al⁴⁸). There is substantial heterogeneity between effect estimates in cohorts of uranium miners, particularly among the earliest cohorts.^49,50

Relative to the parametric g-formula, inverse probability weighting trades fewer parametric assumptions for lower precision, as demonstrated in Figure S4. Further, the parametric g-formula can estimate effects of a more diverse range of dynamic regime effects; for example, the “capped” exposure regime utilized by Edwards et al¹³ would not be possible with inverse probability weighting in our data because it would rely on identifying workers whose exposures exactly match the exposure limit. Similarly, we could not estimate effects of regimes of the type “always exposed exactly at a specific level” unless we observed a sufficient number of participants for whom that was true. To estimate exposure impacts at low doses, the parametric g-formula fits a smooth model to all available data. In contrast, our marginal structural modeling approach relied more explicitly (and transparently) on extrapolation to low exposures. Thus, we view the inverse probability weighting and parametric g-formula methods as complementary, in part because they have different underlying assumptions.

We demonstrated a novel application of weighting methods for dynamic regimes to address several challenges of occupational cohort studies, including healthy worker survivor bias and the direct assessment of new personal exposure limits. The relative simplicity of our approach, relative to the parametric g-formula, make this a useful tool in the occupational epidemiologists’ toolbox.