Assessments of workplace risk are generally based on observational studies of occupational cohorts. Estimates from these studies are often subject to bias due to the healthy worker survivor effect (HWSE), a ubiquitous process that results in the healthiest workers accruing the most exposure over their lifetimes.^1–4 The potential outcomes framework defines causal effects as contrasts between the distributions of counterfactual outcomes under hypothetical interventions.⁵ Counterfactuals may be defined under static regimens that assign exposure independently of a worker’s characteristics, or under dynamic regimens that assign exposure according to a worker’s observed past.

A static workplace intervention corresponds to a target trial^6,7 in which workers hired into an industry at the start of their working lives are assigned a fixed exposure level until retirement age. The effects of static interventions reflect the biologic effect of exposure that would have been observed if workers did not select out of the workforce. Since workers that experience exposure-related adverse health outcomes tend to leave work, such strategies do not correspond to anything commonly observed in the real world. Given the paucity of observed data to estimate such effects, most estimates necessarily rely on the assumption of no unmeasured confounding between leaving work and the outcome.⁸

A dynamic intervention also corresponds to a target trial in which workers hired at the start of their working lives are assigned a fixed exposure level while at work; however, workers may leave and become unexposed for the remainder of follow-up. These strategies more closely resemble the real-world observed data, and their effects are more straightforward to estimate.

The US Occupational Safety and Health Administration (OSHA) is mandated to establish standards for occupational hazards that assure, “on the basis of the best available evidence that no employee will suffer material impairment of health or functional capacity, even if such employee has a regular exposure to the hazard dealt with by such standard for the period of his working life.”⁹ This directive is typically interpreted as requiring that OSHA risk assessments be based on static effects of 45 years of exposure.¹⁰ Since static effects are difficult to estimate ¹¹, we conducted a simulation study to investigate the factors that drive differences between the static and dynamic measures in workplace studies.

Motivated by typical aspects of occupational studies, we simulated 500 cohorts of 50,000 workers, under four scenarios, for a maximum follow-up of 20 years. For each worker and year t of follow-up, we simulated the indicators: W(t), for active employment; E(t) for workplace exposure; Y(t), for the outcome; and H(t), for the intermediate adverse health event, one of the mechanisms through which exposure affects the outcome. Exposure had a direct effect on the outcome in addition to that mediated by H(t). We additionally simulated S, an indicator of a worker’s susceptibility to H(t) and Y(t). Only susceptible workers were at risk of experiencing H(t) and Y(t) and, once they experienced H(t), workers maintained that status. Workers could only terminate employment if in poor health.

In the Table we report static and dynamic exposure effects for each scenario, and their ratios over time. In Scenario 1, a static effect of 0.42 indicates that the 20-year risk of disease if always exposed would be 42% greater than if unexposed. A dynamic effect of 0.07 indicates that, when workers terminated employment for health-related reasons, the 20-year risk was only 7% greater if exposed while at work versus unexposed. The corresponding static-to-dynamic effect ratio of 6.00 in year 20 [R₁(20) = 6.00] indicates that the effect of exposure under a static intervention was six times stronger than under a dynamic intervention.

Figures 2 – 4 present comparisons of Scenarios 2, 3, and 4 with Scenario 1. For each scenario, we present survival curves for exposed and unexposed workers according to static and dynamic interventions. Survival probabilities were identical for the “never expose” regimen under both static and dynamic interventions; survival probabilities were smaller under the static “always expose” versus the dynamic “expose while at work” interventions (Figures 2–4).

The first comparison assesses how the static-to-dynamic effect ratio changes as a function of the strength of the intermediate health events and outcome relationship (Figure 2). Static and dynamic effects were more alike when intermediate health had a stronger effect on the outcome (Scenario 2), reflected by smaller ratios in Scenario 2 than in 1 (Table, R₁(20) = 6.00, R₂(20) = 2.00).

In Figure 3 we contrast Scenarios 1 and 3. Leaving work was determined by health status in the previous year in Scenario 1, but 10 years prior in Scenario 3. Static effects were the same in both scenarios (0.42). However, because exposed workers remained at work longer in Scenario 3, the dynamic effect was larger (0.07 vs. 0.32) and the ratio was smaller (R₁(20) = 6.00, R₃(20) = 1.31).

In Figure 4 we contrast Scenarios 3 and 4, where workers only experienced the adverse health event during their very first year of exposure. While static effects were similar in both scenarios (0.42 vs. 0.43), dynamic effects were smaller in Scenario 4 (0.07 vs. 0.05) and the ratio increased [R₁(20) = 6.00, R₄(20) = 8.60].

Static and dynamic interventions are expected to result in different exposure effect estimates.¹¹ We aimed to examine key features of the data generating distribution likely to drive the differences between static and dynamic intervention effects, since both can answer causal questions. This matter has practical implications in the context of the OSHA mandate: It is important to note that not all causal effects of the same exposure level, on the same disease, in the same population, over the same follow-up period, are necessarily equivalent.

Dynamic parameters better approximate static estimates if the consequences of exposure that cause leaving work are strongly related to the outcome, or if symptomatic workers remain at work despite declining health. In both cases, the amount of exposure accrued while actively employed already places workers at high risk for the outcome. Dynamic parameters generally provide conservative estimates of the disease risk associated with long-term exposure when the consequences of exposure that lead to leaving work occur early in employment. In this case, leaving work provides a screening mechanism for susceptible workers, while a larger proportion of unsusceptible survivors remain at work (eTable 1).