Left truncation, susceptibility, and bias in occupational cohort studies

Abstract

Background: Left truncation occurs when subjects who otherwise meet entry criteria do not remain observable for a later start of follow-up. We investigated left truncation in occupational studies due to inclusion of workers hired before the start of follow-up in a simulation study.

Methods: Using Monte Carlo methods, we simulated null and positive associations between exposure (work duration) and mortality for 500 datasets of 5000 subjects, assuming the absence and presence of heterogeneity in susceptibility to disease and to the effect of exposure. We examined incident hires (followed since hire) and left-truncated prevalent hires (those hired before baseline and remained employed at baseline). We estimated the association (&OV0404;1*) as the mean slope using Cox proportional hazards with a linear term for exposure, under scenarios with and without susceptibility.

Results: With homogeneous susceptibility, there were no differences between incident and prevalent hires. Introducing only disease susceptibility did not change results. However, with heterogeneous susceptibility to the effect of exposure, downward bias was observed among prevalent hires under both the true null and positive exposure-response scenarios. The bias increased with time between hire and baseline (null: &OV0404;1* = 0.05 [SD = 0.08], &OV0404;1* = -0.08 [SD = 0.24], &OV0404;1* = -0.18 [SD = 0.98] if hired <15, 15 to <30, and ≥ 30 years before baseline, respectively), coincident with a decreasing percentage of susceptible subjects.

Conclusions: Prevalent hires induce downward bias in an occupational cohort. This occurs because subjects who are less susceptible to the exposure remain exposed the longest, thereby underestimating the association.

FIGURE 1

Box plots of ${\widehat{\beta }}_1^{\ast }$ estimates across 500 simulated cohorts under the null for prevalent hires, subjects who worked up to 50 years before the start of follow-up and still working when follow-up began. Prevalent hires were divided into strata: hired <15, 15 to <30, and ≥30 years before start of follow-up. Horizontal line indicates the simulated null value. Simulating model: logit P = β₀ + = β₁(ln work duration) + β₂ (ln age) = β₃ (disease susceptible) = β₄ (disease susceptible*ln work duration), with values set to β₀ = −5, β₁ = 0, β₂ = 2, and β₃ = β₄ = 0 for no susceptibility or = 0.5 with variable susceptibility (and either 25% or 50% of cohort susceptible). Data analysis model: $log(\text{HR})={\widehat{\beta }}_1^{\ast }(ln\text{work}\text{duration})$ with age as the timeline.

FIGURE 2

Box plots of ${\widehat{\beta }}_1^{\ast }$ estimates across 500 simulated cohorts for a positive association in prevalent hires, subjects who worked up to 50 years before the start of follow-up and still working when follow-up began. Prevalent hires were divided into strata: hired < 15, 15 to <30, and ≥30 years before start of follow-up. Horizontal line indicates the simulated positive value of β₁ = 0.5. Simulating model: logit P = β₀ − β₁(ln work duration) + β₂(ln age) + β₃(disease susceptible) + β₄(disease susceptible*ln work duration), with values set to β₀ = −7, β₁ = 0.5, β₂ = 1, and β₃ = β₄ = 0 for no susceptibility or = 0.5 with variable susceptibility (and either 25% or 50% of cohort susceptible). Data analysis model: $log(\text{HR})={\widehat{\beta }}_1^{\ast }(ln\text{work}\text{duration})$ with age as the timeline.