Immortal Time Bias With Time-Varying Exposures in Environmental Epidemiology: A Case Study in Lung Cancer Survival

Immortal time bias is a well-recognized bias in clinical epidemiology but is rarely discussed in environmental epidemiology. Under the target trial framework, this bias is formally conceptualized as a misalignment between the start of study follow-up (time 0) and treatment assignment. This misalignment can occur when attained duration of follow-up is encoded into treatment assignment using minimums, maximums, or averages. The bias can be exacerbated in the presence of time trends commonly found in environmental exposures. Using lung cancer cases from the California Cancer Registry (2000-2010) linked with estimated concentrations of particulate matter less than or equal to 2.5 μm in aerodynamic diameter (PM2.5), we replicated previous studies that averaged PM2.5 exposure over follow-up in a time-to-event model. We compared this approach with one that ensures alignment between time 0 and treatment assignment, a discrete-time approach. In the former approach, the estimated overall hazard ratio for a 5-μg/m3 increase in PM2.5 was 1.38 (95% confidence interval: 1.36, 1.40). Under the discrete-time approach, the estimated pooled odds ratio was 0.99 (95% confidence interval: 0.98, 1.00). We conclude that the strong estimated effect in the former approach was likely driven by immortal time bias, due to misalignment at time 0. Our findings highlight the importance of appropriately conceptualizing a time-varying environmental exposure under the target trial framework to avoid introducing preventable systematic errors.