Bias Amplification and Variance Inflation in Distributed Lag Models Using Low-Spatial-Resolution Data

Distributed lag models (DLMs) are often used to estimate lagged associations and identify critical exposure windows. In a simulation study of prenatal nitrogen dioxide (NO2) exposure and birth weight, we demonstrate that bias amplification and variance inflation can manifest under certain combinations of DLM estimation approaches and time-trend adjustment methods when using low-spatial-resolution exposures with extended lags. Our simulations showed that when using high-spatial-resolution exposure data, any time-trend adjustment method produced low bias and nominal coverage for the distributed lag estimator. When using either low- or no-spatial-resolution exposures, bias due to time trends was amplified for all adjustment methods. Variance inflation was higher in low- or no-spatial-resolution DLMs when using a long-term spline to adjust for seasonality and long-term trends due to concurvity between a distributed lag function and secular function of time. NO2-birth weight analyses in a Massachusetts-based cohort showed that associations were negative for exposures experienced in gestational weeks 15-30 when using high-spatial-resolution DLMs; however, associations were null and positive for DLMs with low- and no-spatial-resolution exposures, respectively, which is likely due to bias amplification. DLM analyses should jointly consider the spatial resolution of exposure data and the parameterizations of the time trend adjustment and lag constraints.

Automated summary

Distributed lag models (DLMs) are used to estimate lagged associations and identify critical exposure windows. A simulation study on prenatal NO2 exposure and birth weight revealed that bias amplification and variance inflation can occur in certain combinations of DLM estimation approaches and time-trend adjustment methods with low-spatial-resolution exposures and extended lags. The spatial resolution of exposure data and the parameterizations of the time trend adjustment and lag constraints should be jointly considered in DLM analyses.