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

Abstract

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.

Keywords: Z-bias; air pollution; bias amplification; birth weight; concurvity; distributed lag models; spatial resolution; variance inflation.

Figure 1

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Figure 1

The time-varying association between weekly nitrogen dioxide (NO₂) exposure and birth weight in term deliveries at Beth Israel Deaconess Medical Center (n = 46,153), Boston, Massachusetts, 2000–2016. Estimates were made using natural spline–based distributed lag models (ns-DLMs) (A) and tree-based distributed lag models (TDLMs) (B) under scenarios with 3 different spatial resolutions for exposure (high, low, and no resolution) and 6 methods to adjust for time trends (no adjustment, long-term spline, year and spline, year and harmonics, year and month, and year and season). Black solid lines show the lag-response estimates, gray shaded areas show the 95% confidence intervals for ns-DLMs and 95% Bayesian credible intervals for TDLMs, and the black dashed line indicates the null hypothesis of no effect across all weeks. Web Figure 3 is a zoomed-out version (expanded y-axis) of the no-spatial-resolution ns-DLM with a long-term spline. g, grams; ppb, parts per billion

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Figure 2

Simulation results, showing the time-varying association between nitrogen dioxide (NO₂) exposure and birth weight, of natural spline–based distributed lag models (A) and tree-based distributed lag models (B), across all weeks using 6 methods to adjust for time trends (no adjustment, long-term spline, year and spline, year and harmonics, year and month, and year and season). Simulation inputs include time trends and NO₂ effects from the Massachusetts data. Gray lines show the lag-response relationships from each iteration of the simulation, the black solid line indicates the average across all simulations (500 replicates), the black dashed line indicates the null hypothesis of no effect across all weeks, and the black dotted line indicates the true simulated lag-response relationship. g, grams; ppb, parts per billion.

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Figure 3

Coverage of lag-specific associations between nitrogen dioxide (NO₂) and birth weight in simulations using natural spline–based distributed lag models (DLMs) (A) and tree-based distributed lag models (TDLMs) (B), with 6 methods to adjust for time trends (no adjustment, long-term spline, year and spline, year and harmonics, year and month, and year and season). Simulation inputs include time trends and NO₂ effects from the Massachusetts data. The solid line and points indicate the proportion of simulations over 500 replicates in which the lag-specific 95% confidence interval (or credible intervals for TDLMs) contained the true simulated lag-specific effect, and the black dashed line indicates the 95% nominal coverage.