Although some pollutants emitted in vehicle exhaust, such as benzene, are known to cause leukemia in adults with high exposure levels, less is known about the relationship between traffic-related air pollution (TRAP) and childhood hematologic cancer. In the 1990s, the US EPA enacted the reformulated gasoline program in select areas of the US, which drastically reduced ambient TRAP in affected areas. This created an ideal quasi-experiment to study the effects of TRAP on childhood hematologic cancers. However, existing methods for quasi-experimental analyses can perform poorly when outcomes are rare and unstable, as with childhood cancer incidence. We develop Bayesian spatio-temporal matrix completion methods to conduct causal inference in quasi-experimental settings with rare outcomes. Selective information sharing across space and time enables stable estimation, and the Bayesian approach facilitates uncertainty quantification. We evaluate the methods through simulations and apply them to estimate the causal effects of TRAP on childhood leukemia and lymphoma.

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