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Alzheimer's disease and related dementias (ADRD) present a growing public health burden in the United States. One actionable risk factor for ADRD is air pollution: multiple studies have found associations between air pollution and exacerbation of ADRD. Our study builds on previous studies by applying modern statistical causal inference methodologies-generalized propensity score (GPS) weighting and matching-on a large, longitudinal dataset. We follow 50 million Medicare enrollees to investigate impacts of three air pollutants-fine particular matter (PM${}_{2.5}$), nitrogen dioxide (NO${}_2$), and summer ozone (O${}_3$)-on elderly patients' rate of first hospitalization with ADRD diagnosis. Similar to previous studies using traditional statistical models, our results found increased hospitalization risks due to increased PM${}_{2.5}$ and NO${}_2$ exposure, with less conclusive results for O${}_3$. In particular, our GPS weighting analysis finds IQR increases in PM${}_{2.5}$, NO${}_2$, or O${}_3$ exposure results in hazard ratios of 1.108 (95% CI: 1.097-1.119), 1.058 (1.049-1.067), or 1.045 (1.036-1.054), respectively. GPS matching results are similar for PM${}_{2.5}$ and NO${}_2$ with attenuated effects for O${}_3$. Our results strengthen arguments that long-term PM${}_{2.5}$ and NO${}_2$ exposure increases risk of hospitalization with ADRD diagnosis. Additionally, we highlight strengths and limitations of causal inference methodologies in observational studies with continuous treatments. Keywords: Alzheimer's disease and related dementias, air pollution, Medicare, causal inference, generalized propensity score., (© The Author(s) 2024. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)