March 10, 2015

Application of Propensity Scores to a Continuous Exposure: Effect of Lead Exposure in Early Childhood on Reading and Mathematics Scores

By Michael Elliott, Nanhua Zhang & Dylan Small

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The estimation of causal effects in observational studies is usually limited by the lack of randomization, which can result in different treatment or exposure groups differing systematically with respect to characteristics that influence outcomes. To remove such systematic differences, methods to “balance” subjects on observed covariates across treatment or exposure levels have been developed over the past three decades. These methods have been primarily developed in settings with binary treatment or exposures. However, in many observational studies, the exposures are continuous instead of being binary or discrete, and are usually considered as doses of treatment. In this manuscript we consider estimating the causal effect of early childhood lead exposure on youth academic achievement, where the exposure variable blood lead concentration can take any values that are greater than or equal to 0, using three balancing methods: propensity score analysis, non-bipartite matching, and Bayesian regression trees. We find some evidence that the standard logistic regression analysis controlling for age and socioeconomic confounders used in previous analyses (Zhang et al. (2013)) overstates the effect of lead exposure on performance on standardized mathematics and reading examinations; however, signifi cant declines remain, including at doses currently below the recommended exposure levels.


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