A model-based approach for imputing censored data in source apportionment studies

Sources of particulate matter (PM) air pollution are generally inferred from PM chemical constituent concentrations using source apportionment models. Concentrations of PM constituents are often censored below minimum detection limits (MDL) and most source apportionment models cannot handle these censored data. Frequently, censored data are first substituted by a constant proportion of the MDL or are removed to create a truncated dataset before sources are estimated. When estimating the complete data distribution, these commonly applied methods to adjust censored data perform poorly compared with model-based imputation methods. Model-based imputation has not been used in source apportionment and may lead to better source estimation. However if the censored chemical constituents are not important for estimating sources, censoring adjustment methods may have little impact on source estimation. We focus on two source apportionment models applied in the literature and provide a comprehensive assessment of how censoring adjustment methods, including model-based imputation, impact source estimation. A review of censoring adjustment methods critically informs how censored data should be handled in these source apportionment models. In a simulation study, we demonstrated that model-based multiple imputation frequently leads to better source estimation compared with commonly used censoring adjustment methods. We estimated sources of PM in New York City and found estimated source distributions differed by censoring adjustment method. In this study, we provide guidance for adjusting censored PM constituent data in common source apportionment models, which is necessary for estimation of PM sources and their subsequent health effects.