Using multiple imputation to treat missingness in air pollution time series

Abstract

Introduction: Missing values are common in daily air pollution time series. They can be due to instrument failures, errors in reporting measurements or can be planned by design. Missing values are usually filled in by single imputation, while, with few exceptions, Multiple Imputation (MI) is not adopted in this field, despite it has better properties and brings to more reliable results. In this work, we used MI within the Supersite Project, a project focused to provide detailed measurements of chemical, physical and toxicological parameters in the atmosphere of the Emilia-Romagna region, Italy. Methods: MI was performed according to an iterative procedure suitable for large data sets, based on partitioning the whole set of missing values in several blocks characterized by monotone missing data pattern. Separately for each block, missing values were imputed by sampling from the posterior predictive distribution of each variable, conditioning on a large number of covariates. We selected these covariates from all the available information by applying an ElasticNet algorithm, after having constrained the predictive model to contain lagged values of the outcome variable as well as seasonality terms. Results: MI was performed on time series data arising from monitors located in Bologna, Parma, Rimini and San Pietro Capofiume. The percentage of missing values was heterogeneous depending on the site and on the measured parameter, reaching in some case the 95%. The algorithm detected 8 blocks involving more than 50 missing values and many other small patterns. We generated 10 different imputed data sets to be used for future analyses. Conclusions: MI is a useful tool to treat missingness in air pollution time series. In our application, due to the large amount of missing values, a careful evaluation of the imputed data should be performed, by checking the coherence of relevant quantities after imputation and implementing ad hoc validation methods.