Evaluation of data imputation strategies in complex, deeply-phenotyped data sets: the case of the EU-AIMS Longitudinal European Autism Project

Abstract An increasing number of large-scale multi-modal research initiatives has been conducted in the typically developing population, e.g. Dev. Cogn. Neur. 32:43-54, 2018; PLoS Med. 12(3):e1001779, 2015; Elam and Van Essen, Enc. Comp. Neur., 2013, as well as in psychiatric cohorts, e.g. Trans. Psych. 10(1):100, 2020; Mol. Psych. 19:659–667, 2014; Mol. Aut. 8:24, 2017; Eur. Child and Adol. Psych. 24(3):265–281, 2015. Missing data is a common problem in such datasets due to the difficulty of assessing multiple measures on a large number of participants. The consequences of missing data accumulate when researchers aim to integrate relationships across multiple measures. Here we aim to evaluate different imputation strategies to fill in missing values in clinical data from a large (total N = 764) and deeply phenotyped (i.e. range of clinical and cognitive instruments administered) sample of N = 453 autistic individuals and N = 311 control individuals recruited as part of the EU-AIMS Longitudinal European Autism Project (LEAP) consortium. In particular, we consider a total of 160 clinical measures divided in 15 overlapping subsets of participants. We use two simple but common univariate strategies—mean and median imputation—as well as a Round Robin regression approach involving four independent multivariate regression models including Bayesian Ridge regression, as well as several non-linear models: Decision Trees (Extra Trees., and Nearest Neighbours regression. We evaluate the models using the traditional mean square error towards removed available data, and also consider the Kullback–Leibler divergence between the observed and the imputed distributions. We show that all of the multivariate approaches tested provide a substantial improvement compared to typical univariate approaches. Further, our analyses reveal that across all 15 data-subsets tested, an Extra Trees regression approach provided the best global results. This not only allows the selection of a unique model to impute missing data for the LEAP project and delivers a fixed set of imputed clinical data to be used by researchers working with the LEAP dataset in the future, but provides more general guidelines for data imputation in large scale epidemiological studies.