Imputation of Ordinal Outcomes: A Comparison of Approaches in Traumatic Brain Injury
Kevin Kunzmann, Lorenz Wernisch, Sylvia Richardson, Ewout W. Steyerberg, Hester F. Lingsma, Ari Ercole, Andrew I.R. Maas, David Menon, Lindsay Wilson
Abstract
Loss to follow-up and missing outcomes data are important issues for longitudinal observational studies and clinical trials in traumatic brain injury. One popular solution to missing 6-month outcomes has been to use the last observation carried forward (LOCF). The purpose of the current study was to compare the performance of model-based single-imputation methods with that of the LOCF approach. We hypothesized that model-based methods would perform better as they potentially make better use of available outcome data. The Collaborative European NeuroTrauma Effectiveness Research in Traumatic Brain Injury (CENTER-TBI) study ( n = 4509) included longitudinal outcome collection at 2 weeks, 3 months, 6 months, and 12 months post-injury; a total of 8185 Glasgow Outcome Scale extended (GOSe) observations were included in the database. We compared single imputation of 6-month outcomes using LOCF, a multiple imputation (MI) panel imputation, a mixed-effect model, a Gaussian process regression, and a multi-state model. Model performance was assessed via cross-validation on the subset of individuals with a valid GOSe value within 180 ± 14 days post-injury ( n = 1083). All models were fit on the entire available data after removing the 180 ± 14 days post-injury observations from the respective test fold. The LOCF method showed lower accuracy (i.e., poorer agreement between imputed and observed values) than model-based methods of imputation, and showed a strong negative bias (i.e., it imputed lower than observed outcomes). Accuracy and bias for the model-based approaches were similar to one another, with the multi-state model having the best overall performance. All methods of imputation showed variation across different outcome categories, with better performance for more frequent outcomes. We conclude that model-based methods of single imputation have substantial performance advantages over LOCF, in addition to providing more complete outcome data.