Heckman-type selection models to obtain unbiased estimates with missing measures outcome: Theoretical considerations and an application to missing birth weight data

Abstract

Background: In low-income settings, key outcomes such as biomarkers or clinical assessments are often missing for a substantial proportion of the study population. The aim of this study was to assess the extent to which Heckman-type selection models can create unbiased estimates in such settings. Methods: We introduce the basic Heckman model in a first stage, and then use simulation models to compare the performance of the model to alternative approaches used in the literature for missing outcome data, including complete case analysis (CCA), multiple imputations by chained equations (MICE) and pattern imputation with delta adjustment (PIDA). Last, we use a large population-representative data set on antenatal supplementation (AS) and birth outcomes from Côte d'Ivoire to illustrate the empirical relevance of this method. Results: All models performed well when data were missing at random. When missingness in the outcome data was related to unobserved determinants of the outcome, large and systematic biases were found for CCA and MICE, while Heckman-style selection models yielded unbiased estimates. Using Heckman-type selection models to correct for missingness in our empirical application, we found supplementation effect sizes that were very close to those reported in the most recent systematic review of clinical AS trials. Conclusion: Missingness in health outcome can lead to substantial bias. Heckman-selection models can correct for this selection bias and yield unbiased estimates, even when the proportion of missing data is substantial.