Bias Correction for Replacement Samples in Longitudinal Research

Missing data are commonly encountered problem in longitudinal research. One way researchers handle missing data is through the use of supplemental samples (i.e., the addition of new participants to the original sample after missing data appear at the second or later measurement occasion). Two types of supplemental sample approaches are commonly used: a refreshment approach (additional participants are randomly selected from the population of interest) and a replacement approach (additional participants are selected based on auxiliary variables that explain missingness in the original data). Past research demonstrates that using a replacement approach produces biased parameter estimates because the addition of the replacement sample results in an unrepresentative sample of the population. However, replacement samples have been used in previous studies and the estimation bias has not been corrected. Thus, for this study, we propose and evaluate four ways to correct the bias introduced by replacement samples: a parametric bootstrapping replacement sample correction, a non-parametric bootstrapping replacement sample correction, a primary inverse probability reweighting correction, and a likelihood-based inverse probability reweighting correction. We evaluate their performance using a simulation study and an empirical study.