The performance of missing data treatments for longitudinal data with a time-varying covariate
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The purpose of this study was to investigate the performance of missing data treatments for longitudinal data with a time-varying covariate. For a longitudinal study, data are collected repeatedly from the same individual, and the occurrence of missing observations due to attrition is common. When longitudinal data are nested within individuals, missing data treatments may need to take the nested data structures into account. This study compared the performance of four missing data treatments: listwise deletion and three multiple imputation methods. Nested data structures were ignored in single-level multiple imputation. On the other hand, multivariate multiple imputation addressed nested data structures by data manipulation and multilevel multiple imputation addressed them in the imputation model. The performance of listwise deletion was investigated to compare the performance of multiple imputation methods with a traditional method. In Study 1, longitudinal data with missing observations were simulated. The experimental conditions were sample size, missing rate, missing patterns, and degree of systematic nonresponse. After missing data were treated by four missing data treatments, a two-level mixed-effects model was applied. Bias in estimation of the regression coefficients, standard errors, and variances were investigated. In Study 2, the four missing data treatments were applied to empirical data from a longitudinal study on persons with multiple sclerosis, to demonstrate the applicability of the four missing data treatments. Study 1 showed that multivariate multiple imputation and multilevel multiple imputation resulted in less biased estimates than the other two methods for most study conditions. Single-level multiple imputation resulted in biased variance estimates under all experimental conditions. Listwise deletion also produced biased estimates, especially for the standard error for the fixed effects of time invariant variables. With the application of empirical data, inferences of cross-level interaction fixed-effects were in disagreement among the four methods. The use of multivariate multiple imputation and multilevel multiple imputation found a significant cross-level interaction whereas the other methods did not. The results showed that nested structures should not be ignored at the imputation stage of multiple imputation.