Abstract
In longitudinal studies where the same individuals are followed over time, bias caused by unobserved data raises a serious concern, particularly when the data are missing in a non-ignorable manner. One approach to deal with non-ignorable missing data is a pattern mixture model. In this paper, we combine the pattern mixture model with latent trajectory analysis using the SAS TRAJ procedure, which offers a practical solution to many problems of the same nature. Our model assumes a stochastic process that categorizes a relative large number of missing-data patterns into several latent groups, each of which has unique outcome trajectory, which allows patterns with missing values to share information with patterns with more data points. We estimated the longitudinal trajectories of a memory test over 12 years of follow-up, using data from the prospective epidemiological study of dementia. Missing data patterns were created conditional on survival, and final marginal response was obtained by excluding those who had died at each time point. The approach presented here is appealing since it can be easily implemented using common software.
Highlights
Longitudinal designs, requiring follow-up of the same individuals over time, are increasingly common in epidemiological studies
We offer a practical solution to the non-identifiability problem by using latent trajectory analysis in the framework of pattern-mixture models
To see the trajectory of test score over time among those who were cognitively healthy at baseline, we excluded 126 subjects who were already demented at baseline and 36 subjects who did not complete the WLDR test at baseline
Summary
Longitudinal designs, requiring follow-up of the same individuals over time, are increasingly common in epidemiological studies. Missing data bias is a major problem in longitudinal studies where attrition is inevitable over time, among older adults. Missing At Random (MAR), where missingness depends on participant’s previously observed responses or observed characteristics, and 3. Missing Not At Random (MNAR), where missingness depends on unobserved outcome values (as well as possibly on observed values). Laird (1988), Little and Rubin (1987) defined two general classes of missing-data mechanisms for likelihood-based approaches. A missing-data process is called ignorable if a likelihood-based approach provides valid inferences to the model parameters even when the missingness is ignored, while if not, called non-ignorable. Under MNAR, likelihood-based analyses that ignore the missing-data mechanism may be biased (non-ignorable missingness)
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