Case Studies of Autoregressive Linear Mixed Effects Models: Missing Data and Time-Dependent Covariates
In the previous chapter, we introduced autoregressive linear mixed effects models for analysis of longitudinal data. In this chapter, we provide examples of actual data analysis using these models. We also discuss two topics from the medical field: response-dependent dropouts and response-dependent dose modifications. When the missing mechanism depends on the observed, but not on the unobserved, responses, it is termed missing at random (MAR). The missing process does not need to be simultaneously modeled for the likelihood because the likelihood can be factorized into two parts: one for the measurement process and the other for the missing process. Maximum likelihood estimators are consistent under MAR if the joint distribution of the response vector is correctly specified. For the problem of dose modification, similar concepts are applied. When the dose modification depends on the observed, but not on the unobserved, responses, the dose process does not need to be simultaneously modeled for the likelihood. Here, we analyze schizophrenia data and multiple sclerosis data using autoregressive linear mixed effects models as examples of response-dependent dropouts and response-dependent dose modifications, respectively.
KeywordsAutoregressive linear mixed effects model Dose modification Longitudinal Missing Time-dependent covariate
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