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May Pattern-Mixture Models be used with generalized estimating equations for longitudinal data analysis?

Hedeker et al mentions pattern-mixture models for handling non-ignorable drop-out patterns and estimating the effect of drop out per measurment ocassion on the response variable for handling non-ignorable missingness by coding drop-out patterns by time points via indicator variables.

Hedeker doesn't mention GEE and Pattern-Mixture models. Nonetheless, as an extension, do Pattern-Mixture models work with Generalized Estimating Equations?

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Generally, when dealing with (non)-ignorable missingness, the "GEE" approach is associated with the inverse probability weighted estimators and doubly robust estimators developed by Jamie Robins and his colleagues. For a discussion of pattern mixture models in particular, see this article. There are lots of good ideas in this paper, but I'm honestly not aware of anyone actually going to the trouble of using them in practice since I think there is no software.

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  • $\begingroup$ Well there isn't a software to implement pattern-mixture, but it's fairly intuitive to do it manually. Suppose there are 3 time points measured. The patterns are OOO, MOM, MMM,.... etc. Code an indicator variable if the observant was observed observed observed, or Missing missing missing, and observe the estimated effect of the missingness pattern on the response variable which should also adjust your other covariate estimated effects. $\endgroup$ – user271077 Jun 3 '20 at 15:28
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    $\begingroup$ @Numbers the problem always in these non-ignorable settings is that the distribution of the response is not non-parametrically identified. You can't just "look at the effect of the missingness on the response" because you don't observe the response when you have missingness. $\endgroup$ – guy Jun 3 '20 at 16:01
  • $\begingroup$ So in multiple imputation you have to impute the response variable and the predictor variables? $\endgroup$ – user271077 Jun 3 '20 at 16:04
  • $\begingroup$ The mixture-pattern is like a grouping variable, like a randomization indicator variable. it doesn't matter if you can't have the response variable for the unobserved day. $\endgroup$ – user271077 Jun 9 '20 at 14:18
  • $\begingroup$ @Numbers if I consider the pattern OOM then there is no information about the response at time 3 for this pattern. $\endgroup$ – guy Jun 9 '20 at 17:52

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