12.9. Summary

Analyzing incomplete (longitudinal) data, both of a Gaussian as well as of a non-Gaussian nature, can easily be conducted under the relatively relaxed assumption of missingness at random (MAR), using standard statistical software tools. Likelihood-based methods include the linear mixed model and generalized linear mixed models. In addition, weighted generalized estimating equations (WGEE) can be used as a relatively straightforward fix up of ordinary generalized estimating equations (GEE) so that also this technique is valid under MAR. Alternative methods which allow for ignoring the missing data mechanism under MAR include multiple imputation (MI) and the Expectation-Maximization (EM) algorithm. The GLIMMIX macro and PROC GLIMMIX were both presented as two useful implementations of the generalized estimating equations approach, usefully supplementing the more familiar GENMOD procedure. Further, the GLIMMIX tools are useful for generalized linear mixed modeling, supplementing PROC NLMIXED. The depression trial was used as an illustration.

These considerations imply that traditionally popular but very restricted modes of analysis, including complete case (CC) analysis, last observation carried forward (LOCF), or other simple imputation methods, ought to be abandoned, given the highly restrictive assumptions on which they are based.

Of course, general missingness not at random can never be entirely excluded, and one should therefore ideally supplement an ignorable analysis with a suitable chosen set of sensitivity analyses. Therefore, we presented a formal selection modeling framework for continuous outcomes, for categorical responses, and contrasted these to the pattern-mixture framework. The general MNAR selection model of Diggle and Kenward (1994) for the exercise bike data was fitted using SAS/IML code. Further, we showed explicit sensitivity analysis methods. We presented a local influence analysis for the mastitis data, supplemented with the necessary SAS/IML code. We further sketched frameworks for incomplete binary and ordinal data, based on local influence ideas. Finally, as a sensitivity analysis for pattern-mixture models, identifying restrictions are proposed as a viable strategy.