Robust inference using hierarchical likelihood approach for heavy-tailed longitudinal outcomes with missing data: An alternative to inverse probability weighted generalized estimating equations

We examine methods appropriate for heavy-tailed longitudinal outcomes with possibly missing data. Generalized estimating equations (GEEs) have been widely used in longitudinal studies when data are not heavy-tailed and, in general, are valid only when data are missing completely at random. Robins et al. (1995) showed how inverse probability weighting in such settings (IPW-GEE) can extend validity to data that are missing at random. When data are completely observed, Preisser and Qaqish (1999) proposed the use of robust GEE methods to handle outliers. A natural extension of this to the setting with missing data is to combine these two methods. One alternative for the same setting is to use hierarchical (h-) likelihood (Lee et al., 2006). Here we compare this approach with that of IPW-GEE for heavy-tailed data in the missing data context.