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Although most models for incomplete longitudinal data are formulated within the selection model framework, pattern-mixture models have gained considerable interest in recent years [R.J.A. Little, Pattern-mixture models for multivariate incomplete data, J. Am. Stat. Assoc. 88 (1993), pp. 125-134; R.J.A. Lrittle, A class of pattern-mixture models for normal incomplete data, Biometrika 81 (1994), pp. 471-483], since it is often argued that selection models, although many are identifiable, should be approached with caution, especially in the context of MNAR models [R.J. Glynn, N.M. Laird, and D.B. Rubin, Selection modeling versus mixture modeling with nonignorable nonresponse, in Drawing Inferences from Self-selected Samples, H. Wainer, ed., Springer-Verlag, New York, 1986, pp. 115-142]. In this paper, the focus is on several strategies to fit pattern-mixture models for non-monotone categorical outcomes. The issue of under-identification in pattern-mixture models is addressed through identifying restrictions. Attention will be given to the derivation of the marginal covariate effect in pattern-mixture models for non-monotone categorical data, which is less straightforward than in the case of linear models for continuous data. The techniques developed will be used to analyse data from a clinical study in psychiatry. Ivy Jansen and Geert Molenberghs gratefully acknowledge the support from Fonds Wetenschappelijk Onderzoek-Vlaanderen Research Project G.0002.98 'Sensitivity Analysis for Incomplete and Coarse Data' and from IAP research Network P6/03 of the Belgian Government (Belgian Science Policy).

Commonly used methods to analyze incomplete longitudinal clinical trial data include complete case analysis (CC) and last observation carried forward (LOCF). However, such methods rest on strong assumptions, including missing completely at random (MCAR) for CC and unchanging profile after dropout for LOCF. Such assumptions are too strong to generally hold. Over the last decades, a number of full longitudinal data analysis methods have become available, such as the linear mixed model for Gaussian outcomes, that are valid under the much weaker missing at random (MAR) assumption. Such a method is useful, even if the scientific question is in terms of a single time point, for example, the last planned measurement occasion, and it is generally consistent with the intention-to-treat principle. The validity of such a method rests on the use of maximum likelihood, under which the missing data mechanism is ignorable as soon as it is MAR. In this paper, we will focus on non-Gaussian outcomes, such as binary, categorical or count data. This setting is less straightforward since there is no unambiguous counterpart to the linear mixed model. We first provide an overview of the various modeling frameworks for non-Gaussian longitudinal data, and subsequently focus on generalized linear mixed-effects models, on the one hand, of which the parameters can be estimated using full likelihood, and on generalized estimating equations, on the other hand, which is a nonlikelihood method and hence requires a modification to be valid under MAR. We briefly comment on the position of models that assume missingness not at random and argue they are most useful to perform sensitivity analysis. Our developments are underscored using data from two studies. While the case studies feature binary outcomes, the methodology applies equally well to other discrete-data settings, hence the qualifier ``discrete'' in the title., Comment: Published at http://dx.doi.org/10.1214/088342305000000322 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Models for incomplete longitudinal data under missingness not at random have gained some popularity. At the same time, cautionary remarks have been issued regarding their sensitivity to often unverifiable modeling assumptions. Consequently, there is evidence for a shift towards using ignorable methodology, supplemented with sensitivity analyses to explore the impact of potential deviations of this assumption in the direction of missingness at random. One such tool is local influence. It is shown that local influence tends to pick up a lot of different anomalies in the data at hand, not just deviations in the MNAR mechanism. This particular behavior is described and insight offered in terms of the non-standard behavior of the likelihood ratio test statistic for MAR missingness versus MNAR missingness within a model of the Diggle and Kenward type. (c) 2004 Elsevier B.V. All rights reserved. vy Jansen, Niel Hens, Geert Molenberghs and Marc Aerts gratefully acknowledge support from Fonds Wetenschappelijk Onderzoek-Vlaanderen Research Project G.0002.98 “Sensitivity Analysis for Incomplete and Coarse Data” and from Belgian IUAP/PAI network “Statistical Techniques and Modeling for Complex Substantive Questions with Complex Data”.