Sensitivity Analysis for Pattern-Mixture Models

Chapter 18 is devoted to the study of pattern-mixture models, thus providing an alternative formulation for the common selection model factorization (see also Section 15.4). In Section 18.1, we observed that pattern-mixture models are chronically underidentified, which is clearly seen by means of the Glynn, Laird, and Rubin (1986) “paradox” (Section 18.1.2). Consequently, Little (1993, 1994a, 1995) suggested the use of so-called identifying restrictions to overcome this underidentification. Choosing a set of different restriction schemes, rather than a single one, is an obvious way to pass from a standard approach to sensitivity analysis.

The need to use identifying restrictions is often quoted as an advantage for pattern-mixture models since it forces careful reflection on the nature of the assumptions made. On the other hand, neither of the two case studies in Chapter 18 (the toenail data in Section 18.3 and the Vorozole study in Section 18.4) made use of identifying restrictions. The reason is different for both studies. The pattern-specific models for the toenail data were simple enough (quadratic curves) to allow extrapolation beyond the last measurement obtained in a particular pattern. Only the first two patterns, with a single or only two measurements, posed problems and an ad hoc solution was employed. In the Vorozole study, pattern was included as a covariate in both the fixed-effects and variance portions of the models. Subsequent simplification lead to a model which was easy to extrapolate.