Reparameterizing the pattern mixture model for sensitivity analyses under informative dropout

Pattern mixture models are frequently used to analyze longitudinal data where missingness is induced by dropout. For measured responses, it is typical to model the complete data as a mixture of multivariate normal distributions, where mixing is done over the dropout distribution. Fully parameterized pattern mixture models are not identified by incomplete data; Little (1993, Journal of the American Statistical Association 88, 125-134) has characterized several identifying restrictions that can be used for model fitting. We propose a reparameterization of the pattern mixture model that allows investigation of sensitivity to assumptions about nonidentified parameters in both the mean and variance, allows consideration of a wide range of nonignorable missing-data mechanisms, and has intuitive appeal for eliciting plausible missing-data mechanisms. The parameterization makes clear an advantage of pattern mixture models over parametric selection models, namely that the missing-data mechanism can be varied without affecting the marginal distribution of the observed data. To illustrate the utility of the new parameterization, we analyze data from a recent clinical trial of growth hormone for maintaining muscle strength in the elderly. Dropout occurs at a high rate and is potentially informative. We undertake a detailed sensitivity analysis to understand the impact of missing-data assumptions on the inference about the effects of growth hormone on muscle strength.