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In longitudinal studies, subjects may be lost to follow up and, thus, present incomplete response sequences. When the mechanism underlying the dropout is nonignorable, we need to account for dependence between the longitudinal and the dropout process. We propose to model such a dependence through discrete latent effects, which are outcome-specific and account for heterogeneity in the univariate profiles. Dependence between profiles is introduced by using a probability matrix to describe the corresponding joint distribution. In this way, we separately model dependence within each outcome and dependence between outcomes. The major feature of this proposal, when compared with standard finite mixture models, is that it allows the nonignorable dropout model to properly nest its ignorable counterpart. We also discuss the use of an index of (local) sensitivity to nonignorability to investigate the effects that assumptions about the dropout process may have on model parameter estimates. The proposal is illustrated via the analysis of data from a longitudinal study on the dynamics of cognitive functioning in the elderly., (Copyright © 2018 John Wiley & Sons, Ltd.)

Longitudinal studies collect information on a sample of individuals which is followed over time to analyze the effects of individual and time-dependent characteristics on the observed response. These studies often suffer from attrition: individuals drop out of the study before its completion time and thus present incomplete data records. When the missing mechanism, once conditioned on other (observed) variables, does not depend on current (eventually unobserved) values of the response variable, the dropout mechanism is known to be ignorable. We propose a selection model extending semiparametric variance component models for longitudinal binary responses to allow for dependence between the missing data mechanism and the primary response process. The model is applied to a data set from a methadone maintenance treatment programme held in Sidney, 1986.

This article deals with determination of a sample size that guarantees the success of a trial. We follow a Bayesian approach and we say an experiment is successful if it yields a large posterior probability that an unknown parameter of interest (an unknown treatment effect or an effects-difference) is greater than a chosen threshold. In this context, a straightforward sample size criterion is to select the minimal number of observations so that the predictive probability of a successful trial is sufficiently large. In the paper we address the most typical criticism to Bayesian methods-their sensitivity to prior assumptions-by proposing a robust version of this sample size criterion. Specifically, instead of a single distribution, we consider a class of plausible priors for the parameter of interest. Robust sample sizes are then selected by looking at the predictive distribution of the lower bound of the posterior probability that the unknown parameter is greater than a chosen threshold. For their flexibility and mathematical tractability, we consider classes of epsilon-contamination priors. As specific applications we consider sample size determination for a Phase III trial., ((c) 2008 John Wiley & Sons, Ltd.)