Prediction of Random Effects in Linear Mixed Models under Stochastic Censoring

Mixed model methodology is a tool of choice for analyzing correlated data in a large domain of disciplines and areas of application. Censored data are not rare in practice and they may cause serious defects in the estimation of parameters when not properly accounted for in the statistical analysis. A frequent phenomenon, which generates censored data, lies in the existence of limits of detection (or quantification) of the response measured. Hughes [1] considered mixed linear models for analyzing longitudinal data of this kind, and presented an EM based procedure for calculating EM estimators of parameters in such models; see also [2], [3], [4], [5] and [6]. In the case of left censoring, Moulton and Halsey [7] and Berk and Lachenbruch [8] extended this model in assuming that censored data may come from an additional source of truly low responders: see also [9] for an alternative called the “two-parts model”. Here, our concern is about another extension of the basic model in which the response variable is observed only if the value of a correlated, but non-observable variable, exceeds a given threshold. The corresponding models are called “Stochastic Censoring Models” [10] or “Type II Tobit Models” [11]. In the literature, inference is usually restricted to the case of fixed effects linear and/or nonlinear models. The objective of this presentation is to extend the statistical analysis to mixed models, and in a first stage, to linear models and prediction of random effects. The censoring process is controlled by the variable { } 1 1i w = w which is not observed directly,