An alternative parameterization of the general linear mixture model for longitudinal data with non-ignorable drop-outs

This paper considers the mixture model methodology for handling non-ignorab le drop-outs in longitudinal studies with continuous outcomes. Recently, Ho gan and Laird have developed a mixture model for non-ignorable drop-outs wh ich is a standard linear mixed effects model except that the parameters whi ch characterize change over time depend also upon time of drop-out. That is , the mean response is linear in time, other covariates and drop-out time, and their interactions. One of the key attractions of the mixture modelling approach to drop-outs is that it is relatively easy to explore the sensiti vity of results to model specification. However, the main drawback of mixtu re models is that the parameters that are ordinarily of interest are not im mediately available, but require marginalization of the distribution of out come over drop-out times. Furthermore, although a linear model is assumed f or the conditional mean of the outcome vector given time of drop out, after marginalization, the unconditional mean of the outcome vector is not, in g eneral, linear in the regression parameters. As a result, it is not possibl e to parsimoniously describe the effects of covariates on the marginal dist ribution of the outcome in terms of regression coefficients. The need to ex plicitly average over the distribution of the drop-out times and the absenc e of regression coefficients that describe the effects of covariates on the outcome are two unappealing features of the mixture modelling approach. In this paper we describe a particular parameterization of the general linear mixture model that circumvents both of these problems. Copyright (C) 2001 John Wiley & Sons, Ltd.