Linear Mixed Models for Longitudinal Data with Nonrandom Dropouts

Ahmed M Gad,Noha A Youssif

doi:10.6339/jds.2006.04(4).280

Abstract

Longitudinal studies represent one of the principal research strategies employed in medical and social research. These studies are the most appropriate for studying individual change over time. The prematurely withdrawal of some subjects from the study (dropout) is termed nonrandom when the probability of missingness depends on the missing value. Nonrandom dropout is common phenomenon associated with longitudinal data and it complicates statistical inference. Linear mixed effects model is used to fit longitudinal data in the presence of nonrandom dropout. The stochastic EM algorithm is developed to obtain the model parameter estimates. Also, parameter estimates of the dropout model have been obtained. Standard errors of estimates have been calculated using the developed Monte Carlo method. All these methods are applied to two data sets.

Highlights

Longitudinal studies represent one of the principal research strategies employed in medical and social research
We argue that in nonrandom dropout setting, and depending on the dropout model (1.2), if this value is imputed given its value, the remaining missing values can be assumed as missing at random
The parameter estimates using the stochastic EM algorithm are similar to those obtained by Verbeke and Molenberghs (2004), we have got postive values for the variance component (d22 in particular)

Summary

Introduction

Longitudinal studies represent one of the principal research strategies employed in medical and social research. Let n be the number of time points and Yi be n × 1 vector of intended measurements for the ith subject, which would have been obtained if there were no missing values. Diggle and Kenward (1994) propose a selection model for continuous longitudinal data with nonrandom dropout This model assumes that the probability of dropout for the ith subject at time tdi depends on the history of the measurements up to and including time tdi,. At each iteration of the stochastic EM algorithm the missing data is imputed with a single draw from the conditional distribution of the missing data given the observed data and the current parameter estimates This imputation of the missing values is based on all our current information about θ, and provides us with a plausible pseudo-complete data. The linear mixed model is a possible candidate for such analysis

Linear Mixed Model

The Stochastic EM Algorithm

The mastitis data

The rats data

Concluding Remarks