A comparison of two methods for the estimation of precision with incomplete longitudinal data, jointly modelled with a time-to-event outcome

Several methods for the estimation and comparison of rates of change in longitudinal studies with staggered entry and informative drop-outs have been recently proposed. For multivariate normal linear models, REML estimation is used. There are various approaches to maximizing the corresponding log-likelihood; in this paper we use a restricted iterative generalized least squares method (RIGLS) combined with a nested EM algorithm. An important statistical problem in such approaches is the estimation of the standard errors adjusted for the missing data (observed data information matrix). Louis has provided a general technique for computing the observed data information in terms of completed data quantities within the EM framework. The multiple imputation (MI) method for obtaining variances can be regarded as an alternative to this. The aim of this paper is to develop, apply and compare the Louis and a modified MI method in the setting of longitudinal studies where the source of missing data is either death or disease progression (informative) or end of the study (assumed non-informative). Longitudinal data are simultaneously modelled with the missingness process. The methods are illustrated by modelling CD4 count data from an HIV-1 clinical trial and evaluated through simulation studies. Both methods, Louis and MI, are used with Monte Carlo simulations of the missing data using the appropriate conditional distributions, the former with 100 simulations, the latter with 5 and 10. It is seen that naive SEs based on the completed data likelihood can be seriously biased. This bias was largely corrected by Louis and modified MI methods, which gave broadly similar estimates. Given the relative simplicity of the modified MI method, it may be preferable.