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

Abstract

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.

Risk factors for relapse of antineutrophil cytoplasmic antibody–associated vasculitis

“…The competing risk framework is sensible in this disease and has added new insights into the assessment of baseline risk factors. The use of multiple imputation allows the use of all the data, which may improve the precision of estimates and reduce bias created by missing data (29).…”

Differences in HIV RNA levels before the initiation of antiretroviral therapy among 1864 individuals with known HIV-1 seroconversion dates

“…The total variability was the weighted sum of the variability estimated at the convergence of the model and of the between-imputation variability. The method and its relative efficiency has been described in detail elsewhere [34].…”

Robustness of a parametric model for informatively censored bivariate longitudinal data under misspecification of its distributional assumptions: A simulation study

“…For each complete data set, we re-run the model and we estimate the empirical between data sets variance for each fixed parameter. This 'between data sets' variance (weighted by 6 5 to adjust for finite number of samples) is added to the 'within' variance as estimated by the JMRE model [16,17]. Ideally, the Louis [18] method could be used to estimate SEs based on the observed information of the complete data.…”

“…Ideally, the Louis [18] method could be used to estimate SEs based on the observed information of the complete data. However, Touloumi et al [17] showed that the modified MI method gives results similar to that of the Louis method, while at the same time it is computationally more attractive.…”