 2005 Royal Statistical Society 0035–9254/05/54405 Appl. Statist. (2005) 54, Part 2, pp. 405–423 Bivariate modelling of longitudinal measurements of two human immunodeficiency type 1 disease progression markers in the presence of informative drop-outs N. Pantazis and G.Touloumi University of Athens Medical School, Greece and A. S. Walker and A. G. Babiker Medical Research Council Clinical Trials Unit, London, UK [Received February 2003. Final revision June 2004] Summary. The main statistical problem in many epidemiological studies which involve repeated measurements of surrogate markers is the frequent occurrence of missing data. Standard like- lihood-based approaches like the linear random-effects model fail to give unbiased estimates when data are non-ignorably missing. In human immunodeficiency virus (HIV) type 1 infec- tion, two markers which have been widely used to track progression of the disease are CD4 cell counts and HIV–ribonucleic acid (RNA) viral load levels. Repeated measurements of these markers tend to be informatively censored, which is a special case of non-ignorable missing- ness. In such cases, we need to apply methods that jointly model the observed data and the missingness process. Despite their high correlation, longitudinal data of these markers have been analysed independently by using mainly random-effects models.Touloumi and co-work- ers have proposed a model termed the joint multivariate random-effects model which combines a linear random-effects model for the underlying pattern of the marker with a log-normal survival model for the drop-out process.We extend the joint multivariate random-effects model to model simultaneously the CD4 cell and viral load data while adjusting for informative drop-outs due to disease progression or death. Estimates of all the model’s parameters are obtained by using the restricted iterative generalized least squares method or a modified version of it using the EM algorithm as a nested algorithm in the case of censored survival data taking also into account non-linearity in the HIV–RNA trend. The method proposed is evaluated and compared with simpler approaches in a simulation study. Finally the method is applied to a subset of the data from the ‘Concerted action on seroconversion to AIDS and death in Europe’ study. Keywords: Bivariate response; Informative censoring; Missing data; Repeated measurements 1. Introduction Many epidemiological studies and especially studies of the natural history of diseases with a long time course have designs involving repeated measurements of markers defined as key variables related to progression of the disease. One major statistical problem in such studies, where the main interest is to estimate the rate of change in a continuous variable, is the frequent occurrence of missing data due to missing visits, withdrawal or attrition. Several methods to analyse such unbalanced data are available, provided that the missing data are missing at random. Following Address for correspondence: Nikos Pantazis, Department of Hygiene and Epidemiology, University of Athens Medical School, M. Asias 75, 115 27 Athens, Greece. E-mail: npantaz@med.uoa.gr Downloaded from https://academic.oup.com/jrsssc/article/54/2/405/7112999 by guest on 04 September 2023