Nonlinear mixed-effects models for multi-variate longitudinal data with application to HIV disease dynamics.
The motivation for the study of nonlinear mixed-effects models is due to the growing interest in the estimation of parameters in HIV disease dynamical models using real multivariate longitudinal data with varying degrees of informativeness. Special analytical and approximation techniques are needed to deal with such data because the repeated observations on any experimental unit are likely to be correlated over time while multiple outcomes within the unit will also be correlated. Furthermore, observations may be irregularly made within and between individuals making direct use of standard methods practically impossible. In this thesis, we consider a nonlinear mixed-effects model for a multivariate response variable that takes into account left-censored observations. Then we study a case where data are unbalanced among subjects and also within a subject because for some reason only a subset of the multiple outcomes of the response variable are observed at any one occasion. Dropout models that take into consideration the partially observed outcomes are proposed. We further derive a joint likelihood function which takes into account the multivariate responses and the unbalancedness in such data as a result of censoring and dropout. We then show how the methodology can be used in the estimation of the parameters that characterise HIV dynamical system in the presence of several covariates. We have also used multiple imputation to compare covariate coefficients in the complete data and the partially observed data. Through a simulation study, we have also seen that a small limit of quantification provides better parameter estimates in the sense of standard errors and confidence limits of the parameters. Since there are usually no analytic solutions for such complex models, the stochastic approximation Expectation-Maximisation (SAEM) is used as an approximation method. The methodology is illustrated using a routine observational dataset from two HIV clinics in Malawi.