Abstract
The measurement of human immunodeficiency virus ribonucleic acid levels over time leads to censored longitudinal data. Suitable models for dynamic modelling of these levels need to take this data characteristic into account. If groups of patients with different developments of the levels over time are suspected the model class of finite mixtures of mixed effects models with censored data is required. We describe the model specification and derive the estimation with a suitable expectation–maximization algorithm. We propose a convenient implementation using closed form formulae for the expected mean and variance of the truncated multivariate distribution. Only efficient evaluation of the cumulative multivariate normal distribution function is required. Model selection as well as methods for inference are discussed. The application is demonstrated on the clinical trial ACTG 315 data.
Highlights
Dynamic models for human immunodeficiency virus ribonucleic acid (HIV RNA) levels are used to estimate viral dynamic parameters for the whole population and for each individual patient in an acquired immune deficiency syndrome clinical trial
Previous work on dynamic models for HIV RNA levels used a variant or simplification of non-linear mixed effects models while accounting for censored data and applied the method proposed to a of the HIV type 1 (HIV-1) viral load data from clinical trial ACTG 315 (Lederman et al, 1988)
The performance of the model estimation and selection strategy proposed is evaluated by using the parametric bootstrap. This allows us to check whether the available data are sufficient to estimate the different groups in the data reliably. 100 samples are drawn from the fitted model to the HIV RNA data in Section 3 which was selected as the best model by using the Bayesian information criterion (BIC)
Summary
Dynamic models for human immunodeficiency virus ribonucleic acid (HIV RNA) levels are used to estimate viral dynamic parameters for the whole population and for each individual patient in an acquired immune deficiency syndrome clinical trial. As an alternative approach this paper considers finite mixtures of mixed effects models with censored data for modelling HIV RNA levels over time. The mixture model specification allows us to investigate whether the same functional relationship holds for all patients or whether groups of patients with different HIV RNA level developments exist. This model can either be used (a) if the a priori functional relationship is not known or (b) to check whether the assumed functional relationship is suitable. The model in this paper addresses the problem that interindividual differences might not be sufficiently captured by the random effects These differences are more flexibly modelled by using a mixture model which allows for distinct groups with different HIV RNA level developments over time.
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