Stirrup, OT; (2016) Extending mixed effects models for longitudinal data before and after treatment. Doctoral thesis , UCL (University College London).

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Abstract

For the analysis of longitudinal biomedical data in which the timing of observations in each patient is irregular and in which there is substantial loss to follow-up, it is important that statistical models adequately describe both the patterns of variation within the data and any relationships between the variable of interest and time, clinical characteristics and response to treatment. We develop novel statistical models motivated by the analysis of pre- and post-treatment CD4 cell counts from HIV-infected patients, using the UK Register of Seroconverters and CASCADE datasets. The addition of stochastic process components, specifically Brownian motion, to standard linear mixed effects models has previously been shown to improve model fit for pre-treatment CD4 cell counts. We review and further develop computational techniques for such models, and also propose the use of a more general ‘fractional Brownian motion’ process in this setting. Residual diagnostic plots for such models, based on a marginal multivariate normal distribution, show very heavy tails, and we address this issue by further extending the model to allow between-patient differences in variability over time. It is known from the literature that response to treatment in HIV-patients is dependent on their baseline CD4 level at initiation. In order to further investigate the factors that determine the characteristics of recovery in CD4 counts, we develop a framework for the combined modelling of pre- and post-treatment CD4 cell counts in which key features of the response to treatment for each patient are dependent on a latent variable representing the unobserved ‘true’ baseline value, conditioned on all pre-treatment data for each patient. We further develop the model structure to account for uncertainty in the exact time of seroconversion for each patient, by integration of the log-likelihood function over all possible dates.

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