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Modeling progression of HIV disease
 Žohová, Ivana ; Kulich, Michal (advisor) ; Zvára, Karel (referee)
In the present work we study modeling of HIV disease progression via multistate Markov model. The difficulty in this approach is how to define HIV disease states. These are usually defined in terms of CD4+ T lymphocyte counts, but this marker is a subject to biological fluctuation and, in real life, measurement errors as well. Estimating the model on such a data will lead to intensity estimates depending on frequency of observations. That is why we usually smooth the data before fitting the Markov model. In this work we studied two different approaches - linear mixed-effects model and local polynomial kernel estimator. All modeling is performed on real data and also an illustrative simulation example is included. Another issue considered in this work is determination of sero-conversion time. The sero-conversion distribution is derived based on time of last negative observation, first positive observation and last performed measurement.
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