Title: Combining retrospective and prospective data in characterizing accumulation of antiviral drug resistance mutations
Description: The chapters of this thesis provide novel approaches for estimating the acquisition rates of HIV drug resistance mutations using both retrospective data and prospective data. In the first chapter, the Markov model of Foulkes and DeGruttola (2003) is expanded to allow interval censored times of mutation acquisition. In addition to genotypes collected prospectively during a study, treatment history for study participants is often available. The time on treatment before the start of the study is an additional interval during which mutations can be acquired; therefore, by including this interval, the mutations acquired before the study are incorporated in estimation of transition rates. Since the time on treatment is often known less accurately than the prospectively collected information, the time can be coarsened to incorporate the uncertainty in recorded times. The accuracy of estimated rates is improved when treatment history is included, even when treatment history is known with error.

When treatment history is not available, constructing branching trees using the baseline data provides information about mutation acquisition rates prior to the start of the study. In the second chapter, branching tree parameters for the baseline data and Markov model parameters for the prospective data are written in a single likelihood. Since functions of each parameter set estimate the same quantity, the combined likelihood is maximized according to functions that link the two parameter sets using either constrained maximization or weighted least squares. Since link functions may not hold exactly, the approach also allows error in the links. The accuracy of estimated rates is improved by this approach when compared to using only prospective data for estimation. The link functions in the second chapter assume that the tree set is known, but this assumption may not be valid in general. In the third chapter, a mixture model approach and a bootstrap approach are used to determine the additional variability in estimation of a function due to uncertainty in tree set. The mixture model approach can easily accommodate additional constraints and covariates; furthermore, this approach can easily be extended to population based studies.