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Cancer has complex patterns of progression that includes converging as well as diverging progressional pathways. The path model of colon cancer introduced by Vogelstein was a pioneering contribution to cancer research. Since then, several attempts have been made to obtain mathematical models of cancer progression, i.e., defining classes of models, devising training algorithms, and applying these to cross-sectional data. We study tree-based models and mixtures of such, since they have the desirable features of having relatively few parameters as well as being relatively easy to train. In this talk, we will discuss previous work, including that of Beerenwinkel et al. who provided EM-like algorithms for the so-called Oncogenetic Trees and mixtures of such. We will then introduce Hidden Variable Oncogenetic Trees (HOTs) which allow for errors in the data and thereby more realistic modeling, and we will present proper EM-algorithms for the HOTs as well as HOT-mixtures. The EM-algorithm for a single HOT is shown to perform very well for reasonable-sized data sets, while HOT-mixtures require data sets of sizes that can only be obtained with tomorrow's more cost efficient technologies. To facilitate analysis of complex cytogenetic data sets requiring more than one HOT, we train parameters on a colon cancer (CC) data set and devise a decomposition strategy based on Principal Component Analysis. The method so obtained is then successfully applied to kidney cancer (RCC).