Through the use of microarray technology researchers are now able to si- multaneously measure the expression levels of tens of thousands of genes. Amoung other things, this allows the construction of profiles of activation of various pathways within tumour samples. Using a metacohort of 2116 breast cancer patients, this thesis explores various Bayesian factor regres- sion methods to estimate the probability of pathway activation using gene expression data. The relationship between these probabilities and various histological methods is also examined. The methods of estimation can be broken into two main categories, univari- ate and multivariate. The univariate method has been explored previously, and this thesis aims to replicate the work of Bild et al. (2006), as well as explore other univariate models. In this thesis the univariate models were implemented mainly in R using the rbprobit package, although work was also undertaken in implementing these models in Python using PyMC. The multivariate approach has not been taken before, and is of interest due to the fact that biological pathways do not act in isolation. The multivariate techniques look to find correlation between the various pathways, to give more accurate estimates of the probability of pathway activation. Once the probablities of pathway activation were estimated using the var- ious univariate and multivariate methods, the best model from the two categories was selected. The estimates from these two models were then combined with various histological information (i.e. estrogen receptor sta- tus, progesterone receptor status, and lymph node status), to see whether or not there is any advantage in using a multivariate approach over a uni- variate one, and to determine if pathway activation status is associated with the histological information.
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