Cancer is now the biggest single cause of mortality worldwide, incidence has increased by 11% in four years and cases are forecast to rise by 75% over the next 20 years . Despite the huge amount of resources devoted to combating this terrible disease, progress has been slow. Most patients are still treated with painful blunt instruments like radiation and chemotherapy while new targeted treatments addressing specific genetic causes often only help a small portion of the population. Why haven’t scientists and doctors been able to do more? Because each patient is di˙erent, each cancer is unique and we lack the framework for collecting, processing and understanding the mountain of information that we can generate on cancers, treatments and responses. In the following chapter we review background material on the problem domain, theo-retical underpinnings of the model and discuss similar approaches. In chapter 2 we intro-duce our model, giving full details on the mathematical derivations and implementation. Chapter 3 shows results on simulated data that highlight the strengths of the method. Chapter 4 shows results on three real dose-response datasets compared with other state-of-the-art methods. Chapter 5 shows results predicting cellular counts of cancer cell lines grown in varying micro-environments and chapter 6 summarizes the work and discusses extensions and future directions.