Ioannis Papastathopoulos

My doctoral research was focused on exploring safety issues of Phase II/III clinical studies and pharmaceutical experiments of new drugs. Combination of extreme values of laboratory variables indicate toxic drugs and early detection of signs of a drug's potential for toxicity is vital for pharmaceutical companies evaluation of new drugs.

Most of this work is motivated from the need to build statistical models that incorporate scientific knowledge and capture the characteristics of multivariate laboratory variables that show potential in identifying signals of death induced by drug medication. The models are designed to enable the simulation of a large hypothetical population under drug treatment and can be used to estimate the toxicity of a new drug and predict the frequency of severe adverse events. Few of the major challenges of the project relate to the small sample sizes of Phase II studies which contradicts the asymptotic nature of extreme value methods. A solution to this problem is proposed by extensions of standard extreme value techniques that offer additional structure for the main body of the distribution of the data and improve the estimates of key extremal quantities.

Additionally, accurate estimation of the dependence structure that drives the data in longitudinal trials is of vital importance. For this purpose, the conditional approach to multivariate extremes is used and extended to allow characteristics of multiple dose trials. Moreover graphical model estimation of multivariate extremes is explored and new diagnostic measures for detecting conditional independence are constructed from the theoretical properties of multivariate extreme value distributions.