Statistical methods occur in medicine in manifold situations and are nowadays a core-element in medical research. In this talk we will focus on three topics that are the analysis of shapes, rotational deformations and state transitions. Shapes can be represented by geometric object properties (GOPs) that can be derived from an object representation like discrete skeletal representation (s-rep). Based on the GOPs we will discuss a method to test mean differences of GOPs. The method is designed for data whose representations include both Euclidean and non-Euclidean elements like multivariate directional vectors that are available in a number of different object representations. Based on the multivariate directions, we will further investigate rotational deformations of 3D objects such as bending or twisting that have been observed as the major variations in various medical applications. We will look to a non-parametric as well as a parametric approach for estimation of the rotation axis of the rotational deformation.The non-parametric estimates are obtained by fitting small circles applying sample Frechet means and least-square estimators whereas the parametric estimates are obtained by a Likelihood-based estimation procedure. In addition, we will briefly discuss the pros and cons of both approaches. Finally, we will discuss an innovative application of non-parametric state intensity regression to monitored health data. State intensity regression allows to study the time dependent effects of covariates on the state transitions. The method can handle baseline, time varying as well as dynamic covariates. The framework is applied to resuscitation data of newborns.
