Statistical modeling of dependencies in medicine

Asymmetry is a fundamental feature of data dealing with medical treatment in settings involving complex dependencies, such as cholesterol cardiology risk preventive studies. However, typical measures of dependence, like the correlation coefficient, are symmetric. This severe oversymmetrization brings several biases. To overcome this gap, we develop better dependence modeling and provide statistical guidelines for research on preventative cardiology, bone mineral density, and general medicine. By using pseudo-exponential, pseudo-normal, Marshall-Olkin bivariate exponential, and Hanagal bivariate Weibull models, we demonstrate the ability to discover important latent relationships emerging in recent studies in cardiology. For example, an excessively high level of HDL cholesterol can be dangerous, as can the use of different units for cholesterol and blood pressure measurements. These models eliminate erroneous oversymmetrization while providing greater flexibility than asymmetric copulas. We illustrate the usage of the newly developed dependence models on data from the Framingham Heart Study, the University of Victor Babes study, and the Study of Osteoporotic Fracture (SOF). We create new pseudo-exponential and pseudo-lognormal models and a graphical method for goodness-of-fit for certain bivariate models. We also derive the pseudo-exponential copula and densities for these models.