Penalized regression methods with sparse variables for modeling binary outcomes Abstract: Modeling binary outcomes plays an important role in epidemiology. It is often used to study the influence of risk factors on the occurrence or onset of a disease. Logistic regression via maximum likelihood (ML) has become the established analysis method of choice. However risk factors with very low prevalences are problematic. Risk estimation of such sparse covariates via ML often suffers from strong bias. Even though this challenge is common in epidemiology investigations into appropriate methodology exists are few in number.<br>The dissertation is a treatise of solutions in this context via penalized regression. Penalizing the likelihood function makes estimation even of very sparse covariates possible when classical ML methods often fail. In recent years penalized regression has received increased attention in statistical literature and as a result a number of different variations exist. However these methods have received little to no attention in epidemiologic studies.<br>In this dissertation penalized methods will for the first time be investigated in the context of sparse covariates. Firstly the theory concerning state of the art penalization methods will be treated. Further the investigated methods will be studied using data from epidemiological studies. Lastly accompanying simulation studies are conceived and analyzed. Tuned extensions of existing penalization methods are proposed to improve their untuned counterparts