Background

Logistic regression is one of the most commonly used statistical methods to estimate prognostic models that relate a binary outcome (with levels ‘event’ and ‘non-event’) to a number of binary, categorical or continuous explanatory variables. A low prevalence of events, encountered frequently in clinical or epidemiological studies, but also in other fields of empirical research, causes underestimation and instability of estimates of the event probability in subjects who are likely to experience the rare event. This happens because the analysis is disproportionally influenced by the subjects without events. This effect is even more pronounced when the number of explanatory variables approaches or exceeds the number of outcome events.
Recently, penalized likelihood regression (PLR) methods have become popular for analyses with high-dimensional explanatory variable spaces. PLR methods shrink the estimates of regression coefficients towards zero in order to decrease their mean squared error. While this also decreases the overall mean squared error of predicted event probabilities, in the rare events situation (RES) poor predictions for the subjects which are at high risk for an event are still encountered.
The main objective of this project is to further develop PLR with regard to the high-dimensional RES by elaborating and evaluating novel approaches to estimation, tuning and validation.
The performance of the proposed methods will be evaluated on real-life data sets and in comprehensive simulation studies. Implemented in statistical software packages, the results of this project will be of practical value, whenever predictions for strongly imbalanced binary outcomes have to be derived from high-dimensional data.