Abstracts - Oral Presentations Tuesday, 27 August 2013 I 3: Comparison of penalization approaches in regression models I 3.1 Penalization theory and practice for Cox models Therneau T.M. 1 1 Mayo Clinic, Department of Health Science Research, Rochester, United States The best penalty functions have three properties: they separate models with similar statistical goodness of fit, are computationally tractable, and reflect an actual biological truth. With respect to the third of these statisticians have usually focused on two very diffuse constraints: "a coefficient shouldn´t be too large" and "a lot of them should be zero". The gains from these weak assumptions can be surprisingly large. I will give an example of a strong constraint along with several others using the simple L2 (coefficients not too large) penalty, which is readily available for Cox models in both R and SAS. I 3.2 Two folklores: ridge regression versus the lasso Goeman J. 1 1 Leiden University Medical Center, Leiden, Netherlands Lasso and ridge regression are two forms of penalized regression that shrink the parameters of the fitted regression model to zero. Both can be used in high-dimensional prediction models, allowing regression models to be fitted even when there are more parameters than observations. The difference between the two is that lasso also returns a sparse model, setting many regression parameters to exactly zero, whereas ridge regression always leaves all covariates in the model. Research in mathematical statistics had uncovered many interesting properties of variants of the lasso, showing in particular some oracle properties. These oracle properties say that asymptotically these variants of the lasso have the same mean squared error for estimating the regression coefficients as an oracle that already knows which regression coefficients are truly non-zero. Because of such properties, which ridge regression does not have, mathematical statisticians tend to claim superiority of lasso over ridge regression. Research in biostatistics, however, tends to show that for many high-dimensional data sets ridge regression has a better predictive potential than the lasso. Researchers also find that the lasso tends to be unstable, selecting very different covariates upon slight perturbations of the data. Because of this, biostatisticians often claim superiority of ridge regression over the lasso, at least where prediction is concerned, and warn against overinterpretation of the results of lasso models. In this talk I will review the arguments on both sides, discussing the usefulness of oracle properties. I will end with practical recommendations. I 3.3 Purposeful penalization of likelihood in small samples Heinze G. 1 1 Medical University of Vienna, Center for Medical Statistics, Informatics and Intelligent Systems, Vienna, Austria Often biostatisticians are asked to estimate effects of novel biomarkers in survival studies, while adjusting for a relatively large set of variables, e.g., well-established clinical predictors. Sometimes, such studies additionally suffer from a low number of observed events because the disease under study is rare, or patients have relatively good prognosis. In consequence, the number of events per variable (EPV) is low, which may induce bias away from zero and low precision of regression coefficients obtained by multivariable Cox regression.