A comparative study of variable selection procedures applied in high dimensional medical problems

In health studies, many potential factors are usually introduced to determine an outcome variable. In our study, different statistical methods are applied to analyze trauma annual data, collected by 30 General Hospitals in Greece. The first dataset consists of 1681 observations and 76 factors and the second of 6334 observations and 131 factors, that include demographic, transport and intrahospital data. The statistical methods employed in this work were the nonconcave penalized likelihood methods, SCAD, LASSO, and Hard, the generalized linear logistic regression, and the best subset variable selection, used to detect possible risk factors of death. A variety of different statistical models are considered, with respect to the combinations of factors and the number of observations. A comparative survey reveals differences between results and execution times of each method, and the analysis produces models that identify the significant prognostic factors affecting death from trauma

Tuning Parameter Selection in Penalized Frailty Models

<p>The penalized likelihood approach of Fan and Li (<a href="#cit0008" target="_blank">2001</a>, <a href="#cit0009" target="_blank">2002</a>) differs from the traditional variable selection procedures in that it deletes the non-significant variables by estimating their coefficients as zero. Nevertheless, the desirable performance of this shrinkage methodology relies heavily on an appropriate selection of the tuning parameter which is involved in the penalty functions. In this work, new estimates of the norm of the error are firstly proposed through the use of Kantorovich inequalities and, subsequently, applied to the frailty models framework. These estimates are used in order to derive a tuning parameter selection procedure for penalized frailty models and clustered data. In contrast with the standard methods, the proposed approach does not depend on resampling and therefore results in a considerable gain in computational time. Moreover, it produces improved results. Simulation studies are presented to support theoretical findings and two real medical data sets are analyzed.</p