Penalized Lasso Methods in Health Data: application to trauma and influenza data of Kerman

Background: Two main issues that challenge model building are number of Events Per Variable and multicollinearity among exploratory variables. Our aim is to review statistical methods that tackle these issues with emphasize on penalized Lasso regression model.  The present study aimed to explain problems of traditional regressions due to small sample size and multi-colinearity in trauma and influenza data and to introduce Lasso regression as the most modern shrinkage method. Methods: Two data sets, corresponded to Events Per Variable of 1.5 and 3.4, were used. The outcomes of these two data sets were hospitalization due to trauma and hospitalization of patients suffering influenza respectively. In total, four models were developed: classic Cox and logistic regression models, as well as their penalized lasso form. The tuning parameters were selected through 10-fold cross validation. Results: Traditional Cox model was not able to detect significance of any of variables. Lasso Cox model revealed significance of respiratory rate, focused assessment with sonography in trauma, difference between blood sugar on admission and 3 h after admission, and international normalized ratio. In the second data set, while lasso logistic selected four variables as being significant, classic logistic was able to identify only the importance of one variable. Conclusion: The AIC for lasso models was lower than that for traditional regression models. Lasso method has practical appeal when Events Per Variable is low and multicollinearity exists in the data.