I wanted to create a predictive model of mortality after patients had undergone a surgical procedure. But I also wanted to avoid doing what most researchers do by first performing univariate analysis then using the variables that are found to be significant to perform multivariate analysis using some sort of step-wise feature selection. So I used
glmnet to perform feature selection, and found about 20 of the initial 80 variables to be significant. I then used some of these variables (as supported by literature) to create a statistical model to predict mortality using the
glm function in R. I think the model does fairly well as it has a ROC of 0.8. However when I use the
summary function I notice that of the 15 variables that I am using, 5 of them do not have significant p-values. But if I remove these variables, in my mind the model would not make sense (since the literature supports their use), and in addition the ROC decreases to about 0.75.
Given this situation, how does one go about when analyzing these variables? It seems that they are useful and necessary (as they aid in the discrimination of patients who will die or live when having a procedure performed on them) but do not have a significant p-value.
Forgive me for being light on code, as I wanted more of a 10,000 feet overview of this rather than to get into the nitty-gritty from the get-go. As always, I appreciate the help!