I am trying to determine the illnesses that could contribute to an outcome of a patient ( recovered / dead / transferred to another department) and I'd like to know how big a mistake it is to leave all the predictors in the model even though they are insignificant? By that I mean, how much could an estimated coefficient change for a significant coefficient if I was to leave / exclude the insignificant predictor? Does the fact that there are many predictors influence for the worse the estimation of a model? In that case, should I simply leave out the insignificant predictors and then see how the model changes? Also, what could cause a very wide confidence interval for a coefficient ( with significant p - value) ?
I have a case of a predictor with estimated coefficient to be 9.15 with p-value < e-03. The confidence interval is 2.78 - 3.12e+01. Maybe the problem is with sample size, but then p-value shouldn't be so small. The sample consists of 235 subjects. From which 182 have recovered. From these 182, 6 had a condition x and 176 didn't have. 102 subjects have died, and from these 80 didn't have the condition and 22 had. It does look like a significant increase of outcome being the worst, but still 9x more likelihood does seem a bit absurd. I guess the wide confidence interval then kind of indicates that the prediction could be fallible because of the sample size or whatever?