Weight variables to develop scoring algorithm

Question

I am studying how to develop a prognostic index in medicine. I have read some articles and in all of them metholodgy is quite the same. Most of them use logistic regression, choose variables and build a model. Each variable in the model has a weight. For example, if the score has three variables (ie.fever, cough, pain) each of them adds a number of points and the total sum is the value of the prognostic index. If prognostic index is used to decide if a patient must be admited to a hospital you may say that fever present sums 2 points, cough 1 point and feel perfect substracts 1 point (adds -1 point). If prognostic index I superior than 2 patient is admitted and otherwise not. What I don´t understand after reading some articles using this methodology is how they weight variables. Do they use logistic regression obtained Odds to weight variable contribution to the index? Is it correct to give more weight to larger odds? Are there any other methods to do this? What kind of test would be used to test fitness of this prognostic model? Best regards,. Marcos