The "Summary of Forward Selection" in the output will summarize it all. The p-values of the IV's in the model indicate wether or not the corresponding variable are significant on their own.

I do understand you are performing a forward STEPWISE binomial logistic regression.

Question 2 and 3 : What you describe is probably due to the fact that your two (or more) IV are more or less correlated, in the sense conveying more or less the same information. You should have the same behaviour inverting the order of the variables.

My advice would be to not (only) use significance of a specific parameters, but instead use likelihood ratio test to compare models (IV1 alone) vs. (IV1 + IV2). It may happen that a non "significant" parameter could anyway improve the global fit of a model.

You should find a related example treated in : https://stats.stackexchange.com/questions/6505/likelihood-ratio-test-in-r

thank you very much Jos & Jean

To run what Jean suggested (compare the 2 models) with SAS, you can use the rsqdelta.sas macro in attachment. I included a SAS program with the coronary data to illustrated how to run this macro (amin_rsqdelta.sas).

http://ftp.sas.com/techsup/download/observations/4q96/iokierna/rsqdelta.sas

http://www.datavis.ca/sasmac/rsqdelta.html

PLace the rsqdelta.sas macro in the path:

c:\stat\macro\   (you will probably need to create this path)

PS: Contrary to what I stated earlier, in proc logistic, the order in which you place the variables (age group vs. group age) does not really matter. With the forward selection, in the 1st step, the IV with the highest correlation with the response (dependent variable) is entered. In the 2nd step, the IV with the next highest correlation is entered.

You could also use the Influence plots for logistic regression: macro:

http://euclid.psych.yorku.ca/datavis.ca/sasmac/inflogis.html

It is quite common to add a backward elimination after having completed forward selection. If you did that, you would eliminate one by one the least significant variable until the remaining ones are all significant. In your scenario 3, you would thus drop the first independent variable and end up with variable 2 only. In scenario 1 you would obtain a model without covariates, in scenario 2 you would keep both.

Forward selection/backward elimination has a whole series of problems. Jean pointed towards correlated independent variables. Another problem is inconsistency between forward selection and backward elimination. In forward selection, you start from the base model and add one covariate at a time. In backward elimination you start from the model with all covariates and drop one at a time until they are all significant. It would be a good feature if you ended up with the same model in both cases, but practically mostly you don't.

Multiple testing and adjusting the significance threshold is another issue that requires consideration and it not straightforward to solve.

I have come to like bootstrap approaches where observations and covariates (!) are sampled and the data sets are analyzed. The art here is in the aggregation of the results to identify the relevant covariates. Random forests in the area of clustering and regression trees (CART) are a good example.

In the context of mixed effects models, there is an illustrative paper on the topic of correlated covariates, demonstrating that you frequenty end up with the "wrong" covariate. Peter Bonate: Effect of correlation on covariate selection in linear and nonlinear mixed effect models. Pharmaceutical Statistics 2016.

http://onlinelibrary.wiley.com/doi/10.1002/pst.1776/abstract

PS. Using abbreviations is dangerous: I noticed that you have the tag "Intravenous Therapy" on your post. Intravenous is commonly abbreviated as IV, and so is "independent variable".