Scenario A: In Cox regression, the chi square analysis of the -2 log likelihood (or the omnibus in binomial) is not significant, but some of the values of the Wald statistic corresponding to some of the independent variables (IVs) are significant, in addition to Exp (B) values greater than 1, with a confidence interval (CI) that does not include 1.
Questions: is the model by default not worthwhile because of the insignificant chi squared? Can/should the Exp(B) values pertaining to significant Wald be reported as risk ratios?
Scenario B: Binomial univariate models with regard to certain IVs show up as insignificant or as significant but with very low Nagelkerke R Square values. Then when I lump many of the numerical and categorical IVs together as cofactors for a single test, the omnibus chi squared returns as highly significant, the Negelkerke r squared is much higher (0.3-0.5), overall predicated classification is high (60-80%), but only one or two of the Walds corresponding to the IVs are significant, with some of those that were significant in the univariate models losing significance completely.
Questions: How do I interpret these findings? Do low Nagelkerke R Square values and insignificant Omnibus chi square nullify binomial models regardless of the the Walds? What about classification prediction ratios? Perhaps none of these are relevant, but only the odds ratios? If IVs go from insignificant in univariate to significant in a multivariate model what does this tell us?