How do you get p-values for predictors in a Cox regression analysis in R? I am running a Cox regression analysis in R where both my predictors are binary (Animal_Number: single vs. paired; and Treatment: control vs. exposed). I therefore have four groups (single control, paired control, single exposed and paired exposed). When I run my Cox regression, I get the following output (excerpt):
                                        coef exp(coef) se(coef)      z Pr(>|z|)   
Animal_NumberPaired                   0.2617    1.2991   0.3303  0.792  0.42829   
TreatmentExposed                     -1.4031    0.2458   0.4715 -2.976  0.00292 **
Animal_NumberPaired:TreatmentExposed  1.0246    2.7861   0.5817  1.762  0.07814 .

As I understand it, the three lines presented here are simply the levels of the factors being compared to the baseline experimental group, which was set as single control, i.e., the first line is comparing single control animals with paired control animals.
If this is the case, how then does one find information (coefs, z, p-value, etc.) for purely the effect of Animal_Number, Treatment and their interaction? I can seem to do this in SPSS, and get the following:
                           B    SE      Wald    df  Sig.   Exp(B)
Animal_Number             .244  .331    .545    1   .461   1.276
Treatment               -1.283  .472    7.399   1   .007    .277
Animal_Number*Treatment   .959  .582    2.717   1   .099   2.609

But I want to be able to do it in R. I considered using likelihood ratio tests, to compare full and reduced models, but then information about the coefficients and z is lost. 
 A: @Peter Flom is right.  You are always comparing levels with categorical IVs.  SPSS is simply presenting your results in a way that obscures that fact from you.  
In this specific case, since each of your IV's has only two levels, the reported p-values are the ones you want.  (Note that if you had >2 levels, you would want to use anova() to get the appropriate p-value for the factor.)  
An additional issue here is that you have an interaction term included in your model.  The rule is that when you have an interaction you don't interpret the main effects.  In your case the interaction term is not 'significant' by conventional standards, but it is close enough that I wouldn't want to interpret the main effects anyway.  What this means then is that the results for, say, Animal_Number only pertain to the case where Treatment is control.  Basically, when there is an interaction, there is no such thing as 'the pure effect of a variable'.  
I also notice that the results from R and SPSS differ.  That is unsettling, but based on what's provided, I can't tell why this happened.  
A: I had the same issue too:
Here is the reason.
The contrast method in play is treatment.contrast().
For categorical variables this method creates a dummy for each category
So for animal_number there are two possible dummies
Animal_number single - a dummy variable which is 0 if a case is not single and 1 for single cases
Animal _number paired - a dummy which is 0 for paired cases and 1 for single cases
The same happens for Treatment groups where
Treatment control  is a dummy equal to 1 for control group cases and 0 for exposed group
Treatment exposed - a dummy equal to  0 for control group and 1 for exposed group
For each factor the dummies are perfectly correlated so you must exclude either the intercept or one dummy for each factor.The default is to exclude the dummy for the first level.
Which is single for animal number and  control for Treatment.
|----------------|----------------------|-------------------|------------|
|      Group.    | Animal_number paired.| Treatment exposed.| Interaction|
|----------------|----------------------|-------------------|------------|
|Single control. |    0.                |    0.             |         0  |
|----------------|----------------------|-------------------|------------|
|Single exposed. |    0.                |    1.             |         0  |
|----------------|----------------------|-------------------|------------|
|Paired control. |    1.                |    0.             |         0  |
|----------------|----------------------|-------------------|------------|
|Paired exposed. |    1.                |    1.             |         1  |
|----------------|----------------------|-------------------|------------|

So as you can see the interaction has only 2 outcomes
0/1
The coefficient for the interaction is the average difference  in log hazard ratio for the category =1 compared to the other 3 groups.
for my case i decided to omit the main effects leaving the simple effects
this way;
coxph(Surv(time,status)~Animal_Number*Treatment- Animal_Number-Treatment,data=data)
