Survival analysis: comparing two different regressions (with different samples)

[Budiman Raharjo]

Dear all,

Can one directly compare hazard ratios (Hr) from two different regressions with different samples? For example:

. stset day, faliure(murder) if(country=="FR")
. stcox married

. stset day, failure(murder) if(country=="DE")
. stcox married

Suppose Hr for married = 0.891 (being married makes one a bit less likely to commit murder) for the France sample, and 0.781 for the German sample, can I say that being married in German makes you even less likely to commit murder than it does in France?

Normally I would use SUR (the "suest" and "test") for comparing coefficients from different linear regressions, but neither parametric survival model ("streg") nor semiparametric model ("stcox") is supported by "suest".

[Maarten Buis]

You are dealing with an interaction term (the effect of married may or may not differ between countries). There is an extra complication in that by estimating separate Cox models you allow for different baseline hazard functions between countries. To allow for the latter we can use the strata() option in stcox. After that just include the interaction term between married and country, and the main effect of married. The main effect of country is absorbed by the strata() option. Your code would probably look something like this:

gen byte france = country == "FR" if inlist(country, "FR", "DE")
label define france 1 "France" 0 "Germany"
label value france france

stcox i.france#i.married  i.maried, strata(france)

Using an example dataset that comes with Stata:

. sysuse cancer, clear
(Patient Survival in Drug Trial)

. stcox i.drug#c.age age, strata(drug)

         failure _d:  died
   analysis time _t:  studytime

Iteration 0:   log likelihood = -64.736463
Iteration 1:   log likelihood = -59.394516
Iteration 2:   log likelihood = -59.372188
Iteration 3:   log likelihood = -59.372185
Refining estimates:
Iteration 0:   log likelihood = -59.372185

Stratified Cox regr. -- Breslow method for ties

No. of subjects =           48                  Number of obs    =          48
No. of failures =           31
Time at risk    =          744
                                                LR chi2(3)       =       10.73
Log likelihood  =   -59.372185                  Prob > chi2      =      0.0133

------------------------------------------------------------------------------
          _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  drug#c.age |
          2  |   1.110106   .1132812     1.02   0.306     .9088726    1.355893
          3  |   .9860279   .0992645    -0.14   0.889     .8094646    1.201104
             |
         age |   1.096463   .0533264     1.89   0.058     .9967717    1.206124
------------------------------------------------------------------------------
                                                            Stratified by drug

So the hazard increases by 9% for every year you get older if you get drug 1 (the reference category). This effect of age is (a non-significant) 11% higher for people who receive drug 2, and (a non significant) 1% lower for people who receive drug 3. (See e.g. http://maartenbuis.nl/publications/interactions.html)