Difference between survdiff log-rank and coxph log-rank

Question

I'm using the survival package in R to analyze clinical data. I am analyzing two different groups of patients, when I calculate survdiff in order to compare the curves, I got p= 0.135, but when I adjust the model using coxph and different covariates, let say clinical cancer stages, , I got an overall logrank score of 0.0005793 for 5 covariates. My question is, could I use this late logrank p-value to say that adjusting the model with more covariates the difference between the curves is signifficative?

here is the data

survdiff(formula = my.surv ~ final_table$G)

n=56, 14 observations deleted due to missingness.

                 N Observed Expected (O-E)^2/E (O-E)^2/V
final_table$G=1  4        2     1.43    0.2294     0.247
final_table$G=2 52       24    24.57    0.0133     0.247

 Chisq= 0.2  on 1 degrees of freedom, **p= 0.619** 

And this is the coxph results

coxph(formula = Surv(final_table$Time_surv, final_table$Survival) ~ final_table$G + final_table$ST)

  n= 56, number of events= 26 
  (14 observations deleted due to missingness)

                   coef exp(coef)  se(coef)     z Pr(>|z|)
final_table$G2    2.094e-01 1.233e+00 7.532e-01 0.278    0.781
final_table$STII  1.883e+01 1.501e+08 5.739e+03 0.003    0.997
final_table$STIII 1.998e+01 4.773e+08 5.739e+03 0.003    0.997
final_table$STIV  2.089e+01 1.186e+09 5.739e+03 0.004    0.997

              exp(coef) exp(-coef) lower .95 upper .95
final_table$G2    1.233e+00  8.111e-01    0.2817     5.396
final_table$STII  1.501e+08  6.662e-09    0.0000       Inf
final_table$STIII 4.773e+08  2.095e-09    0.0000       Inf
final_table$STIV  1.186e+09  8.430e-10    0.0000       Inf

Concordance= 0.74  (se = 0.057 )
Rsquare= 0.37   (max possible= 0.957 )
Likelihood ratio test= 25.86  on 4 df,   p=3.381e-05
Wald test            = 4.02  on 4 df,   p=0.4033
Score (logrank) test = 19.67  on 4 df,   **p=0.0005793**

Thanks

Thanks to comments I did this analysis, survdiff with roup and stage

survdiff(formula = Surv(final_table$Time_surv, final_table$Survival) ~ 
final_table$G + final_table$ST)

n=56, 14 observations deleted due to missingness.

                                 N Observed Expected (O-E)^2/E (O-E)^2/V
final_table$G=1, final_table$ST=III  3        2    1.149     0.630     0.668
final_table$G=1, final_table$ST=IV   1        0    0.279     0.279     0.285
final_table$G=2, final_table$ST=I   15        0    8.715     8.715    13.547
final_table$G=2, final_table$ST=II   2        1    1.816     0.367     0.402
final_table$G=2, final_table$ST=III 30       19   13.067     2.693     5.540
final_table$G=2, final_table$ST=IV   5        4    0.973     9.413     9.935

Chisq= 23.2  on 5 degrees of freedom, p= 0.000313

So the final value is totally significant, but now I got 6 curves, more or less this is what I want, how the group and the stage is affecting the survival. What do you think?

Answer 1

Without actual output it is difficult to tell, but generally an "overall logrank score" will test the null hypothesis that all of the coefficients are 0. Therefore a significant result could be due to one or more of your covariates being related to survival while your 2 groups are still identical (or they could be different).

It is better to fit the model with your group variable (and the covariates) and fit another model without your group variable (but still with the same covariates) and compare the 2 fits.