# Difference between survdiff log-rank and coxph log-rank

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?