# 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?

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## 1 Answer

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.

• I've never heard of an "overall logrank score" coming from a Cox model (but when you have a single categorical covariate in your Cox model, than the score test from the Cox model and the logrank test are equivalent). I don't use R so I'm just speculating here, but couldn't it be just a "LR test" that the OP incorrectly interpreted as "LogRank" instead of "Likelihood Ratio"? – boscovich Apr 19 '12 at 18:46
• Anyway, apart from the name of the test, I agree with what you say. – boscovich Apr 19 '12 at 18:55
• @andrea, you are probably correct, I was focusing on the "Overall" part rather than thinking logrank vs liklihood ratio. Either way I would not interpret it the way the original poster wants to without a lot more information. – Greg Snow Apr 19 '12 at 18:55
• Sorry, i forgot to add the data probably is mor clear now, I want to know if adjusting using other covariates I can say that my logrank score test coming from coxph, p=0.0005793 could replace the former survdiff logrank p= 0.619. Thanks and sorry is you find the question too simple, I'm totally newbie in survival analysis – ToniG Apr 20 '12 at 9:06
• It is like I said, that is an overall score that says that at least one of the predictors is important (in this case it is the one that you are adjusting for). The test of G given ST (adjusting for ST) has the p-value 0.781. So you have no evidence that G predicts survival. – Greg Snow Apr 21 '12 at 17:27