# Survival Analysis: Significance in LogRank but not in Cox Regression

Currently, I am trying to extract the HR and 95% CI from a kaplan meier curve (used DigitizeIt plus the spreadsheet provided by Tierney et al)

[Tierney JF, Stewart LA, Ghersi D, Burdett S, Sydes MR. Practical methods for incorporating summary time-to-event data into meta-analysis. Trials. 2007 Dec;8(1):16.]

Copy of KM curve here:

I'm comparing the yellow and blue curves. In the main paper the authors state that the logrank test has found the difference in curves to be significant p=0.03.

I then proceeded to trace the KM curve and input the datapoints into the spreadsheet provided by Tierney et al. The resultant HR between the curves was 1.47(0.85-2.53), the p value will not be significant in this instance.

So then my question is: Is it plausible for the p-values to be divergent in both the logrank and the cox regression? If so, what does that mean?

• The differences of the curves when? The test of $H_{0}: \hat{S_{A}}(t) = \hat{S_{B}}(t)$ for groups $A$ and $B$ using the Kaplan-Meier estimators is specific to a time $t$, not for two survival functions across all times. (Notice that for the first few time periods the blue and yellow curves have identical survival). – Alexis Apr 24 '18 at 19:25
• How did you deal with the censored observations when you traced the curves? Was there a separate table of numbers at risk at different times? Also, what hazard ratio, if any, did the authors report for the yellow versus blue curve? – EdM Apr 24 '18 at 20:00