# What does the p value mean for Cox hazard ratio? [duplicate]

I am puzzled about the interpretation of P value in the Cox hazard ratio analysis. I read from literature that the P value is to "reject the null hypothesis that HR=1". However, in many cases, we have tested multiple variables in the cox analysis, and therefore have multiple P values. For example

X = cbind(lcx,lvef)
call:
coxph(formula = Surv(time_to_therapy, therapy) ~ X)

n= 174, number of events= 54

coef exp(coef)  se(coef)      z Pr(>|z|)
Xlcx   1.218259  3.381297  0.324619  3.753 0.000175 ***
Xlvef -0.004575  0.995436  0.016626 -0.275 0.783187
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

exp(coef) exp(-coef) lower .95 upper .95
Xlcx     3.3813     0.2957    1.7896     6.389
Xlvef    0.9954     1.0046    0.9635     1.028


Here X is a 2-column variable with first column a binary vector named lcx, and the second column a continuous vector named lvef.

How can I interpret the two p values (0.000175 and 0.783187)? In my idea, it should be related to the predictive value of two variables (lcx and lvef)?

• What is Xlvef? I don't see it in the call for the model fit. FWIW, p-values here mean the same as p-values anywhere. – gung - Reinstate Monica Mar 21 '16 at 15:48
• So here I have two p values, I assume they should link to the two variables in the Cox model? – alize Mar 21 '16 at 16:04
• This is as for any multiple regression, one p-value per predictor variable in the part of the coxph output that you show. The associated hazard ratios (exp(coef)) are probably more informative. There should also be several p-values for the overall model fit (based on likelihood-ratio, Wald, and logrank tests) somewhere in the output; those should always be examined before interpreting p-values for individual predictors. – EdM Mar 21 '16 at 16:20
• @gung, I'm not sure that's the best duplicate. The p-values qua p-values are the same as always, but coxph returns $p+3$ of them and it's potentially worth explaining the differences between the hypotheses that each of them purports to test. – Matt Krause Mar 21 '16 at 17:22
• @gung I think the OP may be familiar with testing, but the question concerns interpretation of the hazard ratio, therefore may be a duplicate of a different question. – AdamO Mar 21 '16 at 17:57

Just the same, the $p$-value from LVEF comes from the test of relative risk for groups differing by one unit in LVEF having the same LCX.