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My application is a Cox model with n=685 and one continuous predictor

mod <- coxph(srv ~ predi)

summary(mod) gives a p-value for the coefficient of about $10^{-6}$

anova(mod) gives a p-value of $>10^{-4}$

I can reproduce these p-values using the Anova function in the car package:

library(car)
Anova(mod, test.statistic="Wald")
Anova(mod, test.statistic="LR")

What are possible explanations for this discrepancy? Should I prefer the LR p-value? Neither predi nor the bootstrapped distribution of its Hazard Ratio look normally distributed. Could that be the problem?

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    $\begingroup$ I don't know the exact answer, but I do know that estimating very small p is tricky. This is yet another reason to emphasize effect size rather than p value. $\endgroup$
    – Peter Flom
    Dec 3, 2012 at 14:35

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