Coxph model Pvalue Select

 

I am calculating cox propotional hazards models with the coxph 
function from the survival package.  My data relates to failure of 
various types of endovascular interventions.  I can successfully 
obtain the LR, Wald, and Score test p-values from the coxph.object, as 
well as the hazard ratio as follows: 

formula.obj = Surv(days, status) ~ type 
coxph.model = coxph(formula.obj, df) 
fit = summary(coxph.model) 
hazard.ratio = fit$conf.int[1] 
lower95 = fit$conf.int[3] 
upper95 = fit$conf.int[4] 
logrank.p.value = fit$sctest[3]  （Score (logrank) test）

wald.p.value = fit$waldtest[3]  （Wald test）

lr.p.value = fit$logtest[3]    ----    Likelihood ratio test (优先）

I had intended to report logrank P values with the hazard ratio and CI 
obtained from this function.  In one case the P was 0.04 yet the CI 
crossed one, which confused me, and certainly will raise questions by 
reviewers.  In retrospect I can see that the CI calculated by coxph is 
intimately related to the Wald p-value (which in this specific case 
was 0.06), so this would appear to me not a good strategy for 
reporting my results (mixing the logrank test with the HR and CIs from 
coxph). 

I can report the Wald p-values instead, but I have read that the Wald 
test is inferior to the score test or LR test.  My questions for 
survival analysis jockeys out there / TT: 

1. Should I just stop here and use the wald.p.value?  This appears to 
be what Stata does with the stcox function (albeit Breslow method). 

2. Should I calculate HR and CIs that "agree" with the LR or logrank 
P?  How do I do that? 

Thank you,