I used boot function in R to do bootstrap for 40 times and used boot.ci to get the "normal" confidence interval. The following is my R code:<br>
**1. Define the statistic used in boot function**
``
uni_boot <-function(data,indices,vari){
  d = data[indices,] 
  unifit = coxph(as.formula(paste('Surv(time, status)~', vari))
                ,data = d)
  # return hazard ratio
  summary(unifit)$coef[2]
}
``
**2.Bootstrap**
``
r1 <- boot(data = data, statistic = uni_boot, R = 40,
            vari = variable)
r2 <- boot.ci(boot.out = r1, type = "norm")
``
**Then**, I examine the following things<br>
**Result of r1 object:**<br>
``
    original     bias    std. error
t1* 1.053145 0.03274176   0.1714448
``
**Result of r2 object**<br>
``
Intervals :
Level      Normal
95%   ( 0.684,  1.356 )
Calculations and Intervals on Original Scale
``
The bootstrap sample mean would be ``mean(r1$t)`` 1.085887 which is original plus the bias. However, when I examine the the formula used to calculate the bootstrap interval. It is ``original-bias-V^1/2*Z(1-alpha)`` or ``original-bias-V^1/2*Z(alpha)``.<br>
I followed the formula and did the calculation:<br>
``
1.053145-0.03274176+1.96*0.1714448 got me the upper bound 1.356
1.053145-0.03274176-1.96*0.1714448 got me the lower bound 0.684
``
My understanding of the confidence interval would be the bootstrap mean in the middle of the boot CI. However, the boot CI midpoint here turns to be 1.024. Sometimes, the boot CI from boot.ci wouldn't cover the bootstrap mean ``mean(r1$t)``.<br>
Anything I understand wrongly?