# st: Bootstrap and p-values

 From Giulio Rizzoli To statalist@hsphsun2.harvard.edu Subject st: Bootstrap and p-values Date Sat, 19 Sep 2009 17:17:27 +0200

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Dear all:
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Many medical variables are correlated, so I'm using the bootstrap program to verify the most
```frequently extracted variables within a backward and forward algorithm.
```
In the example below Nyha4 is by far the most extracted variable and therefore the most significant statistically. I usually publish tables of the selected variables with their confidence limits. I imagine that the bias corrected confidence limits provided by bootstrap are the most correct ones. Nonetheless until now I have always published the normal confidence limits, because the p-value can be easily controlled from reviewers, using the formula to calculate the variance under the normality assumption: (lnucl-lnlcl)/(2*1.96))^2 . // lnucl=log of upper C. L. lnlcl=log of lower C. L.
```
```
I would like to know there is a method to calculate the p_value starting from the BC confidence limits. Also it is not clear to me if the reported bias is a quantity that adds to the standard error or must be subtracted from the standard error in calculating the variance. The BC confidence limits are narrower. So i imagine that bias should be subtracted from standard error because bias relates to the part of measurement error that is casual.
```Am I correct?
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If it is so it is important to have a p-value for this estimate but the calculation with the usual zeta= _b/_se assumes a normality distribution. Is it valid in this setting ?
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It woul'd be wonderful if someone has a routine to calculate the different p-values starting from the ereturn list of the bootstrap saved values or could show how to calculate BC related p-values.
```
```
. bootstrap "sw, pr(.1) pe(.05): stcox fsex AOI sonoreint age nyha4 CPRENF CPRESPF CPIABP" _b,reps(1000) dots
```
```
command: sw , pr(.1) pe(.05) : stcox fsex AOI sonoreint age nyha4 CPRENF CPRESPF CPIABP
```statistics:   b_sesso    = _b[fsex]
b_age      = _b[age]
b_nyha4    = _b[nyha4]
................................................................................
>....
Bootstrap statistics                              Number of obs    =       327
Replications     =      1000
------------------------------------------------------------------------------
Variable     |  Reps  Observed      Bias  Std. Err. [95% Conf. Interval]
-------------+----------------------------------------------------------------
b_fsex  |   597 -.3829885 -.1357204   .138327  -.6546561  -.1113208   (N)
|                                      -.8652664  -.3303381   (P)
|                                      -.4775621  -.2981049  (BC)
|                                      -1.328869   .6971875  (BC)
b_age |   550  .0824691  .0245982  .0309384    .021697   .1432412   (N)
|                                       .0681392   .1776492   (P)
|                                      -.1053623   .1156664  (BC)
b_nyha4 |   845  1.043275  .2214171  .3910648   .2757012   1.810849   (N)
|                                        .652275   2.103901   (P)
|                                       .5398257   1.679764  (BC)
------------------------------------------------------------------------------
Note:  N   = normal
P   = percentile
```
BC = bias-corrected
```

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