comparing bootstrapped confidence interval

[Kelvin Wan]

I want to test whether there are differences (i.e getting a p-value) between two means with known 95% bias corrected confidence interval (the mean and the CI are obtained after bootstrap resampling).

May I ask what test I should be using and the syntax ?

Many thanks.

[Carlo Lazzaro]

Kelvin:
probably the easiest way to do it is -bootstrap-ping the difference of the means you're interested in.
I would take a look at Example 3, -bbotstrap- entry, Stata .pdf manual.
The following article (unfortunately it is not free of charge) may be interesting: https://www.ncbi.nlm.nih.gov/pubmed/...3%A8+bootstrap

[Kelvin Wan]

Hi Carlo, thanks for your suggestion. Unfortunately this method does not work for my case.
Basically, I am calculating the area under the ROC curves (using a covariate adjusted method) for variable X and Y in their ability to detect a disease.
I have the values for the AUROC, the standard error of the AUROC and the 95% CI of the AUROC (see image) for both X and Y.
I am trying to test whether there are differences between the AUROC for X and Y.
I would appreciate any suggestions and comments. Thank you!

[Carlo Lazzaro]

Kelvin:
I do hope that what follows can help:

. use http://www.stata-press.com/data/r14/ct

. roccomp status mod1 mod2, graph summary

                              ROC                    -Asymptotic Normal--
                   Obs       Area     Std. Err.      [95% Conf. Interval]
-------------------------------------------------------------------------
mod1               112     0.8828       0.0317        0.82067     0.94498
mod2               112     0.9302       0.0256        0.88005     0.98042
-------------------------------------------------------------------------
Ho: area(mod1) = area(mod2)
    chi2(1) =     2.31       Prob>chi2 =   0.1282


 . bootstrap ((mod1)-(mod2)), reps(50) nodots: roccomp status mod1 mod2, summary


Bootstrap results                               Number of obs     =        112
                                                Replications      =         50

      command:  roccomp status mod1 mod2, summary
        _bs_1:  (mod1)-(mod2)

------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _bs_1 |          1   1.014386     0.99   0.324    -.9881606    2.988161
------------------------------------------------------------------------------


. estat bootstrap, all

Bootstrap results                               Number of obs     =        112
                                                Replications      =         50

      command:  roccomp status mod1 mod2, summary
        _bs_1:  (mod1)-(mod2)

------------------------------------------------------------------------------
             |    Observed               Bootstrap
             |       Coef.       Bias    Std. Err.  [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _bs_1 |           1       -.46   1.0143863   -.9881606   2.988161   (N)
             |                                             -1          3   (P)
             |                                              1          4  (BC)
------------------------------------------------------------------------------
(N)    normal confidence interval
(P)    percentile confidence interval
(BC)   bias-corrected confidence interval

.

[Kelvin Wan]

Hi Carlo, thanks for your detailed explanation. My situation is a bit more complicated and I cannot use the "roccomp" method because I need to adjust for different covariates in my ROC curves for variable X and Y. I am actually using the "roccreg" command to generate the ROC curves, which allows covariate adjustments.

Is there some way to test for differences between the two confidence interval of the ROC curves and get a p-value?

Thanks.

[Carlo Lazzaro]

Kelvin:
sorry I cannot be more helpful.