[R] upperbound of C index Conf.int. greater than 1

[Frank E Harrell Jr]

DAVID ARTETA GARCIA wrote:
> R-users,
> 
> I am bootstrapping the C Index of a model created using lrm{Design} and 
> boot{boot}, and I get that the upperbound of the confidence interval is 
> greater than 1. Here is my code:
> 
>> library(HSAUR)
>> data(plasma)
> 
> ##fit model
>> fit.design <- lrm (ESR ~ fibrinogen + globulin,data=plasma)
>> fit.design$stats[6]
>         C
> 0.8044872
> 
> 
> ##bootstrap C Index
> 
>> cindex <- function(formula,data,indices){
> + d=data[indices,]
> + fit<-lrm(formula,data = d)
> + return(fit$stats[[6]])
> + }
> 
>> results <- boot(data=w,statistic=cindex,R=500,formula = ESR ~ 
>> fibrinogen + globulin)
>> results
> 
> ORDINARY NONPARAMETRIC BOOTSTRAP
> 
> 
> Call:
> boot(data = plasma, statistic = cindex, R = 500, formula = ESR ~ 
> fibrinogen +
>     globulin)
> 
> 
> Bootstrap Statistics :
>      original      bias    std. error
> t1* 0.8044872 0.008834767   0.1574710
>> boot.ci(results,type="basic")
> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
> Based on 500 bootstrap replicates
> 
> CALL :
> boot.ci(boot.out = results, type = "basic")
> 
> Intervals :
> Level      Basic
> 95%   ( 0.6090,  1.1443 )
> Calculations and Intervals on Original Scale
> 
> 
> I see that the std.error is rather large and this might be the problem, 
> but how can I explain this for publication purposes? Is such an interval 
> acceptable?
> Any help would be greatly appreciated
> 
> David

A few observations.

1. With minimal overfitting, rcorr.cens(predict(fit), Y) gives a good 
standard error for Dxy = 2*(C-.5) and bootstrapping isn't very necessary

2. If you bootstrap use the nonparametric bootstrap percentile method or 
  other methods that constrain the confidence interval to be in [0,1].

3. I don't know why the model would be linear on the two predictors you 
are using.

Frank

-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University