How to calculate the “optimism-corrected" or biased-corrected c-statistic (or Sommer's D) for a Cox regression model after bootstrapping

[Cristina Ardura]

Hello,

I have obtained a Cox-regression model of the risk of suffering an acute asthma attack, and I want to assess it's internal validity. I have estimated the c-statistic of this model, as it is a measure of the predictive ability of this model. I would now like to estimate the 'over-fitting' or optimism of my model to be able to calibrate it accordingly. The amount of shrinkage to calibrate for can be determined by comparing the model’s c statistic (called the apparent c statistic) to the c statistic computed by nonparametric bootstrap resampling (which I will call the honest c statistic or optimism-corrected c-statistic.

I have tried several different commands, but all I obtain is a biased-corrected confidence interval for the 'apparent c statistic' and a 'bias' estimate. My question is: Should I just add this 'bias' to the 'apparent c statistic' to obtain the 'optimism-corrected c statistic'? If not, how can I estimate it?

This is what I have tried: My model includes 3 variables: age (Edad) Asthma dx (asma) and number of corticosteroids courses (Vecescorticoidesivim)

*Step 1
stcox Edad Asma Vecescorticoidesivim
estat concordance

return list

matrix concordance = ( r(N), r(D), r(C), r(n_P), r(n_E), r(n_T))
matrix list concordance

*Step 2
capture program drop myboot2
program define myboot2, rclass
preserve
bsample
stcox Edad Asma Vecescorticoidesivim
estat concordance
return scalar N = r(N)
return scalar D = r(D)
return scalar C = r(C)
return scalar n_P = r(n_P)
return scalar n_E = r(n_E)
return scalar n_T = r(n_T)
restore
end

*Step 3
simulate N=r(N) D=r(D) C=r(C) n_P=r(n_P) n_E=r(n_E) n_T=r(n_T), ///
reps(200) seed(12345): myboot2

bstat, stat(concordance) n(100)

estat bootstrap, all


And this is the result:

	Observed coefficient	Bias	Bootstrsp Std. Err.	95% Conf Interval	Type
D	0.29717226	0.007564	0.04701595	0.205-0.389	N
				0.216-0.392	P
				0.211-0.381	BC
C	0.64858613	0.003782	0.02350797	0.603-0.695	N
				0.608-0.696	P
				0.605-0.691	BC

The only interesting values are the 'C' (Harrel's C or c-statistic) and the D (Sommer's D).


Thank you!