From: <khosoda_at_med.kobe-u.ac.jp>

Date: Mon, 23 May 2011 00:56:47 +0900

C Index 0.8222785 0.7195828 0.9249742

Date: Mon, 23 May 2011 00:56:47 +0900

Thank you for your comment, Prof Harrell.

CstatisticCI <- function(x) # x is object of rcorr.cens.

se <- x["S.D."]/2 Low95 <- x["C Index"] - 1.96*se Upper95 <- x["C Index"] + 1.96*se cbind(x["C Index"], Low95, Upper95)}

> CstatisticCI(MyModel.lrm.penalized.rcorr)

Low95 Upper95

C Index 0.8222785 0.7195828 0.9249742

I obtained wider CI than the previous incorrect one. Regarding your comments on overfitting, this is a sample used in model development. However, I performed penalization by pentrace and lrm in rms package. The CI above is CI of penalized model. Results of validation of each model are followings;

First model

> validate(MyModel.lrm, bw=F, B=1000)

index.orig training test optimism index.corrected n Dxy 0.6385 0.6859 0.6198 0.0661 0.5724 1000 R2 0.3745 0.4222 0.3388 0.0834 0.2912 1000 Intercept 0.0000 0.0000 -0.1446 0.1446 -0.1446 1000 Slope 1.0000 1.0000 0.8266 0.1734 0.8266 1000 Emax 0.0000 0.0000 0.0688 0.0688 0.0688 1000 D 0.2784 0.3248 0.2474 0.0774 0.2010 1000 U -0.0192 -0.0192 0.0200 -0.0392 0.0200 1000 Q 0.2976 0.3440 0.2274 0.1166 0.1810 1000 B 0.1265 0.1180 0.1346 -0.0167 0.1431 1000 g 1.7010 2.0247 1.5763 0.4484 1.2526 1000 gp 0.2414 0.2512 0.2287 0.0225 0.2189 1000

penalized model

> validate(MyModel.lrm.penalized, bw=F, B=1000)

index.orig training test optimism index.corrected n Dxy 0.6446 0.6898 0.6256 0.0642 0.5804 1000 R2 0.3335 0.3691 0.3428 0.0264 0.3072 1000 Intercept 0.0000 0.0000 0.0752 -0.0752 0.0752 1000 Slope 1.0000 1.0000 1.0547 -0.0547 1.0547 1000 Emax 0.0000 0.0000 0.0249 0.0249 0.0249 1000 D 0.2718 0.2744 0.2507 0.0236 0.2481 1000 U -0.0192 -0.0192 -0.0027 -0.0165 -0.0027 1000 Q 0.2910 0.2936 0.2534 0.0402 0.2508 1000 B 0.1279 0.1192 0.1336 -0.0144 0.1423 1000 g 1.3942 1.5259 1.5799 -0.0540 1.4482 1000 gp 0.2141 0.2188 0.2298 -0.0110 0.2251 1000

Optimism of slope and intercept were improved from 0.1446 and 0.1734 to -0.0752 and -0.0547, respectively. Emax was improved from 0.0688 to 0.0249. Therefore, I thought overfitting was improved at least to some extent. Well, I'm not sure whether this is enough improvement though.

-- Kohkichi (11/05/22 23:27), Frank Harrell wrote:Received on Sun 22 May 2011 - 15:59:28 GMT

> S.D. is the standard deviation (standard error) of Dxy. It already includes

> the effective sample size in its computation so the sqrt(n) terms is not> needed. The help file for rcorr.cens has an example where the confidence> interval for C is computed. Note that you are making the strong assumption> that there is no overfitting in the model or that you are evaluating C on a> sample not used in model development.> Frank>>> Kohkichi wrote:>>>> Hi,>>>> I'm trying to calculate 95% confidence interval of C statistic of>> logistic regression model using rcorr.cens in rms package. I wrote a>> brief function for this purpose as the followings;>>>> CstatisticCI<- function(x) # x is object of rcorr.cens.>> {>> se<- x["S.D."]/sqrt(x["n"])>> Low95<- x["C Index"] - 1.96*se>> Upper95<- x["C Index"] + 1.96*se>> cbind(x["C Index"], Low95, Upper95)>> }>>>> Then,>>>>> MyModel.lrm.rcorr<- rcorr.cens(x=predict(MyModel.lrm), S=df$outcome)>>> MyModel.lrm.rcorr>> C Index Dxy S.D. n>> missing uncensored>> 0.8222785 0.6445570 0.1047916 104.0000000>> 0.0000000 104.0000000>> Relevant Pairs Concordant Uncertain>> 3950.0000000 3248.0000000 0.0000000>>>>> CstatisticCI(x5factor_final.lrm.pen.rcorr)>> Low95 Upper95>> C Index 0.8222785 0.8021382 0.8424188>>>> I'm not sure what "S.D." in object of rcorr.cens means. Is this standard>> deviation of "C Index" or standard deviation of "Dxy"?>> I thought it is standard deviation of "C Index". Therefore, I wrote the>> code above. Am I right?>>>> I would appreciate any help in advance.>>>> -->> Kohkichi Hosoda M.D.>>>> Department of Neurosurgery,>> Kobe University Graduate School of Medicine,>>>> ______________________________________________>> R-help_at_r-project.org mailing list>> https://stat.ethz.ch/mailman/listinfo/r-help>> PLEASE do read the posting guide>> http://www.R-project.org/posting-guide.html>> and provide commented, minimal, self-contained, reproducible code.>>>>> -----> Frank Harrell> Department of Biostatistics, Vanderbilt University> --> View this message in context: http://r.789695.n4.nabble.com/How-to-calculate-confidence-interval-of-C-statistic-by-rcorr-cens-tp3541709p3542163.html> Sent from the R help mailing list archive at Nabble.com.>> ______________________________________________> R-help_at_r-project.org mailing list> https://stat.ethz.ch/mailman/listinfo/r-help> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html> and provide commented, minimal, self-contained, reproducible code.

______________________________________________ R-help_at_r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.

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