royston {survival}R Documentation

Compute Royston's D for a Cox model


Compute the D statistic proposed by Royston and Sauerbrei along with several pseudo- R square values.


royston(fit, newdata, ties = TRUE, adjust = FALSE)



a coxph fit


optional validation data set


make a correction for ties in the risk score


adjust for possible overfitting


These values are called pseudo R-squared since they involve only the linear predictor, and not the outcome. R.D is the value that corresponsds the Royston and Sauerbrei D statistic. R.KO is the value proposed by Kent and O'Quigley, R.N is the value proposed by Nagelkerke, and C.GH corresponds to Goen and Heller's concordance measure.

An adjustment for D is based on the ratio r= (number of events)/(number of coefficients). For models which have sufficient sample size (r>20) the adjustment will be small.

The Nagelkerke value is the Cox-Snell R-squared divided by a scaling constant. The two separate values are present in the result of summary.coxph as a 2 element vector rsq, and were listed as "Rsquare" and "max possible" in older versions of the print routine. (Since superseded in the default printout by the concordance.) The Nagelkerke estimate is not returned when newdata is present.


a vector containing the value of D, the estimated standard error of D, and three or four pseudo R-squared values.


M. Goen and G. Heller, Concordance probability and discriminatory power in proportional hazards regression. Biometrika 92:965-970, 2005.

N. Nagelkerke, J. Oosting, J. and A. Hart, A simple test for goodness of fit of Cox's proportional hazards model. Biometrics 40:483-486, 1984.

P. Royston and W. Sauerbrei, A new measure of prognostic separation in survival data. Statistics in Medicine 23:723-748, 2004.


# An example used in Royston and Sauerbrei
pbc2 <- na.omit(pbc)  # no missing values
cfit <- coxph(Surv(time, status==2) ~ age + log(bili) + edema + albumin +
                   stage + copper, data=pbc2, ties="breslow")

[Package survival version 3.6-4 Index]