Compute Royston's D for a Cox model

Description

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

Usage

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

Arguments

Details

We refer to these estimates of association as synthetic values, since they involve only the linear predictor, and not the outcome. They exploit mathematical associations which hold for certain models, e.g. between R-squared and a certain chiquare test of association in the linear model, and assume that the same holds in a Cox model where said test is readily available but not a simple R-square computation.

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 (Since superseded in the default printout by the concordance.)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.

Value

a vector containing the value of D, the estimated standard error of D, and three or four synthetic values.

References

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.

Examples

# 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")
royston(cfit)