R2-type Coefficients for Cox proportional hazards models

Usage

OXS(Surv.rsp, lp, lp0)

Nagelk(Surv.rsp, lp, lp0)

XO(Surv.rsp, lp, lp0)

Arguments

Surv.rsp: A Surv(.,.) object containing to the outcome of the test data.
lp: The vector of predictors.
lp0: The vector of predictors obtained from the covariate-free null model.

Value

The estimated R2 coefficient.

Details

The OXS, Nagelk and XO functions implement three types of R2 coefficients for right-censored time-to-event data: (a) The coefficient proposed by O'Quigley et al. (2005) (OXS), (b) the coefficient proposed by Nagelkerke (1991) (Nagelk) and (c) the coefficient proposed by Xu and O'Quigley (1999) (XO).

Because the OXS, Nagelk and XO functions assume that lp and lpnew were derived from a correctly specified Cox proportional hazards model, estimates obtained from these functions are only valid if the Cox model holds.

References

Nagelkerke, N. J. D. (1991).
A note on a general definition of the coefficient of determination.
Biometrika 78, 691–692.

O'Quigley, J., R. Xu, and J. Stare (2005).
Explained randomness in proportional hazards models.
Statistics in Medicine 24, 479–489.

Xu, R. and J. O'Quigley (1999).
A measure of dependence for proportional hazards models.
Journal of Nonparametric Statistics 12, 83–107.

Examples


data(cancer,package="survival")
TR <- ovarian[1:16,]
TE <- ovarian[17:26,]
train.fit  <- survival::coxph(survival::Surv(futime, fustat) ~ age,
                    x=TRUE, y=TRUE, method="breslow", data=TR)

model0 <- survival::coxph(survival::Surv(futime, fustat)~1, data=TR)
model1 <- survival::coxph(survival::Surv(futime, fustat)~age, data=TR)
f0 <- rep(0,nrow(TE))
f1 <- predict(model1, newdata=TE)               
Surv.res <- survival::Surv(TE$futime, TE$fustat)

OXS(Surv.res, f1, f0)
#> [1] 0.4973804
Nagelk(Surv.res, f1, f0)
#> [1] 0.2939943
XO(Surv.res, f1, f0)
#> [1] 0.329469