standscore {PHeval}

Standardized Score Process

Description

This function evaluates the standardized score process of OQuigley (2003). The process helps evaluating the goodness of fit of the proportional hazards model and visualizing the shape of time-dependent effects.

Usage

standscore(formula, data, globstan = TRUE, beta0 = 0)

Arguments

formula

A formula object or character string with the time and censoring status separated by "+" on the left hand side and the covariates separated by "+" on the right. For instance, if the time name is "Time", the censoring status is "Status" and the covariates are "Cov1" and "Cov2", the formula is "Time+Status~Cov1+Cov2".

data

A data.frame with the data. The censoring status should be 1 for failure and 0 for censoring. No missing data accepted.

globstan

With one covariate in the model, globstan has no effect. With several covariates,

• if globstan = TRUE (default) a global standardization by the matrix Sigma is applied to the process. Sigma is the estimator of the variance-covariance matrix between the covariates to the power of - 1 / 2. With this sandardization, each component of the process represents the cumulative regression effect of each covariates.

• if globstan = FALSE, no standardization is applied. In this case, the components of the process are dependent and do not reflect the shapes of the cumulative effects. The confidence bands are not given. The use of globstan = FALSE is aimed at performing tests of the value of the regression coefficients (null hypothesis : regression parameter = beta0).

beta0

a vector of parameters to evaluate the process (by default, parameters set to 0). Its length is the number of covariates. Each value corresponds to the regression coefficient for a covariate, in the same order as appearing in formula.

Details

The program does not handle ties in the data. We suggest to randomly split the ties before using the program.

Value

Score

A vector or matrix with the value of the standardized score process. Each row corresponds to a failure time, each column to a covariate.

Sigma

The matrix used for the standardization of the process. Sigma is the estimator of the variance-covariance matrix between the coviates to the power of - 1 / 2. This value is present only with multiple covariates and globstan = TRUE.

confbandCOV

A matrix with the confidence bands of the process for a constant regression effect associated with the covariate named COV. Each row corresponds to a failure time. The first column is the lower band and the second column is the upper band. This value is present with one covariate or with multiple covariates and globstan = TRUE.

Author(s)

Cecile Chauvel <[e-mail]>

References

Chauvel, C. and OQuigley, J. (2014) Tests for comparing estimated survival functions. Biometrika

101, 535-552. https://doi.org/10.1093/biomet/asu015

Chauvel, C. and OQuigley, J. (2017) Survival model construction guided by fit and predictive strength.

Biometrics 73, 483-494. https://doi.org/10.1111/biom.12611

OQuigley, J. (2008) Proportional hazards regression. Springer New-York. Chapter 8.

See Also

plotscore

Examples

library(survival)
data(ovarian)

#############################################
# Evaluation and plot of the standardized score process at parameter beta0 = 0

score1=standscore(futime+fustat~age+rx,data=ovarian)
plotscore(score1,printCB=TRUE)


#############################################
# Evaluation of the standardized score process at parameter
# beta0 = maximum partial likelihood estimator of beta

beta=coxph(Surv(futime,fustat)~age+rx,data=ovarian)$coeff
score2=standscore(futime+fustat~age+rx,data=ovarian,beta0=beta)

# Separated plots for each regression effect

par(mfrow=c(1,2))
plotscore(score2,printCB=TRUE,component.num=1,main="age")
plotscore(score2,printCB=TRUE,component.num=2,main="rx")

#############################################
# Evaluation and plot of the standardized score process at parameter beta0 = 0
# without global standardization 

fo="futime+fustat~age+rx"
score3=standscore(fo,data=ovarian,globstan=FALSE)
plotscore(score3)