| residuals.cph {Design} | R Documentation |
Calculates martingale, deviance, score or Schoenfeld residuals
(scaled or unscaled) or influence statistics for a
Cox proportional hazards model. This is a slightly modified version
of Therneau's residuals.coxph function. It assumes that x=TRUE and
y=TRUE were specified to cph, except for martingale residuals, which
are stored with the fit by default.
## S3 method for class 'cph':
residuals(object,
type=c("martingale", "deviance", "score", "schoenfeld",
"dfbeta", "dfbetas", "scaledsch"), collapse, weighted, ...)
object |
a cph object |
type |
character string indicating the type of residual desired;
the default is martingale.
Only enough of the string to determine a unique match is required.
Instead of the usual residuals, type="dfbeta" may be specified
to obtain approximate leave-out-one Delta βs. Use
type="dfbetas" to normalize the Delta βs for
the standard errors of the regression coefficient estimates.
Scaled Schoenfeld residuals (type="scaledsch", Grambsch and
Therneau, 1993) better
reflect the log hazard ratio function than ordinary Schoenfeld
residuals, and they are on the regression coefficient scale.
The weights use Grambsch and Therneau's "average variance" method.
|
collapse |
Vector indicating which rows to collapse(sum) over. In time-dependent
models more than one row data can pertain to a single individual.
If there were 4 individuals represented by 3, 1, 2 and 4 rows of data
respectively, then collapse=c(1,1,1, 2, 3,3, 4,4,4,4) could be used to
obtain per subject rather than per observation residuals.
|
weighted |
ignored; only accepts FALSE |
... |
unused |
The object returned will be a vector for martingale and deviance
residuals and matrices for score and schoenfeld residuals, dfbeta, or dfbetas.
There will
be one row of residuals for each row in the input data (without collapse).
One column of score and Schoenfeld
residuals will be returned for each column in the model.matrix.
The scaled Schoenfeld residuals are used in the cox.zph function.
The score residuals are each individual's contribution to the score
vector. Two transformations of this are often more useful: dfbeta is
the approximate change in the coefficient vector if that observation
were dropped, and dfbetas is the approximate change in the coefficients,
scaled by the standard error for the coefficients.
T. Therneau, P. Grambsch, and T.Fleming. "Martingale based residuals for survival models", Biometrika, March 1990.
P. Grambsch, T. Therneau. "Proportional hazards tests and diagnostics based on weighted residuals", unpublished manuscript, Feb 1993.
cph, coxph, residuals.coxph, cox.zph, naresid
# fit <- cph(Surv(start, stop, event) ~ (age + surgery)* transplant,
# data=jasa1)
# mresid <- resid(fit, collapse=jasa1$id)
# Get unadjusted relationships for several variables
# Pick one variable that's not missing too much, for fit
n <- 1000 # define sample size
set.seed(17) # so can reproduce the results
age <- rnorm(n, 50, 10)
blood.pressure <- rnorm(n, 120, 15)
cholesterol <- rnorm(n, 200, 25)
sex <- factor(sample(c('female','male'), n,TRUE))
cens <- 15*runif(n)
h <- .02*exp(.04*(age-50)+.8*(sex=='Female'))
d.time <- -log(runif(n))/h
death <- ifelse(d.time <= cens,1,0)
d.time <- pmin(d.time, cens)
f <- cph(Surv(d.time, death) ~ age + blood.pressure + cholesterol, iter.max=0)
res <- resid(f) # This re-inserts rows for NAs, unlike f$resid
yl <- quantile(res, c(10/length(res),1-10/length(res)), na.rm=TRUE)
# Scale all plots from 10th smallest to 10th largest residual
par(mfrow=c(2,2), oma=c(3,0,3,0))
p <- function(x) {
s <- !is.na(x+res)
plot(lowess(x[s], res[s], iter=0), xlab=label(x), ylab="Residual",
ylim=yl, type="l")
}
p(age); p(blood.pressure); p(cholesterol)
mtext("Smoothed Martingale Residuals", outer=TRUE)
# Assess PH by estimating log relative hazard over time
f <- cph(Surv(d.time,death) ~ age + sex + blood.pressure, x=TRUE, y=TRUE)
r <- resid(f, "scaledsch")
tt <- as.numeric(dimnames(r)[[1]])
par(mfrow=c(3,2))
for(i in 1:3) {
g <- areg.boot(I(r[,i]) ~ tt, B=20)
plot(g, boot=FALSE) # shows bootstrap CIs
} # Focus on 3 graphs on right
# Easier approach:
plot(cox.zph(f)) # invokes plot.cox.zph
par(mfrow=c(1,1))