# residuals.cph

##### Residuals for a cph Fit

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.

- Keywords
- survival

##### Usage

```
## S3 method for class 'cph':
residuals(object,
type=c("martingale", "deviance", "score", "schoenfeld",
"dfbeta", "dfbetas", "scaledsch", "partial"), ...)
```

##### Arguments

- 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 - ...
- see
`residuals.coxph`

##### Value

- 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.

##### concept

model validation

##### References

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 "Proportional hazards tests and diagnostics based on weighted residuals", unpublished manuscript, Feb 1993.

##### See Also

##### Examples

```
# 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))
```

*Documentation reproduced from package rms, version 2.0-2, License: GPL (>= 2)*