rms (version 5.1-2)

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.


# S3 method for cph
      type=c("martingale", "deviance", "score", "schoenfeld", 
             "dfbeta", "dfbetas", "scaledsch", "partial"), …)



a cph object


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 \(\Delta \beta\)s. Use type="dfbetas" to normalize the \(\Delta \beta\)s 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.


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 "Proportional hazards tests and diagnostics based on weighted residuals", unpublished manuscript, Feb 1993.

See Also

cph, coxph, residuals.coxph, cox.zph, naresid


Run this code
# 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]])
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
# }

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