psm is a modification of Therneau's survreg function for
fitting the accelerated failure time family of parametric survival
models. psm uses the rms class for automatic
anova, fastbw, calibrate, validate, and
other functions. Hazard.psm, Survival.psm,
Quantile.psm, and Mean.psm create S functions that
evaluate the hazard, survival, quantile, and mean (expected value)
functions analytically, as functions of time or probabilities and the
linear predictor values. The Nagelkerke R^2 and and adjusted
Maddala-Cox-Snell R^2 are computed. For the latter the notation is
R2(p,m) where p is the number of regression coefficients being
adjusted for and m is the effective sample size (number of uncensored
observations). See R2Measures for more information.
For the print method, format of output is controlled by the
user previously running options(prType="lang") where
lang is "plain" (the default), "latex", or
"html".
The residuals.psm function exists mainly to compute normalized
(standardized) residuals and to censor them (i.e., return them as
Surv objects) just as the original failure time variable was
censored. These residuals are useful for checking the underlying
distributional assumption (see the examples). To get these residuals,
the fit must have specified y=TRUE. A lines method for these
residuals automatically draws a curve with the assumed standardized
survival distribution. A survplot method runs the standardized
censored residuals through npsurv to get Kaplan-Meier estimates,
with optional stratification (automatically grouping a continuous
variable into quantiles) and then through survplot.npsurv to plot
them. Then lines is invoked to show the theoretical curve. Other
types of residuals are computed by residuals using
residuals.survreg.
psm(formula,
data=environment(formula), weights,
subset, na.action=na.delete, dist="weibull",
init=NULL, scale=0,
control=survreg.control(),
parms=NULL,
model=FALSE, x=FALSE, y=TRUE, time.inc, ...)# S3 method for psm
print(x, correlation=FALSE, digits=4, r2=c(0,2,4), coefs=TRUE,
pg=FALSE, title, ...)
Hazard(object, ...)
# S3 method for psm
Hazard(object, ...) # for psm fit
# E.g. lambda <- Hazard(fit)
Survival(object, ...)
# S3 method for psm
Survival(object, ...) # for psm
# E.g. survival <- Survival(fit)
# S3 method for psm
Quantile(object, ...) # for psm
# E.g. quantsurv <- Quantile(fit)
# S3 method for psm
Mean(object, ...) # for psm
# E.g. meant <- Mean(fit)
# lambda(times, lp) # get hazard function at t=times, xbeta=lp
# survival(times, lp) # survival function at t=times, lp
# quantsurv(q, lp) # quantiles of survival time
# meant(lp) # mean survival time
# S3 method for psm
residuals(object, type=c("censored.normalized",
"response", "deviance", "dfbeta",
"dfbetas", "working", "ldcase", "ldresp", "ldshape", "matrix", "score"), ...)
# S3 method for residuals.psm.censored.normalized
survplot(fit, x, g=4, col, main, ...)
# S3 method for residuals.psm.censored.normalized
lines(x, n=100, lty=1, xlim,
lwd=3, ...)
# for type="censored.normalized"
psm returns a fit object with all the information survreg would store as
well as what rms stores and units and time.inc.
Hazard, Survival, and Quantile return S-functions.
residuals.psm with type="censored.normalized" returns a
Surv object which has a special attribute "theoretical"
which is used by the lines
routine. This is the assumed standardized survival function as a function of time or transformed time.
an S statistical model formula. Interactions up to third order are
supported. The left hand side must be a Surv object.
a fit created by psm. For survplot with
residuals from psm, object is the result of
residuals.psm.
a fit created by psm
see survreg.
a list of fixed parameters. For the
set to TRUE to include the model frame in the returned object
set to TRUE to include the design matrix in the object produced
by psm. For the survplot method, x is an optional
stratification variable (character, numeric, or categorical). For
lines.residuals.psm.censored.normalized, x is the result
of residuals.psm. For print it is the result of psm.
set to TRUE to include the Surv() matrix
setting for default time spacing. Used in constructing time axis
in survplot, and also in make confidence bars. Default is 30
if time variable has units="Day", 1 otherwise, unless
maximum follow-up time time.inc.
If time.inc is not given and max time/default time.inc is
time.inc is increased.
set to TRUE to print the correlation matrix
for parameter estimates
number of places to print to the right of the decimal point
vector of integers specifying which R^2 measures to print,
with 0 for Nagelkerke R^2 and 1:4 corresponding to the 4 measures
computed by R2Measures. Default is to print
Nagelkerke (labeled R2) and second and fourth R2Measures
which are the measures adjusted for the number of predictors, first
for the raw sample size then for the effective sample size, which
here is the number of uncensored observations.
specify coefs=FALSE to suppress printing the table
of model coefficients, standard errors, etc. Specify coefs=n
to print only the first n regression coefficients in the
model.
set to TRUE to print g-indexes
a character string title to be passed to prModFit
other arguments to fitting routines, or to pass to survplot from
survplot.residuals.psm.censored.normalized. Passed to the
generic lines function for lines.
a scalar or vector of times for which to evaluate survival probability or hazard
a scalar or vector of linear predictor values at which to evaluate
survival probability or hazard. If both times and lp are
vectors, they must be of the same length.
a scalar or vector of probabilities. The default is .5, so just the
median survival time is returned. If q and lp are both vectors,
a matrix of quantiles is returned, with rows corresponding to lp
and columns to q.
type of residual desired. Default is censored normalized residuals,
defined as (link(Y) - linear.predictors)/scale parameter, where the
link function was usually the log function. See survreg for other
types. type="score" returns the score residual matrix.
number of points to evaluate theoretical standardized survival
function for
lines.residuals.psm.censored.normalized
line type for lines, default is 1
range of times (or transformed times) for which to evaluate the standardized survival function. Default is range in normalized residuals.
line width for theoretical distribution, default is 3
number of quantile groups to use for stratifying continuous variables having more than 5 levels
vector of colors for survplot method, corresponding to levels of x
(must be a scalar if there is no x)
main plot title for survplot. If omitted, is the name or label of
x if x is given. Use main="" to suppress a title when you
specify x.
Frank Harrell
Department of Biostatistics
Vanderbilt University
fh@fharrell.com
The object survreg.distributions contains definitions of properties
of the various survival distributions.
psm does not trap singularity errors due to the way survreg.fit
does matrix inversion. It will trap non-convergence (thus returning
fit$fail=TRUE) if you give the argument failure=2 inside the
control list which is passed to survreg.fit. For example, use
f <- psm(S ~ x, control=list(failure=2, maxiter=20)) to allow up to
20 iterations and to set f$fail=TRUE in case of non-convergence.
This is especially useful in simulation work.
rms, survreg,
residuals.survreg, survreg.object,
survreg.distributions,
pphsm, survplot, survest,
Surv,
na.delete,
na.detail.response, datadist,
latex.psm, GiniMd, prModFit,
ggplot.Predict, plot.Predict,
R2Measures
n <- 400
set.seed(1)
age <- rnorm(n, 50, 12)
sex <- factor(sample(c('Female','Male'),n,TRUE))
dd <- datadist(age,sex)
options(datadist='dd')
# Population hazard function:
h <- .02*exp(.06*(age-50)+.8*(sex=='Female'))
d.time <- -log(runif(n))/h
cens <- 15*runif(n)
death <- ifelse(d.time <= cens,1,0)
d.time <- pmin(d.time, cens)
f <- psm(Surv(d.time,death) ~ sex*pol(age,2),
dist='lognormal')
# Log-normal model is a bad fit for proportional hazards data
print(f, r2=0:4, pg=TRUE)
anova(f)
fastbw(f) # if deletes sex while keeping age*sex ignore the result
f <- update(f, x=TRUE,y=TRUE) # so can validate, compute certain resids
validate(f, B=10) # ordinarily use B=300 or more
plot(Predict(f, age, sex)) # needs datadist since no explicit age, hosp.
# Could have used ggplot(Predict(...))
survplot(f, age=c(20,60)) # needs datadist since hospital not set here
# latex(f)
S <- Survival(f)
plot(f$linear.predictors, S(6, f$linear.predictors),
xlab=expression(X*hat(beta)),
ylab=expression(S(6,X*hat(beta))))
# plots 6-month survival as a function of linear predictor (X*Beta hat)
times <- seq(0,24,by=.25)
plot(times, S(times,0), type='l') # plots survival curve at X*Beta hat=0
lam <- Hazard(f)
plot(times, lam(times,0), type='l') # similarly for hazard function
med <- Quantile(f) # new function defaults to computing median only
lp <- seq(-3, 5, by=.1)
plot(lp, med(lp=lp), ylab="Median Survival Time")
med(c(.25,.5), f$linear.predictors)
# prints matrix with 2 columns
# fit a model with no predictors
f <- psm(Surv(d.time,death) ~ 1, dist="weibull")
f
pphsm(f) # print proportional hazards form
g <- survest(f)
plot(g$time, g$surv, xlab='Time', type='l',
ylab=expression(S(t)))
f <- psm(Surv(d.time,death) ~ age,
dist="loglogistic", y=TRUE)
r <- resid(f, 'cens') # note abbreviation
survplot(npsurv(r ~ 1), conf='none')
# plot Kaplan-Meier estimate of
# survival function of standardized residuals
survplot(npsurv(r ~ cut2(age, g=2)), conf='none')
# both strata should be n(0,1)
lines(r) # add theoretical survival function
#More simply:
survplot(r, age, g=2)
options(datadist=NULL)
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