# psm

##### Parametric Survival Model

`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.

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`

.

##### Usage

```
psm(formula=formula(data),
data=parent.frame(), 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, coefs=TRUE,
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"), …)

# 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"

##### Arguments

- formula
an S statistical model formula. Interactions up to third order are supported. The left hand side must be a

`Surv`

object.- object
a fit created by

`psm`

. For`survplot`

with residuals from`psm`

,`object`

is the result of`residuals.psm`

.- fit
a fit created by

`psm`

- data,subset,weights,dist,scale,init,na.action,control
see

`survreg`

.- parms
a list of fixed parameters. For the \(t\)-distribution this is the degrees of freedom; most of the distributions have no parameters.

- model
set to

`TRUE`

to include the model frame in the returned object- x
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`

.- y
set to

`TRUE`

to include the`Surv()`

matrix- time.inc
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 \(< 1\). Then max time/10 is used as`time.inc`

. If`time.inc`

is not given and max time/default`time.inc`

is \(> 25\),`time.inc`

is increased.- correlation
set to

`TRUE`

to print the correlation matrix for parameter estimates- digits
number of places to print to the right of the decimal point

- coefs
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.- title
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`

.- times
a scalar or vector of times for which to evaluate survival probability or hazard

- lp
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.- q
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
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.- n
number of points to evaluate theoretical standardized survival function for

`lines.residuals.psm.censored.normalized`

- lty
line type for

`lines`

, default is 1- xlim
range of times (or transformed times) for which to evaluate the standardized survival function. Default is range in normalized residuals.

- lwd
line width for theoretical distribution, default is 3

- g
number of quantile groups to use for stratifying continuous variables having more than 5 levels

- col
vector of colors for

`survplot`

method, corresponding to levels of`x`

(must be a scalar if there is no`x`

)- main
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`

.

##### Details

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.

##### Value

`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.

##### See Also

`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`

##### Examples

```
# NOT RUN {
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
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)
# }
```

*Documentation reproduced from package rms, version 5.1-3.1, License: GPL (>= 2)*