# validate.cph

##### Validation of a Fitted Cox or Parametric Survival Model's Indexes of Fit

This is the version of the `validate`

function specific to models
fitted with `cph`

or `psm`

.

- Keywords
- models, regression, survival

##### Usage

```
# fit <- cph(formula=Surv(ftime,event) ~ terms, x=TRUE, y=TRUE, ...)
## S3 method for class 'cph':
validate(fit, method="boot", B=40, bw=FALSE, rule="aic", type="residual",
sls=.05, aics=0, pr=FALSE, dxy=FALSE, u, tol=1e-9, \dots)
```## S3 method for class 'psm':
validate(fit, method="boot",B=40,
bw=FALSE, rule="aic", type="residual", sls=.05, aics=0, pr=FALSE,
dxy=FALSE, tol=1e-12, rel.tolerance=1e-5, maxiter=15, \dots)

##### Arguments

- fit
- a fit derived
`cph`

. The options`x=TRUE`

and`y=TRUE`

must have been specified. If the model contains any stratification factors and dxy=TRUE, the options`surv=TRUE`

and`time.inc=u`

mus - method
- see
`validate`

- B
- number of repetitions. For
`method="crossvalidation"`

, is the number of groups of omitted observations. - rel.tolerance
- maxiter
- bw
`TRUE`

to do fast step-down using the`fastbw`

function, for both the overall model and for each repetition.`fastbw`

keeps parameters together that represent the same factor.- rule
- Applies if
`bw=TRUE`

.`"aic"`

to use Akaike's information criterion as a stopping rule (i.e., a factor is deleted if the $\chi^2$ falls below twice its degrees of freedom), or`"p"`

to use $P$-values. - type
`"residual"`

or`"individual"`

- stopping rule is for individual factors or for the residual $\chi^2$ for all variables deleted- sls
- significance level for a factor to be kept in a model, or for judging the residual $\chi^2$.
- aics
- cutoff on AIC when
`rule="aic"`

. - pr
`TRUE`

to print results of each repetition- tol
- ...
- see
`validate`

or`predab.resample`

- dxy
- set to
`TRUE`

to validate Somers' $D_{xy}$ using`rcorr.cens`

, which takes longer. - u
- must be specified if the model has any stratification factors and
`dxy=TRUE`

. In that case, strata are not included in $X\beta$ and the survival curves may cross. Predictions at time`t=u`

are correlated with observed su

##### Details

Statistics validated include the Nagelkerke $R^2$,
$D_{xy}$, slope shrinkage, the discrimination index $D$
[(model L.R. $\chi^2$ - 1)/L], the unreliability index
$U$ = (difference in -2 log likelihood between uncalibrated
$X\beta$ and
$X\beta$ with overall slope calibrated to test sample) / L,
and the overall quality index $Q = D - U$.
L is -2 log likelihood with beta=0. The "corrected" slope
can be thought of as shrinkage factor that takes into account overfitting.
See `predab.resample`

for the list of resampling methods.

##### Value

- matrix with rows corresponding to $D_{xy}$, Slope, $D$, $U$, and $Q$, and columns for the original index, resample estimates, indexes applied to whole or omitted sample using model derived from resample, average optimism, corrected index, and number of successful resamples. The values corresponting to the row $D_{xy}$ are equal to $2 * (C - 0.5)$ where C is the C-index or concordance probability. If the user is correlating the linear predictor (predicted log hazard) with survival time and she wishes to get the more usual correlation using predicted survival time or predicted survival probability, $D_{xy}$ should be negated.

##### Side Effects

prints a summary, and optionally statistics for each re-fit (if `pr=TRUE`

)

##### concept

- model validation
- predictive accuracy
- bootstrap

##### See Also

`validate`

, `predab.resample`

,
`fastbw`

, `rms`

, `rms.trans`

,
`calibrate`

, `rcorr.cens`

,
`cph`

, `coxph.fit`

##### Examples

```
n <- 1000
set.seed(731)
age <- 50 + 12*rnorm(n)
label(age) <- "Age"
sex <- factor(sample(c('Male','Female'), n, TRUE))
cens <- 15*runif(n)
h <- .02*exp(.04*(age-50)+.8*(sex=='Female'))
dt <- -log(runif(n))/h
e <- ifelse(dt <= cens,1,0)
dt <- pmin(dt, cens)
units(dt) <- "Year"
S <- Surv(dt,e)
f <- cph(S ~ age*sex, x=TRUE, y=TRUE)
# Validate full model fit
validate(f, B=10) # normally B=150
# Validate a model with stratification. Dxy is the only
# discrimination measure for such models, by Dxy requires
# one to choose a single time at which to predict S(t|X)
f <- cph(S ~ rcs(age)*strat(sex),
x=TRUE, y=TRUE, surv=TRUE, time.inc=2)
validate(f, dxy=TRUE, u=2, B=10) # normally B=150
# Note u=time.inc
```

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