# 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`

. Also included is a small
function `dxy.cens`

that retrieves \(D_{xy}\) and its
standard error from the `survival`

package's
`survConcordance.fit`

function. This allows for incredibly fast
computation of \(D_{xy}\) or the c-index even for hundreds of
thousands of observations. `dxy.cens`

negates \(D_{xy}\)
if log relative hazard is being predicted. If `y`

is a
left-censored `Surv`

object, times are negated and a
right-censored object is created, then \(D_{xy}\) is negated.

- Keywords
- models, regression, survival

##### Usage

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

dxy.cens(x, y, type=c('time','hazard'))

##### 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`

must also have been given, where`u`

is the same value of`u`

given to`validate`

.- 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. For`dxy.cens`

, specify`type="hazard"`

if`x`

is on the hazard or cumulative hazard (or their logs) scale, causing negation of the correlation index.- 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"`

.- force
see

`fastbw`

- estimates
see

`print.fastbw`

- pr
`TRUE`

to print results of each repetition- tol,…
see

`validate`

or`predab.resample`

- dxy
set to

`TRUE`

to validate Somers' \(D_{xy}\) using`dxy.cens`

, which is fast until n > 500,000. Uses the`survival`

package's`survConcordance.fit`

service function for`survConcordance`

.- 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 survival times. Does not apply to`validate.psm`

.- x
a numeric vector

- y
a

`Surv`

object that may be uncensored or right-censored

##### 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 \(Q = D - U\). \(g\) is the
\(g\)-index on the log relative hazard (linear predictor) scale.
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 corresponding 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, \(D_{xy}\) is automatically negated.

##### Side Effects

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

)

##### See Also

`validate`

, `predab.resample`

,
`fastbw`

, `rms`

, `rms.trans`

,
`calibrate`

, `rcorr.cens`

,
`cph`

, `survival-internal`

,
`gIndex`

, `survConcordance`

##### Examples

```
# NOT RUN {
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, u=2, B=10) # normally B=150
# Note u=time.inc
# }
```

*Documentation reproduced from package rms, version 5.1-4, License: GPL (>= 2)*