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 optionsx=TRUE
andy=TRUE
must have been specified. If the model contains any stratification factors and dxy=TRUE, the optionssurv=TRUE
andtime.inc=u
must also have been given, whereu
is the same value ofu
given tovalidate
.- 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 thefastbw
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. Fordxy.cens
, specifytype="hazard"
ifx
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
orpredab.resample
- dxy
set to
TRUE
to validate Somers' \(D_{xy}\) usingdxy.cens
, which is fast until n > 500,000. Uses thesurvival
package'ssurvConcordance.fit
service function forsurvConcordance
.- 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 timet=u
are correlated with observed survival times. Does not apply tovalidate.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
# }