Learn R Programming

rms (version 4.1-3)

validate.cph: Validation of a Fitted Cox or Parametric Survival Model's Indexes of Fit

Description

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.

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, force=NULL, estimates=TRUE,
pr=FALSE, dxy=TRUE, 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, force=NULL, estimates=TRUE, pr=FALSE, dxy=TRUE, tol=1e-12, rel.tolerance=1e-5, maxiter=15, \dots)

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 mus
method
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
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
pr
TRUE to print results of each repetition
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
x
a numeric vector
y
a Surv object that may be uncensored or right-censored

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, $D_{xy}$ is automatically negated.

Side Effects

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

concept

  • model validation
  • predictive accuracy
  • bootstrap

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.

See Also

validate, predab.resample, fastbw, rms, rms.trans, calibrate, rcorr.cens, cph, survival-internal, gIndex, survConcordance

Examples

Run this code
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

Run the code above in your browser using DataLab