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.

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

number of repetitions. For method="crossvalidation", is the number of groups of omitted observations.

rel.tolerance

maxiter

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".

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.

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

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

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.

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, dxy=TRUE, u=2, B=10)   # normally B=150
# Note u=time.inc

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