R: Validation of a Fitted Cox or Parametric Survival Model's...

validate.cph {rms} | R Documentation

## 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 Dxy and its standard error from the `survival` package's `survConcordance.fit` function. This allows for incredibly fast computation of Dxy or the c-index even for hundreds of thousands of observations. `dxy.cens` negates Dxy 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 Dxy is negated.

### Usage

    # fit <- cph(formula=Surv(ftime,event) ~ terms, x=TRUE, y=TRUE, \dots)
    ## 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, ...)

    ## 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, ...)

    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-square 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-square 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-square.
`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' Dxy 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, Dxy, slope shrinkage, the discrimination index D [(model L.R. chi-square - 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 Dxy, 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 Dxy 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, Dxy is automatically negated.

### Side Effects

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

### Author(s)

Frank Harrell
Department of Biostatistics, Vanderbilt University
f.harrell@vanderbilt.edu

### See Also

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

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

[Package rms version 5.1-1 Index]