Uses bootstrapping or cross-validation to get bias-corrected (overfitting-
corrected) estimates of predicted vs. observed values based on
subsetting predictions into intervals (for survival models) or on
nonparametric smoothers (for other models). There are calibration
functions for Cox (cph), parametric survival models (psm),
binary and ordinal logistic models (lrm) and ordinary least
squares (ols). For survival models,
"predicted" means predicted survival probability at a single
time point, and "observed" refers to the corresponding Kaplan-Meier
survival estimate, stratifying on intervals of predicted survival, or,
if the polspline package is installed, the predicted survival
probability as a function of transformed predicted survival probability
using the flexible hazard regression approach (see the val.surv
function for details). For logistic and linear models, a nonparametric
calibration curve is estimated over a sequence of predicted values. The
fit must have specified x=TRUE, y=TRUE. The print and
plot methods for lrm and ols models (which use
calibrate.default) print the mean absolute error in predictions,
the mean squared error, and the 0.9 quantile of the absolute error.
Here, error refers to the difference between the predicted values and
the corresponding bias-corrected calibrated values.
Below, the second, third, and fourth invocations of calibrate
are, respectively, for ols and lrm, cph, and
psm. The first and second plot invocation are
respectively for lrm and ols fits or all other fits.
calibrate(fit, ...)
# S3 method for default
calibrate(fit, predy,
method=c("boot","crossvalidation",".632","randomization"),
B=40, bw=FALSE, rule=c("aic","p"),
type=c("residual","individual"),
sls=.05, aics=0, force=NULL, estimates=TRUE, pr=FALSE, kint,
smoother="lowess", digits=NULL, ...)
# S3 method for cph
calibrate(fit, cmethod=c('hare', 'KM'),
method="boot", u, m=150, pred, cuts, B=40,
bw=FALSE, rule="aic", type="residual", sls=0.05, aics=0, force=NULL,
estimates=TRUE,
pr=FALSE, what="observed-predicted", tol=1e-12, maxdim=5, ...)
# S3 method for psm
calibrate(fit, cmethod=c('hare', 'KM'),
method="boot", u, m=150, pred, cuts, B=40,
bw=FALSE,rule="aic",
type="residual", sls=.05, aics=0, force=NULL, estimates=TRUE,
pr=FALSE, what="observed-predicted", tol=1e-12, maxiter=15,
rel.tolerance=1e-5, maxdim=5, ...)# S3 method for calibrate
print(x, B=Inf, ...)
# S3 method for calibrate.default
print(x, B=Inf, ...)
# S3 method for calibrate
plot(x, xlab, ylab, subtitles=TRUE, conf.int=TRUE,
cex.subtitles=.75, riskdist=TRUE, add=FALSE,
scat1d.opts=list(nhistSpike=200), par.corrected=NULL, ...)
# S3 method for calibrate.default
plot(x, xlab, ylab, xlim, ylim,
legend=TRUE, subtitles=TRUE, cex.subtitles=.75, riskdist=TRUE,
scat1d.opts=list(nhistSpike=200), ...)
matrix specifying mean predicted survival in each interval, the
corresponding estimated bias-corrected Kaplan-Meier estimates,
number of subjects, and other statistics. For linear and logistic models,
the matrix instead has rows corresponding to the prediction points, and
the vector of predicted values being validated is returned as an attribute.
The returned object has class "calibrate" or
"calibrate.default".
plot.calibrate.default invisibly returns the vector of estimated
prediction errors corresponding to the dataset used to fit the model.
a fit from ols, lrm, cph or psm
an object created by calibrate
see validate.
For print.calibrate, B is an
upper limit on the number of resamples for which
information is printed about which variables were selected in each
model re-fit. Specify zero to suppress printing. Default is to print
all re-samples.
method for validating survival predictions using
right-censored data. The default is cmethod='hare' to use the
hare function in the polspline package. Specify
cmethod='KM' to use less precision stratified Kaplan-Meier
estimates. If the polspline package is not available, the
procedure reverts to cmethod='KM'.
the time point for which to validate predictions for survival
models. For cph fits, you must have specified surv=TRUE,
time.inc=u, where u is the constant specifying the time to
predict.
group predicted u-time units survival into intervals containing
m subjects on the average (for survival models only)
vector of predicted survival probabilities at which to evaluate the
calibration curve. By default, the low and high prediction values
from datadist are used, which for large sample size is the 10th
smallest to the 10th largest predicted probability.
actual cut points for predicted survival probabilities. You may
specify only one of m and cuts (for survival models only)
set to TRUE to print intermediate results for each re-sample
The default is "observed-predicted", meaning to estimate optimism
in this difference. This is preferred as it accounts for skewed
distributions of predicted probabilities in outer intervals. You can
also specify "observed". This argument applies to survival models only.
criterion for matrix singularity (default is 1e-12)
see hare
for psm, this is passed to
survreg.control (default is 15 iterations)
parameter passed to
survreg.control for psm (default is 1e-5).
a scalar or vector of predicted values to calibrate (for lrm,
ols). Default is 50 equally spaced points between the 5th
smallest and the 5th largest predicted values. For lrm the
predicted values are probabilities (see kint).
For an ordinal logistic model the default predicted
probability that \(Y\geq\) the middle level. Specify kint to specify the
intercept to use, e.g., kint=2 means to calibrate \(Prob(Y\geq
b)\), where \(b\) is the second level of \(Y\).
a function in two variables which produces \(x\)- and
\(y\)-coordinates by smoothing the input y. The default is to
use lowess(x, y, iter=0).
If specified, predicted values are rounded to
digits digits before passing to the smoother. Occasionally,
large predicted values on the logit scale will lead to predicted
probabilities very near 1 that should be treated as 1, and the
round function will fix that. Applies to calibrate.default.
other arguments to pass to predab.resample, such as group,
cluster, and subset.
Also, other arguments for plot.
defaults to "Predicted x-units Survival" or to a suitable label for other models
defaults to "Fraction Surviving x-units" or to a suitable label for other models
2-vectors specifying x- and y-axis limits, if not using defaults
set to FALSE to suppress subtitles in plot describing method and for lrm
and ols the mean absolute error and original sample size
set to FALSE to suppress plotting 0.95 confidence intervals for
Kaplan-Meier estimates
character size for plotting subtitles
set to FALSE to suppress the distribution of
predicted risks (survival probabilities) from being plotted
set to TRUE to add the calibration plot to an existing
plot
a list specifying options to send to scat1d if
riskdist=TRUE. See scat1d.
a list specifying graphics parameters col,
lty, lwd, pch to be used in drawing
overfitting-corrected estimates. Default is col="blue",
lty=1, lwd=1, pch=4.
set to FALSE to suppress legends (for lrm, ols
only) on the calibration plot, or specify a list with elements x
and y containing the coordinates of the upper left corner of the
legend. By default, a legend will be drawn in the lower right 1/16th of
the plot.
prints, and stores an object pred.obs or .orig.cal
Frank Harrell
Department of Biostatistics
Vanderbilt University
fh@fharrell.com
If the fit was created using penalized maximum likelihood estimation,
the same penalty and penalty.scale parameters are used during
validation.
set.seed(1)
n <- 200
d.time <- rexp(n)
x1 <- runif(n)
x2 <- factor(sample(c('a', 'b', 'c'), n, TRUE))
f <- cph(Surv(d.time) ~ pol(x1,2) * x2, x=TRUE, y=TRUE, surv=TRUE, time.inc=1.5)
#or f <- psm(S ~ \dots)
pa <- 'polspline' %in% row.names(installed.packages())
if(pa) {
cal <- calibrate(f, u=1.5, B=20) # cmethod='hare'
plot(cal)
}
cal <- calibrate(f, u=1.5, cmethod='KM', m=50, B=20) # usually B=200 or 300
plot(cal, add=pa)
set.seed(1)
y <- sample(0:2, n, TRUE)
x1 <- runif(n)
x2 <- runif(n)
x3 <- runif(n)
x4 <- runif(n)
f <- lrm(y ~ x1 + x2 + x3 * x4, x=TRUE, y=TRUE)
cal <- calibrate(f, kint=2, predy=seq(.2, .8, length=60),
group=y)
# group= does k-sample validation: make resamples have same
# numbers of subjects in each level of y as original sample
plot(cal)
#See the example for the validate function for a method of validating
#continuation ratio ordinal logistic models. You can do the same
#thing for calibrate
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