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calibrate

Resampling Model Calibration

Description

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.

Usage

calibrate(fit, ...)
## Default S3 method:
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 class '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 class '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 class 'calibrate'
print(x, B=Inf, ...)
## S3 method for class 'calibrate.default'
print(x, B=Inf, ...)

## S3 method for class '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 class 'calibrate.default'
plot(x, xlab, ylab, xlim, ylim,
  legend=TRUE, subtitles=TRUE, cex.subtitles=.75, riskdist=TRUE,
  scat1d.opts=list(nhistSpike=200), ...)

Arguments

fit

a fit from ols, lrm, cph or psm

x

an object created by calibrate
method, B, bw, rule, type, sls, aics, force, estimates

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.

cmethod

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'.

u

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.

m

group predicted u-time units survival into intervals containing m subjects on the average (for survival models only)

pred

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.
cuts

actual cut points for predicted survival probabilities. You may specify only one of m and cuts (for survival models only)

pr

set to TRUE to print intermediate results for each re-sample

what

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.

tol

criterion for matrix singularity (default is 1e-12)
maxdim

see hare
maxiter

for psm, this is passed to survreg.control (default is 15 iterations)

rel.tolerance

parameter passed to survreg.control for psm (default is 1e-5).

predy

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).

kint

For an ordinal logistic model the default predicted probability that Y≥q the middle level. Specify kint to specify the intercept to use, e.g., kint=2 means to calibrate Prob(Y≥q b), where b is the second level of Y.

smoother

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).

digits

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.

xlab

defaults to "Predicted x-units Survival" or to a suitable label for other models

ylab

defaults to "Fraction Surviving x-units" or to a suitable label for other models

xlim,ylim

2-vectors specifying x- and y-axis limits, if not using defaults
subtitles

set to FALSE to suppress subtitles in plot describing method and for lrm and ols the mean absolute error and original sample size

conf.int

set to FALSE to suppress plotting 0.95 confidence intervals for Kaplan-Meier estimates

cex.subtitles

character size for plotting subtitles
riskdist

set to FALSE to suppress the distribution of predicted risks (survival probabilities) from being plotted
add

set to TRUE to add the calibration plot to an existing plot
scat1d.opts

a list specifying options to send to scat1d if riskdist=TRUE. See scat1d.
par.corrected

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.
legend

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.

Details

If the fit was created using penalized maximum likelihood estimation, the same penalty and penalty.scale parameters are used during validation.

Value

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.

Side Effects

prints, and stores an object pred.obs or .orig.cal

Author(s)

Frank Harrell
Department of Biostatistics
Vanderbilt University
fh@fharrell.com

See Also

Examples

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
rms

Regression Modeling Strategies

v6.2-0
GPL (>= 2)
Authors
Frank E Harrell Jr <fh@fharrell.com>
Initial release
2021-03-17

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