Check Parallelism Assumption of Ordinal Semiparametric Models

For all the observations used a model fit, computes the estimated probability that Y is greater than each of a number of cutoffs, and compares this to smoothed estimated probabilities as a function of predicted probabilities, to obtain internal model calibration plots with multiple cutpoints. When Y is uncensored these are smoothed moving empirical cumulative distribution function estimates, and when Y has censored observations these are smoothing moving Kaplan-Meier estimates. Hmisc::movStats() is used to do the moving overlapping window calculations. When hare=TRUE, adaptive linear spline hazard regression estimates are also made, using polspline::hare(). When ordsurv=TRUE, adaptive ordinal regression estimates are made in addition.

Usage

intCalibration(
  fit,
  ycuts,
  m,
  x,
  onlydata = FALSE,
  eps = 25,
  bass = 9,
  tsmooth = "lowess",
  hare = TRUE,
  ordsurv = TRUE,
  dec = 4,
  xlab = bquote(hat(P)(.(yname) > y)),
  ylab = "Nonparametric Estimate",
  nrow = 1,
  ...
)

Arguments

fit: a fit object for which there is a survest() method, with x=TRUE, y=TRUE in effect
ycuts: a vector of cutpoints on Y
m: used when ycuts is not given. The lowest cutoff is chosen as the first Y value having at meast m uncensored observations to its left, and the highest cutoff is chosen so that there are at least m uncensored observations to the right of it. Cutoffs are equally spaced between these values in terms of number of uncensored observations. If omitted, m is set to the minimum of 50 and one quarter of the uncensored sample size.
x: a variable for which calibration-in-the-small is desired, instead of plotting predicted vs. observed probabilities. x will typically be chosen by virtue of being a strong predictor (such that lack of fit will matter more) but doesn't have to be in the model.
onlydata: set to TRUE to return a data frame suitable for plotting instead of actually plotting
eps, bass, tsmooth, hare, ordsurv: see Hmisc::movStats()
dec: number of digits to the right of the decimal place to which to round computed ycuts
xlab: x-axis label with default constructed from the Y-variable name in the model fit (y-axis label when x is specified)
ylab: y-axis label
nrow: if hare=TRUE or ordsurv=TRUE, the number of rows in the graph (must be 1 or 2)
...: other arguments passed to Hmisc::movStats(). To control the number of knots for ordsurv=TRUE specify k= here.

Value

ggplot2 object or a data frame

Details

These plots are plots of calibration-in-the-small. Alternate calibration-in-the-small plots may be obtained by specifying a predictor variable x against which to plot both predicted and observed probabilties as a function of x. This is the only place in the rms package where the "total effect" of a predictor is estimated instead of a partial effect. When x varies and moving overlapping windows of predicted and observed exceedance probabilities are estimated, if x is collinear with other predictors, they will "come along for the ride".

The function also prints information on calibration-in-the-large, i.e., the mean predicted probability of being beyond each cutpoint vs. the overall proportion of observations above that cutpoint. This is when x is not given.

Author

Frank Harrell

Examples

if (FALSE) { # \dontrun{
getHdata(nhgh)
f <- orm(gh ~ rcs(age, 4), data=nhgh, family='loglog', x=TRUE, y=TRUE)
intCalibration(f, ycuts=c(5, 5.5, 6, 6.5))
f <- update(f, family='cloglog')
intCalibration(f, ycuts=c(5, 5.5, 6, 6.5))
intCalibration(f, ycuts=c(5, 6, 7), x=nhgh$age)
} # }