Function Generators For Exceedance and Survival Probabilities

For an orm object ExProb generates a function for computing the estimates of the function Prob(Y>=y) given one or more values of the linear predictor using the reference (median) intercept. This function can optionally be evaluated at only a set of user-specified y values, otherwise a right-step function is returned. There is a plot method for plotting the step functions, and if more than one linear predictor was evaluated multiple step functions are drawn. ExProb is especially useful for nomogram. Survival generates a similar function but for computing survival probabilities Prob(Y>y) and adding an origin of zero. Plotting of survival curves is done with a survplot method. For survival estimation when interval censoring is present, times are taken as interval midpoints with intervals corresponding to intercepts in the model.

Optionally a normal approximation (normality for the linear predictor) for a confidence interval for exceedance probabilities will be computed, if conf.int > 0 is specified to the function generated from calling ExProb or Survival. For ExProb, a "lims" attribute is included in the result computed by the derived cumulative probability function. For Survival, the result is a data frame if conf.int is specified or both time and the requested linear predictor are varying. In the data frame the limits are variables lower and upper.

Usage

ExProb(object, ...)

# S3 method for class 'orm'
ExProb(object, codes = FALSE, ...)

# S3 method for class 'ExProb'
plot(x, ..., data=NULL,
                      xlim=NULL, xlab=x$yname, ylab=expression(Prob(Y>=y)),
                      col=par('col'), col.vert='gray85', pch=20,
                      pch.data=21, lwd=par('lwd'), lwd.data=lwd,
                      lty.data=2, key=TRUE)

# S3 method for class 'orm'
Survival(object, ...)

Arguments

object

a fit object from orm. For Survival the fit may be from orm.fit. This is used to estimate survival curves when there are no predictors in the model. In the case the link function (family argument to orm.fit) does not affect survival probabilities but does affect confidence limits. To get the same confidence intervals as survival:survfit.formula use ormfit(y=, family='loglog') to correspond to survfit(..., conf.type='log-log').

codes

if TRUE, ExProb use the integer codes \(1,2,\ldots,k\) for the \(k\)-level response instead of its original unique values

...

ignored for ExProb. Passed to plot for plot.ExProb

data

Specify data if you want to add stratified empirical probabilities to the graph. If data is a numeric vector, it is assumed that no groups are present. Otherwise data must be a list or data frame where the first variable is the grouping variable (corresponding to what made the linear predictor vary) and the second variable is the data vector for the y variable. The rows of data should be sorted to be in order of the linear predictor argument.

x

an object created by running the function created by ExProb

xlim

limits for x-axis; default is range of observed y

xlab

x-axis label

ylab

y-axis label

col

color for horizontal lines and points

col.vert

color for vertical discontinuities

pch

plotting symbol for predicted curves

lwd

line width for predicted curves

pch.data,lwd.data,lty.data

plotting parameters for data

key

set to FALSE to suppress key in plot if data is given

Value

ExProb and Survival return an R function. Running the function returns an object of class "ExProb" for ExProb, or a data frame or vector for Survival.

Author

Frank Harrell and Shengxin Tu

See also

orm, Quantile.orm

Examples