polspline (version 1.0.4)

hare: Hare: hazard regression

Description

Fit a hazard regression model: linear splines are used to model the baseline hazard, covariates, and interactions. Fitted models can be, but do not need to be, proportional hazards models.

Usage

hare(data, delta, cov, penalty, maxdim, exclude, include, prophaz = FALSE,
additive = FALSE, linear, fit, silent = TRUE)

Arguments

data

vector of observations. Observations may or may not be right censored. All observations should be nonnegative.

delta

binary vector with the same length as data. Elements of data for which the corresponding element of delta is 0 are assumed to be right censored, elements of data for which the corresponding element of

cov

covariates: matrix with as many rows as the length of data. May be omitted if there are no covariates. (If there are no covariates, however, heft will provide a more flexible model using cubic sp

penalty

the parameter to be used in the AIC criterion. The method chooses the number of knots that minimizes -2 * loglikelihood + penalty * (dimension). The default is to use penalty = log(samplesize) as in BIC. The effect of this par

maxdim

maximum dimension (default is $6*\mbox{length(data)}^0.2)$.

exclude

combinations to be excluded - this should be a matrix with 2 columns - if for example exclude[1, 1] = 2 and exclude[1, 2] = 3 no interaction between covariate 2 and 3 is included. 0 represents time.

include

those combinations that can be included. Should have the same format as exclude. Only one of exclude and include can be specified .

prophaz

should the model selection be restricted to proportional hazards models?

additive

should the model selection be restricted to additive models?

linear

vector indicating for which of the variables no knots should be entered. For example, if linear = c(2, 3) no knots for either covariate 2 or 3 are entered. 0 represents time. The default is none.

fit

hare object. If fit is specified, hare adds basis functions starting with those in fit.

silent

suppresses the printing of diagnostic output about basis functions added or deleted, Rao-statistics, Wald-statistics and log-likelihoods.

Value

• An object of class hare, which is organized to serve as input for plot.hare, summary.hare, dhare (conditional density), hhare (conditional hazard rate), phare (conditional probabilities), qhare (conditional quantiles), and rhare (random numbers). The object is a list with the following members:
• ncov
  number of covariates.
• ndim
  number of dimensions of the fitted model.
• fcts
  matrix of size ndim x 6. each row is a basis function. First element: first covariate involved (0 means time);

  second element: which knot (0 means: constant (time) or linear (covariate));

  third element: second covariate involved (NA means: this is a function of one variable);

  fourth element: knot involved (if the third element is NA, of no relevance);

  fifth element: beta;

  sixth element: standard error of beta.

• knots
  a matrix with ncov rows. Covariate i has row i+1, time has row 1. First column: number of knots in this dimension; other columns: the knots, appended with NAs to make it a matrix.
• penalty
  the parameter used in the AIC criterion.
• max
  maximum element of survival data.
• ranges
  column i gives the range of the i-th covariate.
• logl
  matrix with two columns. The i-th element of the first column is the loglikelihood of the model of dimension i. The second column indicates whether this model was fitted during the addition stage (1) or during the deletion stage (0).
• sample
  sample size.

References

Charles Kooperberg, Charles J. Stone and Young K. Truong (1995). Hazard regression. Journal of the American Statistical Association, 90, 78-94.

Charles J. Stone, Mark Hansen, Charles Kooperberg, and Young K. Truong. The use of polynomial splines and their tensor products in extended linear modeling (with discussion) (1997). Annals of Statistics, 25, 1371--1470.

See Also

heft, plot.hare, summary.hare, dhare, hhare, phare, qhare, rhare.

Examples

fit <- hare(testhare[,1], testhare[,2], testhare[,3:8])