# hare: Hare: hazard regression In polspline: Polynomial Spline Routines

 hare R Documentation

## 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 `delta` is 1 are assumed to be uncensored. If `delta` is missing, all observations are assumed to be uncensored. `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 splines.) `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 parameter is summarized in `summary.hare`. `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 `NA`s 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.

### Author(s)

Charles Kooperberg clk@fredhutch.org.

### 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.

`heft`, `plot.hare`, `summary.hare`, `dhare`, `hhare`, `phare`, `qhare`, `rhare`.
``````fit <- hare(testhare[,1], testhare[,2], testhare[,3:8])