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.

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

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.

- 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.

Charles Kooperberg clk@fredhutch.org.

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])
```

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