polspline: heft – R documentation

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heft

Heft: hazard estimation with flexible tails

Description

Hazard estimation using cubic splines to approximate the log-hazard function and special functions to allow non-polynomial shapes in both tails.

Usage

heft(data, delta, penalty, knots, leftlin, shift, leftlog,
rightlog, maxknots, mindist, 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.
`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.heft`.
`knots`	ordered vector of values, which forces the method to start with these knots. If `knots` is not specified, a default knot-placement rule is employed.
`leftlin`	if `leftlin` is `TRUE` an extra basis-function, which is linear to the left of the first knot, is included in the basis. If any of `data` is exactly 0, the default of `leftlin` is `TRUE`, otherwise it is `FALSE`.
`shift`	parameter for the log terms. Default is `quantile(data[delta == 1], .75)`.
`leftlog`	coefficient of \code{log(x/(x+shift))}, which must be greater than `-1`. (In particular, if `leftlog` equals zero no \code{log(x/(x+shift))} term is included.) If `leftlog` is missing its maximum likelihood estimate is used. If any of `data` is exactly zero, `leftlog` is set to zero.
`rightlog`	coefficient of \code{log(x+shift)}, which must be greater than `-1`. (In particular, if `leftlog` equals zero no \code{log(x+shift)} term is included.) If `rightlog` is missing its maximum likelihood estimate is used.
`maxknots`	maximum number of knots allowed in the model (default is \code{4 n^0.2}*, where n is the length of `data`.
`mindist`	minimum distance in order statistics between knots. The default is 5.
`silent`	suppresses the printing of diagnostic output about knots added or deleted, Rao-statistics, Wald-statistics and log-likelihoods.

Value

An object of class heft, which is organized to serve as input for plot.heft, summary.heft, dheft (density), hheft (hazard rate), pheft (probabilities), qheft (quantiles), and rheft (random numbers). The object is a list with the following members:

`knots`	vector of the locations of the knots in the `heft` model.
`logl`	the `k`-th element is the log-likelihood of the fit with `k` knots.
`thetak`	coefficients of the knot part of the spline. The k-th coefficient is the coefficient of (x-t(k))^3_+. If a coefficient is zero the corresponding knot was considered and then deleted from the model.
`thetap`	coefficients of the polynomial part of the spline. The first element is the constant term and the second element is the linear term.
`thetal`	coefficients of the logarithmic terms. The first element equals `leftlog` and the second element equals `rightlog`.
`penalty`	the penalty that was used.
`shift`	parameter used in the definition of the log terms.
`sample`	the sample size.
`logse`	the standard errors of `thetal`.
`max`	the largest element of data.
`ad`	vector indicating whether a model of this dimension was not fit (2), fit during the addition stage (0) or during the deletion stage (1).

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.

Examples

fit1 <- heft(testhare[,1], testhare[,2])
# modify tail behavior
fit2 <- heft(testhare[,1], testhare[,2], leftlog = FALSE, rightlog = FALSE, 
          leftlin = TRUE)   
fit3 <- heft(testhare[,1], testhare[,2], penalty = 0)   # select largest model

polspline

Polynomial Spline Routines

v1.1.19

GPL (>= 2)

Authors

Charles Kooperberg [aut, cre], Cleve Moler [ctb] (LINPACK routines in src), Jack Dongarra [ctb] (LINPACK routines in src)

Initial release

2020-05-15