sscox: Estimating Relative Risk Using Smoothing Splines

In gss: General Smoothing Splines

Estimating Relative Risk Using Smoothing Splines

Description

Estimate relative risk using smoothing spline ANOVA models. The symbolic model specification via formula follows the same rules as in lm, but with the response of a special form.

Usage

sscox(formula, type=NULL, data=list(), weights=NULL, subset,
      na.action=na.omit, partial=NULL, alpha=1.4, id.basis=NULL,
      nbasis=NULL, seed=NULL, random=NULL, prec=1e-7, maxiter=30,
      skip.iter=FALSE)

Arguments

formula	Symbolic description of the model to be fit, where the response is of the form Surv(futime,status,start=0).
type	List specifying the type of spline for each variable. See mkterm for details.
data	Optional data frame containing the variables in the model.
weights	Optional vector of counts for duplicated data.
subset	Optional vector specifying a subset of observations to be used in the fitting process.
na.action	Function which indicates what should happen when the data contain NAs.
partial	Optional symbolic description of parametric terms in partial spline models.
alpha	Parameter defining cross-validation score for smoothing parameter selection.
id.basis	Index of observations to be used as "knots."
nbasis	Number of "knots" to be used. Ignored when id.basis is specified.
seed	Seed to be used for the random generation of "knots." Ignored when id.basis is specified.
random	Input for parametric random effects (frailty) in nonparametric mixed-effect models. See mkran for details.
prec	Precision requirement for internal iterations.
maxiter	Maximum number of iterations allowed for internal iterations.
skip.iter	Flag indicating whether to use initial values of theta and skip theta iteration. See ssanova for notes on skipping theta iteration.

Details

A proportional hazard model is assumed, and the relative risk is estimated via penalized partial likelihood. The model specification via formula is for the log relative risk. For example, Suve(t,d)~u*v prescribes a model of the form

log f(u,v) = g_{u}(u) + g_{v}(v) + g_{u,v}(u,v)

with the terms denoted by "u", "v", and "u:v"; relative risk is defined only up to a multiplicative constant, so the constant term is not included in the model.

sscox takes standard right-censored lifetime data, with possible left-truncation and covariates; in Surv(futime,status,start=0)~..., futime is the follow-up time, status is the censoring indicator, and start is the optional left-truncation time.

Parallel to those in a ssanova object, the model terms are sums of unpenalized and penalized terms. Attached to every penalized term there is a smoothing parameter, and the model complexity is largely determined by the number of smoothing parameters.

The selection of smoothing parameters is through a cross-validation mechanism designed for density estimation under biased sampling, with a fudge factor alpha; alpha=1 is "unbiased" for the minimization of Kullback-Leibler loss but may yield severe undersmoothing, whereas larger alpha yields smoother estimates.

A subset of the observations are selected as "knots." Unless specified via id.basis or nbasis, the number of "knots" q is determined by max(30,10n^{2/9}), which is appropriate for the default cubic splines for numerical vectors.

Value

sscox returns a list object of class "sscox".

The method predict.sscox can be used to evaluate the fits at arbitrary points along with standard errors. The method project.sscox can be used to calculate the Kullback-Leibler projection for model selection.

Note

The function Surv(futime,status,start=0) is defined and parsed inside sscox, not quite the same as the one in the survival package. The estimation is invariant of monotone transformations of time.

The results may vary from run to run. For consistency, specify id.basis or set seed.

References

Gu, C. (2013), Smoothing Spline ANOVA Models (2nd Ed). New York: Springer-Verlag.

Gu, C. (2014), Smoothing Spline ANOVA Models: R Package gss. Journal of Statistical Software, 58(5), 1-25. URL http://www.jstatsoft.org/v58/i05/.

Examples

## Relative Risk
data(stan)
fit.rr <- sscox(Surv(futime,status)~age,data=stan)
est.rr <- predict(fit.rr,data.frame(age=c(35,40)),se=TRUE)
## Base Hazard
risk <- predict(fit.rr,stan)
fit.bh <- sshzd(Surv(futime,status)~futime,data=stan,offset=log(risk))
tt <- seq(0,max(stan$futime),length=51)
est.bh <- hzdcurve.sshzd(fit.bh,tt,se=TRUE)
## Clean up
## Not run: rm(stan,fit.rr,est.rr,risk,fit.bh,tt,est.bh)

gss documentation built on Aug. 16, 2023, 9:07 a.m.