| sscox {gss} | R Documentation |
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.
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)
formula |
Symbolic description of the model to be fit, where
the response is of the form |
type |
List specifying the type of spline for each variable.
See |
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
|
seed |
Seed to be used for the random generation of "knots."
Ignored when |
random |
Input for parametric random effects (frailty) in
nonparametric mixed-effect models. See |
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 |
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.
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.
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.
Chong Gu, chong@stat.purdue.edu
Gu, C. (2002), Smoothing Spline ANOVA Models. New York: Springer-Verlag.
## 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)