survPenObject: Fitted survPen object

In survPen: Multidimensional Penalized Splines for Survival and Net Survival Models

Fitted survPen object

Description

A fitted survPen object returned by function survPen and of class "survPen". Method functions predict and summary are available for this class.

Value

A survPen object has the following elements:

call	original survPen call
formula	formula object specifying the model
t0.name	name of the vector of origin times
t1.name	name of the vector of follow-up times
event.name	name of the vector of right-censoring indicators
expected.name	name of the vector of expected hazard
haz	fitted hazard
coefficients	estimated regression parameters. Unpenalized parameters are first, followed by the penalized ones
type	"net" for net survival estimation with penalized excess hazard model or "overall" for overall survival with penalized hazard model
df.para	degrees of freedom associated with fully parametric terms (unpenalized)
df.smooth	degrees of freedom associated with penalized terms
p	number of regression parameters
edf	effective degrees of freedom
edf1	alternative effective degrees of freedom ; used as an upper bound for edf2
edf2	effective degrees of freedom corrected for smoothing parameter uncertainty
aic	Akaike information criterion with number of parameters replaced by edf when there are penalized terms. Corresponds to 2*edf - 2*ll.unpen
aic2	Akaike information criterion corrected for smoothing parameter uncertainty. Be careful though, this is still a work in progress, especially when one of the smoothing parameters tends to infinity.
iter.beta	vector of numbers of iterations needed to estimate the regression parameters for each smoothing parameters trial. It thus contains iter.rho+1 elements.
X	design matrix of the model
S	penalty matrix of the model
S.scale	vector of rescaling factors for the penalty matrices
S.list	Equivalent to pen but with every element multiplied by its associated smoothing parameter
S.smf	List of penalty matrices associated with all "smf" calls
S.tensor	List of penalty matrices associated with all "tensor" calls
S.tint	List of penalty matrices associated with all "tint" calls
S.rd	List of penalty matrices associated with all "rd" calls
smooth.name.smf	List of names for the "smf" calls associated with S.smf
smooth.name.tensor	List of names for the "tensor" calls associated with S.tensor
smooth.name.tint	List of names for the "tint" calls associated with S.tint
smooth.name.rd	List of names for the "rd" calls associated with S.rd
S.pen	List of all the rescaled penalty matrices redimensioned to df.tot size. Every element of S.pen noted S.pen[[i]] is made from a penalty matrix pen[[i]] returned by smooth.cons and is multiplied by S.scale
grad.unpen.beta	gradient vector of the log-likelihood with respect to the regression parameters
grad.beta	gradient vector of the penalized log-likelihood with respect to the regression parameters
Hess.unpen.beta	hessian of the log-likelihood with respect to the regression parameters
Hess.beta	hessian of the penalized log-likelihood with respect to the regression parameters
Hess.beta.modif	if TRUE, the hessian of the penalized log-likelihood has been perturbed at convergence
ll.unpen	log-likelihood at convergence
ll.pen	penalized log-likelihood at convergence
deriv.rho.beta	transpose of the Jacobian of beta with respect to the log smoothing parameters
deriv.rho.inv.Hess.beta	list containing the derivatives of the inverse of Hess with respect to the log smoothing parameters
deriv.rho.Hess.unpen.beta	list containing the derivatives of Hess.unpen with respect to the log smoothing parameters
lambda	estimated or given smoothing parameters
nb.smooth	number of smoothing parameters
iter.rho	number of iterations needed to estimate the smoothing parameters
optim.rho	identify whether the smoothing parameters were estimated or not; 1 when exiting the function NR.rho; default is NULL
method	criterion used for smoothing parameter estimation
criterion.val	value of the criterion used for smoothing parameter estimation at convergence
LCV	Likelihood cross-validation criterion at convergence
LAML	negative Laplace approximate marginal likelihood at convergence
grad.rho	gradient vector of criterion with respect to the log smoothing parameters
Hess.rho	hessian matrix of criterion with respect to the log smoothing parameters
inv.Hess.rho	inverse of Hess.rho
Hess.rho.modif	if TRUE, the hessian of LCV or LAML has been perturbed at convergence
Ve	Frequentist covariance matrix
Vp	Bayesian covariance matrix
Vc	Bayesian covariance matrix corrected for smoothing parameter uncertainty (see Wood et al. 2016)
Vc.approx	Kass and Steffey approximation of Vc (see Wood et al. 2016)
Z.smf	List of matrices that represents the sum-to-zero constraint to apply for smf splines
Z.tensor	List of matrices that represents the sum-to-zero constraint to apply for tensor splines
Z.tint	List of matrices that represents the sum-to-zero constraint to apply for tint splines
list.smf	List of all smf.smooth.spec objects contained in the model
list.tensor	List of all tensor.smooth.spec objects contained in the model
list.tint	List of all tint.smooth.spec objects contained in the model
list.rd	List of all rd.smooth.spec objects contained in the model
U.F	Eigen vectors of S.F, useful for the initial reparameterization to separate penalized ad unpenalized subvectors. Allows stable evaluation of the log determinant of S and its derivatives
is.pwcst	TRUE if there is a piecewise constant (excess) hazard specification. In that case the cumulative hazard can be derived without Gauss-Legendre quadrature
pwcst.breaks	if is.pwcst is TRUE, vector of breaks defining the sub-intervals on which the hazard is constant. Otherwise NULL.
factor.structure	List containing the levels and classes of all factor variables present in the data frame used for fitting
converged	convergence indicator, TRUE or FALSE. TRUE if Hess.beta.modif=FALSE and Hess.rho.modif=FALSE (or NULL)

References

Wood, S.N., Pya, N. and Saefken, B. (2016), Smoothing parameter and model selection for general smooth models (with discussion). Journal of the American Statistical Association 111, 1548-1575

survPen documentation built on Sept. 14, 2023, 1:06 a.m.