# Multidimensional Penalized Splines for (Excess) Hazard Models, Relative Mortality Ratio Models and Marginal Intensity Models

## Documentation for package ‘survPen’ version 2.0.0

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Package NEWS.

## Help Pages

%cross% | Matrix cross-multiplication between two matrices
%mult% | Matrix multiplication between two matrices
%vec% | Matrix multiplication between a matrix and a vector
colSums2 | colSums of a matrix
constraint | Sum-to-zero constraint
cor.var | Implementation of the corrected variance Vc
crs | Bases for cubic regression splines (equivalent to "cr" in 'mgcv')
crs.FP | Penalty matrix constructor for cubic regression splines
CumulHazard | Cumulative hazard (integral of hazard) only
datCancer | Patients diagnosed with cervical cancer
DerivCumulHazard | Cumulative hazard (integral of hazard) and its first and second derivatives wrt regression parameters beta
deriv_R | Derivative of a Choleski factor
design.matrix | Design matrix for the model needed in Gauss-Legendre quadrature
expected.table | French women mortality table
grad_rho | Gradient vector of LCV and LAML wrt rho (log smoothing parameters)
grad_rho_mult | Gradient vector of LCV and LAML wrt rho (log smoothing parameters). Version for multiplicative decomposition : relative mortality ratio model
HazGL | Gauss-Legendre evaluations
HeartFailure | Patients with heart failure at risk of recurrent hospitalization events
Hess_rho | Hessian matrix of LCV and LAML wrt rho (log smoothing parameters)
Hess_rho_mult | Hessian matrix of LCV and LAML wrt rho (log smoothing parameters). Version for multiplicative decomposition : relative mortality ratio model
instr | Position of the nth occurrence of a string in another one
inv.repam | Reverses the initial reparameterization for stable evaluation of the log determinant of the penalty matrix
list.wicss | List of ICSS standards for age-standardization of cancer (net) survival
model.cons | Design and penalty matrices for the model
NR.beta | Inner Newton-Raphson algorithm for regression parameters estimation
NR.rho | Outer Newton-Raphson algorithm for smoothing parameters estimation via LCV or LAML optimization
predict.survPen | Hazard and Survival prediction from fitted 'survPen' model
predSNS | Prediction of grouped indicators : population (net) survival (PNS) and age-standardized (net) survival (SNS)
print.summary.survPen | print summary for a 'survPen' fit
pwcst | Defining piecewise constant (excess) hazard in survPen formulae
rd | Defining random effects in survPen formulae
repam | Applies initial reparameterization for stable evaluation of the log determinant of the penalty matrix
robust.var | Implementation of the robust variance Vr
smf | Defining smooths in survPen formulae
smooth.cons | Design and penalty matrices of penalized splines in a smooth.spec object
smooth.cons.integral | Design matrix of penalized splines in a smooth.spec object for Gauss-Legendre quadrature
smooth.spec | Covariates specified as penalized splines
splitmult | Split original dataset at specified times to fit a multiplicative model
summary.survPen | Summary for a 'survPen' fit
survPen | (Excess) hazard model with (multidimensional) penalized splines and integrated smoothness estimation
survPen.fit | (Excess) hazard model with multidimensional penalized splines for given smoothing parameters
survPenObject | Fitted survPen object
tensor | Defining smooths in survPen formulae
tensor.in | tensor model matrix for two marginal bases
tensor.prod.S | Tensor product for penalty matrices
tensor.prod.X | tensor model matrix
tint | Defining smooths in survPen formulae