Multidimensional Penalized Splines for (Excess) Hazard Models, Relative Mortality Ratio Models and Marginal Intensity Models
colSums of a matrix
Sum-to-zero constraint
Implementation of the corrected variance Vc
Penalty matrix constructor for cubic regression splines
Bases for cubic regression splines (equivalent to "cr" in mgcv)
Cumulative hazard (integral of hazard) only
Derivative of a Choleski factor
Cumulative hazard (integral of hazard) and its first and second deriva...
Design matrix for the model needed in Gauss-Legendre quadrature
Gradient vector of LCV and LAML wrt rho (log smoothing parameters). Ve...
Gradient vector of LCV and LAML wrt rho (log smoothing parameters)
Matrix cross-multiplication between two matrices
Matrix multiplication between two matrices
Matrix multiplication between a matrix and a vector
Gauss-Legendre evaluations
Hessian matrix of LCV and LAML wrt rho (log smoothing parameters). Ver...
Hessian matrix of LCV and LAML wrt rho (log smoothing parameters)
Position of the nth occurrence of a string in another one
Reverses the initial reparameterization for stable evaluation of the l...
Design and penalty matrices for the model
Inner Newton-Raphson algorithm for regression parameters estimation
Outer Newton-Raphson algorithm for smoothing parameters estimation via...
Hazard and Survival prediction from fitted survPen model
Prediction of grouped indicators : population (net) survival (PNS) and...
print summary for a survPen fit
Defining piecewise constant (excess) hazard in survPen formulae
Defining random effects in survPen formulae
Applies initial reparameterization for stable evaluation of the log de...
Implementation of the robust variance Vr
Defining smooths in survPen formulae
Design matrix of penalized splines in a smooth.spec object for Gauss-L...
Design and penalty matrices of penalized splines in a smooth.spec obje...
Covariates specified as penalized splines
Split original dataset at specified times to fit a multiplicative mode...
Summary for a survPen fit
(Excess) hazard model with multidimensional penalized splines for give...
(Excess) hazard model with (multidimensional) penalized splines and in...
Fitted survPen object
tensor model matrix for two marginal bases
Tensor product for penalty matrices
tensor model matrix
Fits (excess) hazard, relative mortality ratio or marginal intensity models with multidimensional penalized splines allowing for time-dependent effects, non-linear effects and interactions between several continuous covariates. In survival and net survival analysis, in addition to modelling the effect of time (via the baseline hazard), one has often to deal with several continuous covariates and model their functional forms, their time-dependent effects, and their interactions. Model specification becomes therefore a complex problem and penalized regression splines represent an appealing solution to that problem as splines offer the required flexibility while penalization limits overfitting issues. Current implementations of penalized survival models can be slow or unstable and sometimes lack some key features like taking into account expected mortality to provide net survival and excess hazard estimates. In contrast, survPen provides an automated, fast, and stable implementation (thanks to explicit calculation of the derivatives of the likelihood) and offers a unified framework for multidimensional penalized hazard and excess hazard models. Later versions (>2.0.0) include penalized models for relative mortality ratio, and marginal intensity in recurrent event setting. survPen may be of interest to those who 1) analyse any kind of time-to-event data: mortality, disease relapse, machinery breakdown, unemployment, etc 2) wish to describe the associated hazard and to understand which predictors impact its dynamics, 3) wish to model the relative mortality ratio between a cohort and a reference population, 4) wish to describe the marginal intensity for recurrent event data. See Fauvernier et al. (2019a) <doi:10.21105/joss.01434> for an overview of the package and Fauvernier et al. (2019b) <doi:10.1111/rssc.12368> for the method.