Fit the 2d GLAM with covariates

GLAM_2d_covariates() fits a GLAM for the hazard with two time scales, with covariates.

Usage

GLAM_2d_covariates(
  R,
  Y,
  Bu,
  Bs,
  Z,
  Wprior = NULL,
  P,
  ridge = 0,
  control_algorithm = list(maxiter = 20, conv_crit = 1e-05, verbose = FALSE)
)

Arguments

R

A 3d-array of dimensions nu by ns by n containing exposure times.

Y

A 3d-array of dimensions nu by ns by n containing event indicators.

Bu

A matrix of B-splines for the u time scale of dimension nu by cu.

Bs

A matrix of B-splines for the s time scale of dimension ns by cs.

Z

(optional) A regression matrix of covariates values of dimensions n by p.

Wprior

An optional matrix of a-priori weights.

P

The penalty matrix of dimension cucs by cucs.

ridge

A ridge penalty parameter: default is 0.

control_algorithm

A list with optional values for the parameters of the iterative processes:

• maxiter The maximum number of iteration for the IWSL algorithm. Default is 20.

• conv_crit The convergence criteria, expressed as difference between estimates at iteration i and i+1. Default is 1e-5.

• verbose A Boolean. Default is FALSE. If TRUE monitors the iteration process.

Value

A list with the following elements:

• Alpha The matrix of estimated P-splines coefficients of dimension cu by cs.

• Cov_alpha The variance-covariance matrix of the Alpha coefficients, of dimension cucs by cucs.

• beta The vector of length p of estimated covariates coefficients.

• Cov_beta The variance-covariance matrix of the beta coefficients, of dimension p by p.

• SE_beta The vector of length p of estimated Standard Errors for the beta coefficients.

• Eta0 The matrix of values of the baseline linear predictor (log-hazard) of dimension nu by ns.

• H The hat-matrix.

• deviance The deviance.

• ed The effective dimension of the model.

• aic The value of the AIC.

• bic The value of the BIC.

• Bbases a list with the B-spline bases Bu and Bs.