tvcure.object: Object resulting from the fit of a tvcure model using...

In tvcure: Additive Cure Survival Model with Time-Varying Covariates

Object resulting from the fit of a tvcure model using function 'tvcure'.

Description

An object returned by the tvcure function: this is a list with various components related to the fit of such a model.

Value

A tvcure_object is a list with following elements:

• formula1 : A formula describing the linear predictor in the long-term (cure) survival (or quantum) submodel.

• formula2 : A formula describing the linear predictor in the short-term (cure) survival (or timing) submodel.

• baseline : Baseline ("S0" or "F0") used to specify the dependence of the cumulative hazard dynamics on covariates.

• id : the <id> of the unit associated to the data in a given line in the data frame.

• time : the integer time at which the observations are reported. For a given unit, it should be a sequence of CONSECUTIVE integers starting at 1 for the first observation.

• event : a sequence of 0-1 event indicators. For the lines corresponding to a given unit, it starts with 0 values concluded by a 0 in case of right-censoring or by a 1 if the event is observed at the end of the follow-up.

• regr1 : List returned by DesignFormula when evaluated on formula1.

• regr2 : List returned by DesignFormula when evaluated on formula2.

• K0 : Number of B-splines used to specify \log f_0(t).

• fit : A list containing different elements describing the fitted tvcure model:

  • llik : Log likelihood value of the fitted tvcure model at convergence.

  • lpen : Log of the penalized joint posterior at convergence.

  • dev : Deviance of the fitted tvcure model at convergence.

  • mu.ij : Expected value \mu_{ij}=h_p(t_{ij}|z(t_{ij}),x(t_{ij})) for the event indicator of unit i at time t_{ij}.

  • res : Standardized residual (d_{ij}-\mu_{ij})/\sqrt{\mu_{ij}} for unit i at time t_{ij} where \mu_{ij}=h_p(t_{ij}|z(t_{ij}),x(t_{ij})) and d_{ij} is the event indicator.

  • phi : Vector of length K_0 containing the estimated B-splines coefficients in \log f_0(t).

  • marginalized : Marginalization indicator (over penalty parameters) when reporting regression and spline parameter estimates.

  • nbeta : Number of regression and spline parameters in the long-term (cure) survival (or quantum) submodel.

  • ci.level : Selected level for credible intervals.

  • beta : (nbeta x 6) matrix containing the point estimates, standard errors, credible intervals, Z-scores and P-values of the regression and spline parameters in the long-term (cure) survival (or quantum) submodel.

  • ngamma : Number of regression and spline parameters in the short-term (cure) survival (or timing) submodel.

  • gamma : (ngamma x 6) matrix containing the point estimates, standard errors, credible intervals, Z-scores and P-values of the regression and spline parameters in the short-term (cure) survival (or timing) submodel.

  • gam : ngamma-vector with the point estimates of the regression and spline parameters in the short-term (cure) survival (or timing) submodel.

  • grad.beta : Gradient of the log joint posterior of <beta>, the regression and spline parameters in the long-term (cure) survival (or quantum) submodel.

  • Hes.beta : Hessian of the log joint posterior of <beta>.

  • Hes.beta0 : Hessian of the log joint posterior of <beta> (with the roughness penalty part omitted).

  • grad.gamma : Gradient of the log joint posterior of <gamma>, the regression and spline parameters in the short-term (cure) survival (or timing) submodel.

  • Hes.gamma : Hessian of the log joint posterior of <gamma>.

  • Hes.gamma0 : Hessian of the log joint posterior of <gamma> (with the roughness penalty part omitted).

  • Mcal.1 : Hessian of the log joint posterior of the spline parameters in <beta> conditionally on the non-penalized parameters.

  • Mcal.2 : Hessian of the log joint posterior of the spline parameters in <gamma> conditionally on the non-penalized parameters.

  • Hes.betgam : (nbeta x ngamma) matrix with the cross derivatives of the log joint posterior of (<beta>,<gamma>).

  • grad.regr : Gradient of the log joint posterior of <beta,gamma>.

  • Hes.regr : Hessian of the log joint posterior of <beta,gamma>.

  • Hes.regr0 : Hessian of the log joint posterior of <beta,gamma> (with the roughness penalty part omitted).

  • grad.phi : Gradient of the log joint posterior of <phi>, the spline parameters in \log f_0(t).

  • Hes.phi : Hessian of the log joint posterior of <phi>.

  • Hes.phi0 : Hessian of the log joint posterior of <phi> (with the roughness penalty part omitted).

  • T : Follow-up time after which a unit is declared cured in the absence of a past event.

  • t.grid : Grid of discrete time values on (1,T): 1,...,T.

  • f0.grid : Estimated values for f_0(t) on t.grid.

  • F0.grid : Estimated values for F_0(t) on t.grid.

  • S0.grid : Estimated values for S_0(t) on t.grid.

  • dlf0.grid : (ngrid x length(phi)) matrix with the jth line containing the gradient of \log f_0(t_j) w.r.t. <phi>.

  • dlF0.grid : (ngrid x length(phi)) matrix with the jth line containing the gradient of \log F_0(t_j) w.r.t. <phi>.

  • dlS0.grid : (ngrid x length(phi)) matrix with the jth line containing the gradient of \log S_0(t_j) w.r.t. <phi>.

  • k.ref : Index of the reference component in <phi> set to 0.0.

  • a, b : Hyperparameters of the Gamma(a,b) prior for the penalty parameters of the additive terms.

  • criterion : Criterion used to assess convergence of the estimation procedure.

  • grad.psi : Gradient of the log joint posterior of <phi[-k.ref]>, i.e. the spline parameters in \log f_0(t) with the fixed reference component omitted.

  • Hes.psi0 : Hessian of the log joint posterior of <phi[-k.ref]> (with the roughness penalty part omitted).

  • Hes.psi : Hessian of the log joint posterior of <phi[-k.ref]>.

  • tau : Selected value for the penalty parameter \tau tuning the smoothness of \log f_0(t).

  • pen.order0 : Penalty order for the P-splines used to specify \log f_0(t).

  • logscale : Logical: when TRUE, select \lambda_1 or \lambda_2 by maximizing p(\log(\lambda_k)|D), maximize p(\lambda_k|D) otherwise. (Default= TRUE).

  • lambda1 : Selected values for the penalty parameters \lambda_1 tuning the smoothness of the additive terms in the long-term (cure) survival (or quantum) submodel.

  • pen.order1 : Penalty order for the P-splines in the long-term survival (or quantum) submodel.

  • lambda2 : Selected values for the penalty parameters \lambda_2 tuning the smoothness of the additive terms in the short-term (cure) survival (or timing) submodel.

  • pen.order2 : Penalty order for the P-splines in the short-term survival (or timing) submodel.

  • tau.method : Method used to calculate the posterior mode of p(\tau_0|{\cal D}).

  • lambda.method : Method used to select the penalty parameters of the additive terms in the long-term survival (or quantum) submodel.

  • ED1 : Effective degrees of freedom for each of the additive terms in the long-term survival (or quantum) submodel, with the selected statistical test for significance and its P-value.

  • ED2 : Effective degrees of freedom for each of the additive terms in the short-term survival (or timing) submodel, with the selected statistical test for significance and its P-value.

  • ED1.Tr : Effective degrees of freedom for each of the additive terms in the long-term survival (or quantum) submodel, with Wood's statistical test for significance and its P-value.

  • ED2.Tr : Effective degrees of freedom for each of the additive terms in the short-term survival (or timing) submodel, with Wood's statistical test for significance and its P-value.

  • ED1.Chi2 : Effective degrees of freedom for each of the additive terms in the long-term survival (or quantum) submodel, with a Chi-square test for significance and its P-value.

  • ED2.Chi2 : Effective degrees of freedom for each of the additive terms in the short-term survival (or timing) submodel, with a Chi-square test for significance and its P-value.

  • nobs : Total number of observations.

  • n : Total number of units or subjects.

  • d : Total number of observed events.

  • ED1.tot : Total effective degrees of freedom for the long-term survival (or quantum) submodel.

  • ED2.tot : Total effective degrees of freedom for the short-term survival (or timing) submodel.

  • ED.tot : Total effective degrees of freedom for the tvcure model.

  • AIC : Akaike information criterion for the fitted model with a penalty calculated using the total effective degrees of freedom, -2log(L) + 2*ED.tot, larger values being preferred during model selection.

  • BIC : Bayesian (Schwarz) information criterion for the fitted model with a penalty calculated using the total effective degrees of freedom and the total number of observed events, -2log(L) + log(d)*ED.tot, smaller values being preferred during model selection.

  • levidence : Log-evidence of the fitted model, larger values being preferred during model selection.

  • iter : Number of iterations required to achieve convergence.

  • elapsed.time : Total duration (in seconds) of the estimation procedure.

• call : Function call.

• converged : Binary convergence status.

• logLik : Log-likelihood of the fitted model.

Author(s)

Philippe Lambert [e-mail]

References

Lambert, P. and Kreyenfeld, M. (2025). Time-varying exogenous covariates with frequently changing values in double additive cure survival model: an application to fertility. Journal of the Royal Statistical Society, Series A. <doi:10.1093/jrsssa/qnaf035>

See Also

tvcure, print.tvcure, plot.tvcure

tvcure documentation built on April 12, 2025, 1:58 a.m.