tvcure.object {tvcure} | R Documentation |
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 byDesignFormula
when evaluated onformula1
. -
regr2
: List returned byDesignFormula
when evaluated onformula2
. -
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 uniti
at timet_{ij}
. -
res
: Standardized residual(d_{ij}-\mu_{ij})/\sqrt{\mu_{ij}}
for uniti
at timet_{ij}
where\mu_{ij}=h_p(t_{ij}|z(t_{ij}),x(t_{ij}))
andd_{ij}
is the event indicator. -
phi
: Vector of lengthK_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 forf_0(t)
ont.grid
. -
F0.grid
: Estimated values forF_0(t)
ont.grid
. -
S0.grid
: Estimated values forS_0(t)
ont.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 maximizingp(\log(\lambda_k)|D)
, maximizep(\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 ofp(\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 p.lambert@uliege.be
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