predict.mexhaz: Predictions based on a mexhaz model
In mexhaz: Mixed Effect Excess Hazard Models
predict.mexhaz R Documentation
Predictions based on a mexhaz model
Description
Function for predicting the (excess) hazard and the
corresponding (net) survival from a model fitted with the mexhaz
function for a particular vector of covariates. If the survival model
was fitted with an expected hazard (excess hazard model), the estimates
obtained are excess hazard and net survival estimates. Corresponding
variance estimates are based on the Delta Method or Monte Carlo
simulation (based on the assumption of multivariate normality of the
model parameter estimates). This function allows the computation of the
hazard and the survival at one time point for several vectors of
covariates or for one vector of covariates at several time
points. When the model includes a random effect, two types of
predictions can be made: (i) marginal predictions (obtained by
integration over the random effect distribution) or (ii) conditional
predictions either for a particular cluster (using the corresponding
shrinkage estimate) or for the value 0 of the random effect.
Usage
## S3 method for class 'mexhaz'
predict(object, time.pts, data.val = data.frame(.NotUsed = NA),
cluster = NULL, marginal = FALSE, conf.int = c("delta", "simul", "none"),
level = 0.95, delta.type.h = c("log", "plain"), delta.type.s = c("log-log",
"log", "plain"), nb.sim = 10000, keep.sim = FALSE, include.gradient = FALSE, ...)
Arguments
object
an object of class mexhaz, corresponding to a
hazard-based regression model fitted with the mexhaz function.
time.pts
a vector of numerical values representing the time
points at which predictions are requested. Time values greater than
the maximum follow-up time on which the model estimation was based
are discarded.
data.val
a data.frame containing the values of the
covariates at which predictions should be calculated.
cluster
a vector of size either one or the number of
observations in data.val corresponding to the cluster(s) for
which conditional predictions should be calculated. In the first
case, conditional predictions for all observations are obtained for
the same cluster, while in the second case, conditional predictions
can be made for a different cluster for each observation in
data.val. Standard errors of prediction are obtained with the
approximation of the conditional mean squared error of prediction
(without the second-order bias correction term) described in Booth
and Hobert. This argument is not used if the model is a fixed effect
model. The default value is NULL: this corresponds to
marginal predictions (if marginal is set to TRUE, the preferred
option), or to conditional predictions for the value 0 of the random
effect (if marginal is set to FALSE).
marginal
logical value controlling the type of predictions
returned by the function when the model includes a random
intercept. When TRUE, marginal predictions are computed. The
marginal survival is obtained by integrating the predicted survival over the
distribution of the random effect. The marginal hazard rate is
obtained as the opposite of the marginal time
derivative of the survival divided by the marginal survival. When
FALSE (default value), conditional predictions depending on the
value of the cluster argument are calculated.
conf.int
method to be used to compute confidence
limits. Selection can be made between the following options:
"delta" for the Delta Method (default value);
"simul" for Monte Carlo simulations (can be time-consuming,
especially for models using B-splines for the logarithm of the
baseline hazard);
"none" indicates absence of confidence limits estimation.
level
a number in (0,1) specifying the level of confidence for
computing the confidence intervals of the hazard and the survival. The
default value is set to 0.95.
delta.type.h
type of confidence limits for the hazard when
using the Delta Method. With the default value ("log"), the
confidence limits are based on a Wald-type confidence interval for
the logarithm of the hazard, otherwise they are based directly on
a Wald-type CI for the hazard.
delta.type.s
type of confidence limits for the survival when
using the Delta Method. With the default value ("log-log"),
the confidence limits are based on a Wald-type confidence interval
for the logarithm of the cumulative hazard; when the argument is
set to "log", they are based on a Wald-type CI for the
cumulative hazard; otherwise they are based directly on a
Wald-type CI for the survival.
include.gradient
logical value allowing the function to return
the components of the gradient of the logarithm of the hazard and of
the logarithm of the cumulative hazard for each prediction. This
argument is used only if conf.int is set to "delta". The
default value is FALSE.
nb.sim
integer value representing the number of simulations
used to estimate the confidence limits for the (excess) hazard
and the (net) survival. This argument is used only if
conf.int is set to "simul".
keep.sim
logical value determining if the simulated hazard and
survival values should be returned (only used when
conf.int is set to "simul"). These simulated values can be used by the
riskfunc function to compute simulation-based confidence
intervals for hazard ratios / risk ratios. The default value is set
to FALSE.
...
for potential additional parameters.
Value
An object of class predMexhaz that can be used by
the function plot.predMexhaz to produce graphics of the (excess) hazard and
the (net) survival. It contains the following elements:
call
the mexhaz function call on which the model is based.
results
a data.frame consisting of: the time
points at which the (excess) hazard and the (net) survival have been
calculated; the values of the covariates used to estimate the
(excess) hazard and the (net) survival; the
(excess) hazard values with their confidence limits; and the (net) survival values with their confidence limits.
variances
a data.frame consisting of two columns: the
variance of the logarithm of the (excess) hazard and the variance of
the (excess) cumulative hazard for each time points or each
vector of covariates. The object variances is produced only when
conf.int is set to "delta".
grad.loghaz
a data.frame consisting of the components of
the gradient of the logarithm of the (excess) hazard for each time points or each
vector of covariates. The number of columns corresponds to the number
of model parameters. This object is produced only when
conf.int is set to "delta" and include.gradient
to TRUE.
grad.logcum
a data.frame consisting of the components of
the gradient of the logarithm of the (excess) cumulative hazard for each time points or each
vector of covariates. The number of columns corresponds to the number
of model parameters. This object is produced only when
conf.int is set to "delta" and include.gradient
to TRUE.
vcov
a matrix corresponding to the covariance matrix used to
compute the confidence intervals.
type
this item can take the value
multitime (computation of the hazard and the survival at
at several time points for one vector of covariates) or
multiobs (computation of the hazard and the survival at
at one time point for several vectors of covariates). It is
used by plot.predMexhaz and points.predMexhaz.
type.me
the type of predictions produced in case of a model
including a random intercept. Can take the values conditional
or marginal.
ci.method
the method used to compute confidence limits.
level
level of confidence used to compute confidence limits.
delta.type
type of confidence limits for the hazard and the
survival when using the Delta Method.
nb.sim
number of simulations used to estimate the confidence
limits when ci.method is set to "simul".
sim.haz
matrix containing the simulated hazards (each column
representing a simulated vector of values); only returned when
keep.sim is set to TRUE.
sim.surv
matrix containing the simulated survival probabilities (each column
representing a simulated vector of values); only returned when
keep.sim is set to TRUE.
Author(s)
Hadrien Charvat, Aurelien Belot
References
Charvat H, Remontet L, Bossard N, Roche L, Dejardin O,
Rachet B, Launoy G, Belot A; CENSUR Working Survival Group. A
multilevel excess hazard model to estimate net survival on
hierarchical data allowing for non-linear and non-proportional effects
of covariates. Stat Med 2016;35:3066-3084 (doi: 10.1002/sim.6881)
Booth JG, Hobert JP. Standard errors of prediction in generalized
linear mixed models. J Am Stat Assoc 1998;93:262-272 (doi: 10.2307/2669622).
See Also
print.predMexhaz, plot.predMexhaz,
points.predMexhaz, lines.predMexhaz
Examples
data(simdatn1)
## Fit of a fixed-effect hazard model, with the baseline hazard
## described by a linear B-spline with two knots at 1 and 5 year and
## with effects of age (agecr), deprivation index (depindex) and sex
## (IsexH)
Mod_bs1_2 <- mexhaz(formula=Surv(time=timesurv,
event=vstat)~agecr+depindex+IsexH, data=simdatn1, base="exp.bs",
degree=1, knots=c(1,5), verbose=0)
## Prediction at several time points for one vector of covariates
Pred_Modbs1_2A <- predict(Mod_bs1_2, time.pts=seq(0.1,10,by=0.1),
data.val=data.frame(agecr=0,depindex=0.5,IsexH=1))
## Prediction for several vectors of covariates at one time point
Pred_Modbs1_2B <- predict(Mod_bs1_2, time.pts=10,
data.val=data.frame(agecr=c(-0.2,-0.1,0), depindex=c(0.5,0.5,0.5),
IsexH=c(1,1,1)))
## Prediction for all individuals of the study population
## at one time point
Pred_Modbs1_2C <- predict(Mod_bs1_2, time.pts=10,
data.val=simdatn1)
# Example of cluster-specific prediction (not run)
## Fit of a mixed-effect excess hazard model, with the baseline hazard
## described by a cubic B-spline with two knots at 1 and 5 year
# Mod_bs3_2mix <- mexhaz(formula=Surv(time=timesurv,
# event=vstat)~agecr+IsexH, data=simdatn1, base="exp.bs", degree=3,
# knots=c(1,5), expected="popmrate", random="clust", verbose=1000)
## Prediction at several time points for an individual in cluster 15
## with a specific vector of covariates
# Pred_Modbs3_2A <- predict(Mod_bs3_2mix,
# time.pts=seq(0.1,10,by=0.1), data.val=data.frame(agecr=0.2, IsexH=1),
# cluster=15)
mexhaz documentation built on Oct. 31, 2022, 5:08 p.m.
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| predict.mexhaz | R Documentation |
Predictions based on a mexhaz model
Description
Function for predicting the (excess) hazard and the
corresponding (net) survival from a model fitted with the mexhaz
function for a particular vector of covariates. If the survival model
was fitted with an expected hazard (excess hazard model), the estimates
obtained are excess hazard and net survival estimates. Corresponding
variance estimates are based on the Delta Method or Monte Carlo
simulation (based on the assumption of multivariate normality of the
model parameter estimates). This function allows the computation of the
hazard and the survival at one time point for several vectors of
covariates or for one vector of covariates at several time
points. When the model includes a random effect, two types of
predictions can be made: (i) marginal predictions (obtained by
integration over the random effect distribution) or (ii) conditional
predictions either for a particular cluster (using the corresponding
shrinkage estimate) or for the value 0 of the random effect.
Usage
## S3 method for class 'mexhaz'
predict(object, time.pts, data.val = data.frame(.NotUsed = NA),
cluster = NULL, marginal = FALSE, conf.int = c("delta", "simul", "none"),
level = 0.95, delta.type.h = c("log", "plain"), delta.type.s = c("log-log",
"log", "plain"), nb.sim = 10000, keep.sim = FALSE, include.gradient = FALSE, ...)
Arguments
object |
an object of class |
time.pts |
a vector of numerical values representing the time points at which predictions are requested. Time values greater than the maximum follow-up time on which the model estimation was based are discarded. |
data.val |
a |
cluster |
a vector of size either one or the number of
observations in |
marginal |
logical value controlling the type of predictions
returned by the function when the model includes a random
intercept. When |
conf.int |
method to be used to compute confidence
limits. Selection can be made between the following options:
|
level |
a number in (0,1) specifying the level of confidence for
computing the confidence intervals of the hazard and the survival. The
default value is set to |
delta.type.h |
type of confidence limits for the hazard when
using the Delta Method. With the default value ( |
delta.type.s |
type of confidence limits for the survival when
using the Delta Method. With the default value ( |
include.gradient |
logical value allowing the function to return
the components of the gradient of the logarithm of the hazard and of
the logarithm of the cumulative hazard for each prediction. This
argument is used only if |
nb.sim |
integer value representing the number of simulations
used to estimate the confidence limits for the (excess) hazard
and the (net) survival. This argument is used only if
|
keep.sim |
logical value determining if the simulated hazard and
survival values should be returned (only used when
|
... |
for potential additional parameters. |
Value
An object of class predMexhaz that can be used by
the function plot.predMexhaz to produce graphics of the (excess) hazard and
the (net) survival. It contains the following elements:
call |
the |
results |
a |
variances |
a |
grad.loghaz |
a |
grad.logcum |
a |
vcov |
a matrix corresponding to the covariance matrix used to compute the confidence intervals. |
type |
this item can take the value
|
type.me |
the type of predictions produced in case of a model
including a random intercept. Can take the values |
ci.method |
the method used to compute confidence limits. |
level |
level of confidence used to compute confidence limits. |
delta.type |
type of confidence limits for the hazard and the survival when using the Delta Method. |
nb.sim |
number of simulations used to estimate the confidence
limits when |
sim.haz |
matrix containing the simulated hazards (each column
representing a simulated vector of values); only returned when
|
sim.surv |
matrix containing the simulated survival probabilities (each column
representing a simulated vector of values); only returned when
|
Author(s)
Hadrien Charvat, Aurelien Belot
References
Charvat H, Remontet L, Bossard N, Roche L, Dejardin O, Rachet B, Launoy G, Belot A; CENSUR Working Survival Group. A multilevel excess hazard model to estimate net survival on hierarchical data allowing for non-linear and non-proportional effects of covariates. Stat Med 2016;35:3066-3084 (doi: 10.1002/sim.6881)
Booth JG, Hobert JP. Standard errors of prediction in generalized linear mixed models. J Am Stat Assoc 1998;93:262-272 (doi: 10.2307/2669622).
See Also
print.predMexhaz, plot.predMexhaz,
points.predMexhaz, lines.predMexhaz
Examples
data(simdatn1) ## Fit of a fixed-effect hazard model, with the baseline hazard ## described by a linear B-spline with two knots at 1 and 5 year and ## with effects of age (agecr), deprivation index (depindex) and sex ## (IsexH) Mod_bs1_2 <- mexhaz(formula=Surv(time=timesurv, event=vstat)~agecr+depindex+IsexH, data=simdatn1, base="exp.bs", degree=1, knots=c(1,5), verbose=0) ## Prediction at several time points for one vector of covariates Pred_Modbs1_2A <- predict(Mod_bs1_2, time.pts=seq(0.1,10,by=0.1), data.val=data.frame(agecr=0,depindex=0.5,IsexH=1)) ## Prediction for several vectors of covariates at one time point Pred_Modbs1_2B <- predict(Mod_bs1_2, time.pts=10, data.val=data.frame(agecr=c(-0.2,-0.1,0), depindex=c(0.5,0.5,0.5), IsexH=c(1,1,1))) ## Prediction for all individuals of the study population ## at one time point Pred_Modbs1_2C <- predict(Mod_bs1_2, time.pts=10, data.val=simdatn1) # Example of cluster-specific prediction (not run) ## Fit of a mixed-effect excess hazard model, with the baseline hazard ## described by a cubic B-spline with two knots at 1 and 5 year # Mod_bs3_2mix <- mexhaz(formula=Surv(time=timesurv, # event=vstat)~agecr+IsexH, data=simdatn1, base="exp.bs", degree=3, # knots=c(1,5), expected="popmrate", random="clust", verbose=1000) ## Prediction at several time points for an individual in cluster 15 ## with a specific vector of covariates # Pred_Modbs3_2A <- predict(Mod_bs3_2mix, # time.pts=seq(0.1,10,by=0.1), data.val=data.frame(agecr=0.2, IsexH=1), # cluster=15)
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