survival.twostage: Twostage survival model for multivariate survival data
In mets: Analysis of Multivariate Event Times
survival.twostage R Documentation
Twostage survival model for multivariate survival data
Description
Fits Clayton-Oakes or bivariate Plackett models for bivariate survival data
using marginals that are on Cox form. The dependence can be modelled via
Regression design on dependence parameter.
Random effects, additive gamma model.
If clusters contain more than two subjects, we use a composite likelihood
based on the pairwise bivariate models, for full MLE see twostageMLE.
The two-stage model is constructed such that
given the gamma distributed random effects it is assumed that the survival functions
are indpendent, and that the marginal survival functions are on Cox form (or additive form)
P(T > t| x) = S(t|x)= exp( -exp(x^T \beta) A_0(t) )
One possibility is to model the variance within clusters via a regression design, and
then one can specify a regression structure for the independent gamma distributed
random effect for each cluster, such that the variance is given by
\theta = h( z_j^T \alpha)
where z is specified by theta.des, and a possible link function var.link=1 will
will use the exponential link h(x)=exp(x), and var.link=0 the identity link h(x)=x.
The reported standard errors are based on the estimated information from the
likelihood assuming that the marginals are known (unlike the twostageMLE and for the
additive gamma model below).
Can also fit a structured additive gamma random effects model, such
as the ACE, ADE model for survival data. In this case the
random.design specificies the random effects for each subject within a cluster. This is
a matrix of 1's and 0's with dimension n x d. With d random effects.
For a cluster with two subjects, we let the random.design rows be
v_1 and v_2.
Such that the random effects for subject
1 is
v_1^T (Z_1,...,Z_d)
, for d random effects. Each random effect
has an associated parameter (\lambda_1,...,\lambda_d).
By construction subjects 1's random effect are Gamma distributed with
mean \lambda_j/v_1^T \lambda
and variance \lambda_j/(v_1^T \lambda)^2. Note that the random effect
v_1^T (Z_1,...,Z_d) has mean 1 and variance 1/(v_1^T \lambda).
It is here asssumed that lamtot=v_1^T \lambda is fixed within clusters
as it would be for the ACE model below.
Based on these parameters the relative contribution (the heritability, h) is
equivalent to the expected values of the random effects: \lambda_j/v_1^T \lambda
The DEFAULT parametrization (var.par=1) uses the variances of the random effecs
\theta_j = \lambda_j/(v_1^T \lambda)^2
For alternative parametrizations one can specify how the parameters relate to \lambda_j
with the argument var.par=0.
For both types of models the basic model assumptions are that
given the random effects of the clusters the survival distributions within a cluster
are independent and ' on the form
P(T > t| x,z) = exp( -Z \cdot Laplace^{-1}(lamtot,lamtot,S(t|x)) )
with the inverse laplace of the gamma distribution with mean 1 and variance 1/lamtot.
The parameters (\lambda_1,...,\lambda_d) are related to the parameters of the model
by a regression construction pard (d x k), that links the d
\lambda parameters
with the (k) underlying \theta parameters
\lambda = theta.des \theta
here using theta.des to specify these low-dimension association. Default is a diagonal matrix.
This can be used to make structural assumptions about the variances of the random-effects
as is needed for the ACE model for example.
The case.control option that can be used with the pair specification of the pairwise parts
of the estimating equations. Here it is assumed that the second subject of each pair is the proband.
Usage
survival.twostage(
margsurv,
data = parent.frame(),
method = "nr",
detail = 0,
clusters = NULL,
silent = 1,
weights = NULL,
theta = NULL,
theta.des = NULL,
var.link = 1,
baseline.iid = 1,
model = "clayton.oakes",
marginal.trunc = NULL,
marginal.survival = NULL,
strata = NULL,
se.clusters = NULL,
numDeriv = 1,
random.design = NULL,
pairs = NULL,
dim.theta = NULL,
numDeriv.method = "simple",
additive.gamma.sum = NULL,
var.par = 1,
no.opt = FALSE,
...
)
Arguments
margsurv
Marginal model
data
data frame
method
Scoring method "nr", for lava NR optimizer
detail
Detail
clusters
Cluster variable
silent
Debug information
weights
Weights
theta
Starting values for variance components
theta.des
design for dependence parameters, when pairs are given the indeces of the
theta-design for this pair, is given in pairs as column 5
var.link
Link function for variance: exp-link.
baseline.iid
to adjust for baseline estimation, using phreg function on same data.
model
model
marginal.trunc
marginal left truncation probabilities
marginal.survival
optional vector of marginal survival probabilities
strata
strata for fitting, see example
se.clusters
for clusters for se calculation with iid
numDeriv
to get numDeriv version of second derivative, otherwise uses sum of squared scores for each pair
random.design
random effect design for additive gamma model, when pairs are given the
indeces of the pairs random.design rows are given as columns 3:4
pairs
matrix with rows of indeces (two-columns) for the pairs considered in the pairwise
composite score, useful for case-control sampling when marginal is known.
dim.theta
dimension of the theta parameter for pairs situation.
numDeriv.method
uses simple to speed up things and second derivative not so important.
additive.gamma.sum
for two.stage=0, this is specification of the lamtot in the models via
a matrix that is multiplied onto the parameters theta (dimensions=(number random effects x number
of theta parameters), when null then sums all parameters.
var.par
is 1 for the default parametrization with the variances of the random effects,
var.par=0 specifies that the \lambda_j's are used as parameters.
no.opt
for not optimizng
...
Additional arguments to maximizer NR of lava.
and ascertained sampling
Author(s)
Thomas Scheike
References
Twostage estimation of additive gamma frailty models for survival data.
Scheike (2019), work in progress
Shih and Louis (1995) Inference on the association parameter in copula models for bivariate
survival data, Biometrics, (1995).
Glidden (2000), A Two-Stage estimator of the dependence
parameter for the Clayton Oakes model, LIDA, (2000).
Measuring early or late dependence for bivariate twin data
Scheike, Holst, Hjelmborg (2015), LIDA
Estimating heritability for cause specific mortality based on twins studies
Scheike, Holst, Hjelmborg (2014), LIDA
Additive Gamma frailty models for competing risks data, Biometrics (2015)
Eriksson and Scheike (2015),
Examples
data(diabetes)
# Marginal Cox model with treat as covariate
margph <- phreg(Surv(time,status)~treat+cluster(id),data=diabetes)
### Clayton-Oakes, MLE
fitco1<-twostageMLE(margph,data=diabetes,theta=1.0)
summary(fitco1)
### Plackett model
mph <- phreg(Surv(time,status)~treat+cluster(id),data=diabetes)
fitp <- survival.twostage(mph,data=diabetes,theta=3.0,Nit=40,
clusters=diabetes$id,var.link=1,model="plackett")
summary(fitp)
### Clayton-Oakes
fitco2 <- survival.twostage(mph,data=diabetes,theta=0.0,detail=0,
clusters=diabetes$id,var.link=1,model="clayton.oakes")
summary(fitco2)
fitco3 <- survival.twostage(margph,data=diabetes,theta=1.0,detail=0,
clusters=diabetes$id,var.link=0,model="clayton.oakes")
summary(fitco3)
### without covariates but with stratafied
marg <- phreg(Surv(time,status)~+strata(treat)+cluster(id),data=diabetes)
fitpa <- survival.twostage(marg,data=diabetes,theta=1.0,
clusters=diabetes$id,model="clayton.oakes")
summary(fitpa)
fitcoa <- survival.twostage(marg,data=diabetes,theta=1.0,clusters=diabetes$id,
model="clayton.oakes")
summary(fitcoa)
### Piecewise constant cross hazards ratio modelling
########################################################
d <- subset(simClaytonOakes(2000,2,0.5,0,stoptime=2,left=0),!truncated)
udp <- piecewise.twostage(c(0,0.5,2),data=d,method="optimize",
id="cluster",timevar="time",
status="status",model="clayton.oakes",silent=0)
summary(udp)
## Reduce Ex.Timings
### Same model using the strata option, a bit slower
########################################################
## makes the survival pieces for different areas in the plane
##ud1=surv.boxarea(c(0,0),c(0.5,0.5),data=d,id="cluster",timevar="time",status="status")
##ud2=surv.boxarea(c(0,0.5),c(0.5,2),data=d,id="cluster",timevar="time",status="status")
##ud3=surv.boxarea(c(0.5,0),c(2,0.5),data=d,id="cluster",timevar="time",status="status")
##ud4=surv.boxarea(c(0.5,0.5),c(2,2),data=d,id="cluster",timevar="time",status="status")
## everything done in one call
ud <- piecewise.data(c(0,0.5,2),data=d,timevar="time",status="status",id="cluster")
ud$strata <- factor(ud$strata);
ud$intstrata <- factor(ud$intstrata)
## makes strata specific id variable to identify pairs within strata
## se's computed based on the id variable across strata "cluster"
ud$idstrata <- ud$id+(as.numeric(ud$strata)-1)*2000
marg2 <- timereg::aalen(Surv(boxtime,status)~-1+factor(num):factor(intstrata),
data=ud,n.sim=0,robust=0)
tdes <- model.matrix(~-1+factor(strata),data=ud)
fitp2 <- survival.twostage(marg2,data=ud,se.clusters=ud$cluster,clusters=ud$idstrata,
model="clayton.oakes",theta.des=tdes,step=0.5)
summary(fitp2)
### now fitting the model with symmetry, i.e. strata 2 and 3 same effect
ud$stratas <- ud$strata;
ud$stratas[ud$strata=="0.5-2,0-0.5"] <- "0-0.5,0.5-2"
tdes2 <- model.matrix(~-1+factor(stratas),data=ud)
fitp3 <- survival.twostage(marg2,data=ud,clusters=ud$idstrata,se.cluster=ud$cluster,
model="clayton.oakes",theta.des=tdes2,step=0.5)
summary(fitp3)
### same model using strata option, a bit slower
fitp4 <- survival.twostage(marg2,data=ud,clusters=ud$cluster,se.cluster=ud$cluster,
model="clayton.oakes",theta.des=tdes2,step=0.5,strata=ud$strata)
summary(fitp4)
## Reduce Ex.Timings
### structured random effects model additive gamma ACE
### simulate structured two-stage additive gamma ACE model
data <- simClaytonOakes.twin.ace(4000,2,1,0,3)
out <- twin.polygen.design(data,id="cluster")
pardes <- out$pardes
pardes
des.rv <- out$des.rv
head(des.rv)
aa <- phreg(Surv(time,status)~x+cluster(cluster),data=data,robust=0)
ts <- survival.twostage(aa,data=data,clusters=data$cluster,detail=0,
theta=c(2,1),var.link=0,step=0.5,
random.design=des.rv,theta.des=pardes)
summary(ts)
mets documentation built on May 29, 2024, 3:51 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
| survival.twostage | R Documentation |
Twostage survival model for multivariate survival data
Description
Fits Clayton-Oakes or bivariate Plackett models for bivariate survival data using marginals that are on Cox form. The dependence can be modelled via
Regression design on dependence parameter.
Random effects, additive gamma model.
If clusters contain more than two subjects, we use a composite likelihood based on the pairwise bivariate models, for full MLE see twostageMLE.
The two-stage model is constructed such that given the gamma distributed random effects it is assumed that the survival functions are indpendent, and that the marginal survival functions are on Cox form (or additive form)
P(T > t| x) = S(t|x)= exp( -exp(x^T \beta) A_0(t) )
One possibility is to model the variance within clusters via a regression design, and then one can specify a regression structure for the independent gamma distributed random effect for each cluster, such that the variance is given by
\theta = h( z_j^T \alpha)
where z is specified by theta.des, and a possible link function var.link=1 will
will use the exponential link h(x)=exp(x), and var.link=0 the identity link h(x)=x.
The reported standard errors are based on the estimated information from the
likelihood assuming that the marginals are known (unlike the twostageMLE and for the
additive gamma model below).
Can also fit a structured additive gamma random effects model, such
as the ACE, ADE model for survival data. In this case the
random.design specificies the random effects for each subject within a cluster. This is
a matrix of 1's and 0's with dimension n x d. With d random effects.
For a cluster with two subjects, we let the random.design rows be
v_1 and v_2.
Such that the random effects for subject
1 is
v_1^T (Z_1,...,Z_d)
, for d random effects. Each random effect
has an associated parameter (\lambda_1,...,\lambda_d).
By construction subjects 1's random effect are Gamma distributed with
mean \lambda_j/v_1^T \lambda
and variance \lambda_j/(v_1^T \lambda)^2. Note that the random effect
v_1^T (Z_1,...,Z_d) has mean 1 and variance 1/(v_1^T \lambda).
It is here asssumed that lamtot=v_1^T \lambda is fixed within clusters
as it would be for the ACE model below.
Based on these parameters the relative contribution (the heritability, h) is
equivalent to the expected values of the random effects: \lambda_j/v_1^T \lambda
The DEFAULT parametrization (var.par=1) uses the variances of the random effecs
\theta_j = \lambda_j/(v_1^T \lambda)^2
For alternative parametrizations one can specify how the parameters relate to \lambda_j
with the argument var.par=0.
For both types of models the basic model assumptions are that given the random effects of the clusters the survival distributions within a cluster are independent and ' on the form
P(T > t| x,z) = exp( -Z \cdot Laplace^{-1}(lamtot,lamtot,S(t|x)) )
with the inverse laplace of the gamma distribution with mean 1 and variance 1/lamtot.
The parameters (\lambda_1,...,\lambda_d) are related to the parameters of the model
by a regression construction pard (d x k), that links the d
\lambda parameters
with the (k) underlying \theta parameters
\lambda = theta.des \theta
here using theta.des to specify these low-dimension association. Default is a diagonal matrix. This can be used to make structural assumptions about the variances of the random-effects as is needed for the ACE model for example.
The case.control option that can be used with the pair specification of the pairwise parts of the estimating equations. Here it is assumed that the second subject of each pair is the proband.
Usage
survival.twostage(
margsurv,
data = parent.frame(),
method = "nr",
detail = 0,
clusters = NULL,
silent = 1,
weights = NULL,
theta = NULL,
theta.des = NULL,
var.link = 1,
baseline.iid = 1,
model = "clayton.oakes",
marginal.trunc = NULL,
marginal.survival = NULL,
strata = NULL,
se.clusters = NULL,
numDeriv = 1,
random.design = NULL,
pairs = NULL,
dim.theta = NULL,
numDeriv.method = "simple",
additive.gamma.sum = NULL,
var.par = 1,
no.opt = FALSE,
...
)
Arguments
margsurv |
Marginal model |
data |
data frame |
method |
Scoring method "nr", for lava NR optimizer |
detail |
Detail |
clusters |
Cluster variable |
silent |
Debug information |
weights |
Weights |
theta |
Starting values for variance components |
theta.des |
design for dependence parameters, when pairs are given the indeces of the theta-design for this pair, is given in pairs as column 5 |
var.link |
Link function for variance: exp-link. |
baseline.iid |
to adjust for baseline estimation, using phreg function on same data. |
model |
model |
marginal.trunc |
marginal left truncation probabilities |
marginal.survival |
optional vector of marginal survival probabilities |
strata |
strata for fitting, see example |
se.clusters |
for clusters for se calculation with iid |
numDeriv |
to get numDeriv version of second derivative, otherwise uses sum of squared scores for each pair |
random.design |
random effect design for additive gamma model, when pairs are given the indeces of the pairs random.design rows are given as columns 3:4 |
pairs |
matrix with rows of indeces (two-columns) for the pairs considered in the pairwise composite score, useful for case-control sampling when marginal is known. |
dim.theta |
dimension of the theta parameter for pairs situation. |
numDeriv.method |
uses simple to speed up things and second derivative not so important. |
additive.gamma.sum |
for two.stage=0, this is specification of the lamtot in the models via a matrix that is multiplied onto the parameters theta (dimensions=(number random effects x number of theta parameters), when null then sums all parameters. |
var.par |
is 1 for the default parametrization with the variances of the random effects,
var.par=0 specifies that the |
no.opt |
for not optimizng |
... |
Additional arguments to maximizer NR of lava. and ascertained sampling |
Author(s)
Thomas Scheike
References
Twostage estimation of additive gamma frailty models for survival data. Scheike (2019), work in progress
Shih and Louis (1995) Inference on the association parameter in copula models for bivariate survival data, Biometrics, (1995).
Glidden (2000), A Two-Stage estimator of the dependence parameter for the Clayton Oakes model, LIDA, (2000).
Measuring early or late dependence for bivariate twin data Scheike, Holst, Hjelmborg (2015), LIDA
Estimating heritability for cause specific mortality based on twins studies Scheike, Holst, Hjelmborg (2014), LIDA
Additive Gamma frailty models for competing risks data, Biometrics (2015) Eriksson and Scheike (2015),
Examples
data(diabetes)
# Marginal Cox model with treat as covariate
margph <- phreg(Surv(time,status)~treat+cluster(id),data=diabetes)
### Clayton-Oakes, MLE
fitco1<-twostageMLE(margph,data=diabetes,theta=1.0)
summary(fitco1)
### Plackett model
mph <- phreg(Surv(time,status)~treat+cluster(id),data=diabetes)
fitp <- survival.twostage(mph,data=diabetes,theta=3.0,Nit=40,
clusters=diabetes$id,var.link=1,model="plackett")
summary(fitp)
### Clayton-Oakes
fitco2 <- survival.twostage(mph,data=diabetes,theta=0.0,detail=0,
clusters=diabetes$id,var.link=1,model="clayton.oakes")
summary(fitco2)
fitco3 <- survival.twostage(margph,data=diabetes,theta=1.0,detail=0,
clusters=diabetes$id,var.link=0,model="clayton.oakes")
summary(fitco3)
### without covariates but with stratafied
marg <- phreg(Surv(time,status)~+strata(treat)+cluster(id),data=diabetes)
fitpa <- survival.twostage(marg,data=diabetes,theta=1.0,
clusters=diabetes$id,model="clayton.oakes")
summary(fitpa)
fitcoa <- survival.twostage(marg,data=diabetes,theta=1.0,clusters=diabetes$id,
model="clayton.oakes")
summary(fitcoa)
### Piecewise constant cross hazards ratio modelling
########################################################
d <- subset(simClaytonOakes(2000,2,0.5,0,stoptime=2,left=0),!truncated)
udp <- piecewise.twostage(c(0,0.5,2),data=d,method="optimize",
id="cluster",timevar="time",
status="status",model="clayton.oakes",silent=0)
summary(udp)
## Reduce Ex.Timings
### Same model using the strata option, a bit slower
########################################################
## makes the survival pieces for different areas in the plane
##ud1=surv.boxarea(c(0,0),c(0.5,0.5),data=d,id="cluster",timevar="time",status="status")
##ud2=surv.boxarea(c(0,0.5),c(0.5,2),data=d,id="cluster",timevar="time",status="status")
##ud3=surv.boxarea(c(0.5,0),c(2,0.5),data=d,id="cluster",timevar="time",status="status")
##ud4=surv.boxarea(c(0.5,0.5),c(2,2),data=d,id="cluster",timevar="time",status="status")
## everything done in one call
ud <- piecewise.data(c(0,0.5,2),data=d,timevar="time",status="status",id="cluster")
ud$strata <- factor(ud$strata);
ud$intstrata <- factor(ud$intstrata)
## makes strata specific id variable to identify pairs within strata
## se's computed based on the id variable across strata "cluster"
ud$idstrata <- ud$id+(as.numeric(ud$strata)-1)*2000
marg2 <- timereg::aalen(Surv(boxtime,status)~-1+factor(num):factor(intstrata),
data=ud,n.sim=0,robust=0)
tdes <- model.matrix(~-1+factor(strata),data=ud)
fitp2 <- survival.twostage(marg2,data=ud,se.clusters=ud$cluster,clusters=ud$idstrata,
model="clayton.oakes",theta.des=tdes,step=0.5)
summary(fitp2)
### now fitting the model with symmetry, i.e. strata 2 and 3 same effect
ud$stratas <- ud$strata;
ud$stratas[ud$strata=="0.5-2,0-0.5"] <- "0-0.5,0.5-2"
tdes2 <- model.matrix(~-1+factor(stratas),data=ud)
fitp3 <- survival.twostage(marg2,data=ud,clusters=ud$idstrata,se.cluster=ud$cluster,
model="clayton.oakes",theta.des=tdes2,step=0.5)
summary(fitp3)
### same model using strata option, a bit slower
fitp4 <- survival.twostage(marg2,data=ud,clusters=ud$cluster,se.cluster=ud$cluster,
model="clayton.oakes",theta.des=tdes2,step=0.5,strata=ud$strata)
summary(fitp4)
## Reduce Ex.Timings
### structured random effects model additive gamma ACE
### simulate structured two-stage additive gamma ACE model
data <- simClaytonOakes.twin.ace(4000,2,1,0,3)
out <- twin.polygen.design(data,id="cluster")
pardes <- out$pardes
pardes
des.rv <- out$des.rv
head(des.rv)
aa <- phreg(Surv(time,status)~x+cluster(cluster),data=data,robust=0)
ts <- survival.twostage(aa,data=data,clusters=data$cluster,detail=0,
theta=c(2,1),var.link=0,step=0.5,
random.design=des.rv,theta.des=pardes)
summary(ts)
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.