| cor.cif {mets} | R Documentation |
Cross-odds-ratio, OR or RR risk regression for competing risks
Description
Fits a parametric model for the log-cross-odds-ratio for the
predictive effect of for the cumulative incidence curves for T_1
experiencing cause i given that T_2 has experienced a cause k :
\log(COR(i|k)) = h(\theta,z_1,i,z_2,k,t)=_{default} \theta^T z =
with the log cross odds ratio being
COR(i|k) =
\frac{O(T_1 \leq t,cause_1=i | T_2 \leq t,cause_2=k)}{
O(T_1 \leq t,cause_1=i)}
the conditional odds divided by the unconditional odds, with the odds being, respectively
O(T_1 \leq t,cause_1=i | T_2 \leq t,cause_1=k) =
\frac{
P_x(T_1 \leq t,cause_1=i | T_2 \leq t,cause_2=k)}{
P_x((T_1 \leq t,cause_1=i)^c | T_2 \leq t,cause_2=k)}
and
O(T_1 \leq t,cause_1=i) =
\frac{P_x(T_1 \leq t,cause_1=i )}{P_x((T_1 \leq t,cause_1=i)^c )}.
Here B^c is the complement event of B,
P_x is the distribution given covariates
(x are subject specific and z are cluster specific covariates), and
h() is a function that is the simple identity
\theta^T z by default.
Usage
cor.cif(
cif,
data,
cause = NULL,
times = NULL,
cause1 = 1,
cause2 = 1,
cens.code = NULL,
cens.model = "KM",
Nit = 40,
detail = 0,
clusters = NULL,
theta = NULL,
theta.des = NULL,
step = 1,
sym = 0,
weights = NULL,
par.func = NULL,
dpar.func = NULL,
dimpar = NULL,
score.method = "nlminb",
same.cens = FALSE,
censoring.weights = NULL,
silent = 1,
...
)
Arguments
cif |
a model object from the timereg::comp.risk function with the marginal cumulative incidence of cause1, i.e., the event of interest, and whose odds the comparision is compared to the conditional odds given cause2 |
data |
a data.frame with the variables. |
cause |
specifies the causes related to the death times, the value cens.code is the censoring value. When missing it comes from marginal cif. |
times |
time-vector that specifies the times used for the estimating euqations for the cross-odds-ratio estimation. |
cause1 |
specificies the cause considered. |
cause2 |
specificies the cause that is conditioned on. |
cens.code |
specificies the code for the censoring if NULL then uses the one from the marginal cif model. |
cens.model |
specified which model to use for the ICPW, KM is Kaplan-Meier alternatively it may be "cox" |
Nit |
number of iterations for Newton-Raphson algorithm. |
detail |
if 0 no details are printed during iterations, if 1 details are given. |
clusters |
specifies the cluster structure. |
theta |
specifies starting values for the cross-odds-ratio parameters of the model. |
theta.des |
specifies a regression design for the cross-odds-ratio parameters. |
step |
specifies the step size for the Newton-Raphson algorithm. |
sym |
specifies if symmetry is used in the model. |
weights |
weights for estimating equations. |
par.func |
parfunc |
dpar.func |
dparfunc |
dimpar |
dimpar |
score.method |
"nlminb", can also use "nr". |
same.cens |
if true then censoring within clusters are assumed to be the same variable, default is independent censoring. |
censoring.weights |
these probabilities are used for the bivariate censoring dist. |
silent |
1 to suppress output about convergence related issues. |
... |
Not used. |
Details
The OR dependence measure is given by
OR(i,k) =
\log (
\frac{O(T_1 \leq t,cause_1=i | T_2 \leq t,cause_2=k)}{
O(T_1 \leq t,cause_1=i) | T_2 \leq t,cause_2=k)}
This measure is numerically more stabile than the COR measure, and is symetric in i,k.
The RR dependence measure is given by
RR(i,k) =
\log (
\frac{P(T_1 \leq t,cause_1=i , T_2 \leq t,cause_2=k)}{
P(T_1 \leq t,cause_1=i) P(T_2 \leq t,cause_2=k)}
This measure is numerically more stabile than the COR measure, and is symetric in i,k.
The model is fitted under symmetry (sym=1), i.e., such that it is assumed
that T_1 and T_2 can be interchanged and leads to
the same cross-odd-ratio (i.e.
COR(i|k) = COR(k|i)),
as would be expected for twins
or without symmetry as might be the case with mothers and daughters (sym=0).
h() may be specified as an R-function of the parameters,
see example below, but the default is that it is simply \theta^T z.
Value
returns an object of type 'cor'. With the following arguments:
theta |
estimate of proportional odds parameters of model. |
var.theta |
variance for gamma. |
hess |
the derivative of the used score. |
score |
scores at final stage. |
score |
scores at final stage. |
theta.iid |
matrix of iid decomposition of parametric effects. |
Author(s)
Thomas Scheike
References
Cross odds ratio Modelling of dependence for Multivariate Competing Risks Data, Scheike and Sun (2012), Biostatistics.
A Semiparametric Random Effects Model for Multivariate Competing Risks Data, Scheike, Zhang, Sun, Jensen (2010), Biometrika.
Examples
library("timereg")
data(multcif);
multcif$cause[multcif$cause==0] <- 2
zyg <- rep(rbinom(200,1,0.5),each=2)
theta.des <- model.matrix(~-1+factor(zyg))
times=seq(0.05,1,by=0.05) # to speed up computations use only these time-points
add <- timereg::comp.risk(Event(time,cause)~+1+cluster(id),data=multcif,cause=1,
n.sim=0,times=times,model="fg",max.clust=NULL)
add2 <- timereg::comp.risk(Event(time,cause)~+1+cluster(id),data=multcif,cause=2,
n.sim=0,times=times,model="fg",max.clust=NULL)
out1 <- cor.cif(add,data=multcif,cause1=1,cause2=1)
summary(out1)
out2 <- cor.cif(add,data=multcif,cause1=1,cause2=1,theta.des=theta.des)
summary(out2)
##out3 <- cor.cif(add,data=multcif,cause1=1,cause2=2,cif2=add2)
##summary(out3)
###########################################################
# investigating further models using parfunc and dparfunc
###########################################################
## Reduce Ex.Timings
set.seed(100)
prt<-simnordic.random(2000,cordz=2,cormz=5)
prt$status <-prt$cause
table(prt$status)
times <- seq(40,100,by=10)
cifmod <- timereg::comp.risk(Event(time,cause)~+1+cluster(id),data=prt,
cause=1,n.sim=0,
times=times,conservative=1,max.clust=NULL,model="fg")
theta.des <- model.matrix(~-1+factor(zyg),data=prt)
parfunc <- function(par,t,pardes)
{
par <- pardes %*% c(par[1],par[2]) +
pardes %*% c( par[3]*(t-60)/12,par[4]*(t-60)/12)
par
}
head(parfunc(c(0.1,1,0.1,1),50,theta.des))
dparfunc <- function(par,t,pardes)
{
dpar <- cbind(pardes, t(t(pardes) * c( (t-60)/12,(t-60)/12)) )
dpar
}
head(dparfunc(c(0.1,1,0.1,1),50,theta.des))
names(prt)
or1 <- or.cif(cifmod,data=prt,cause1=1,cause2=1,theta.des=theta.des,
same.cens=TRUE,theta=c(0.6,1.1,0.1,0.1),
par.func=parfunc,dpar.func=dparfunc,dimpar=4,
score.method="nr",detail=1)
summary(or1)
cor1 <- cor.cif(cifmod,data=prt,cause1=1,cause2=1,theta.des=theta.des,
same.cens=TRUE,theta=c(0.5,1.0,0.1,0.1),
par.func=parfunc,dpar.func=dparfunc,dimpar=4,
control=list(trace=TRUE),detail=1)
summary(cor1)
### piecewise contant OR model
gparfunc <- function(par,t,pardes)
{
cuts <- c(0,80,90,120)
grop <- diff(t<cuts)
paru <- (pardes[,1]==1) * sum(grop*par[1:3]) +
(pardes[,2]==1) * sum(grop*par[4:6])
paru
}
dgparfunc <- function(par,t,pardes)
{
cuts <- c(0,80,90,120)
grop <- diff(t<cuts)
par1 <- matrix(c(grop),nrow(pardes),length(grop),byrow=TRUE)
parmz <- par1* (pardes[,1]==1)
pardz <- (pardes[,2]==1) * par1
dpar <- cbind( parmz,pardz)
dpar
}
head(dgparfunc(rep(0.1,6),50,theta.des))
head(gparfunc(rep(0.1,6),50,theta.des))
or1g <- or.cif(cifmod,data=prt,cause1=1,cause2=1,
theta.des=theta.des, same.cens=TRUE,
par.func=gparfunc,dpar.func=dgparfunc,
dimpar=6,score.method="nr",detail=1)
summary(or1g)
names(or1g)
head(or1g$theta.iid)