mets (version 0.1-8)

cor.cif: 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, times = NULL, cause1 = 1,
    cause2 = 1, cens.code = 0, cens.model = "KM", Nit = 40,
    detail = 0, clusters = NULL, theta = NULL,
    theta.des = NULL, step = 1, sym = 0, weights = NULL,
    score.method = "nlminb", same.cens = FALSE,
    censoring.probs = NULL, silent = 1, ...)

Arguments

cif

a model object from the 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.

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.

score.method

"nlminb", can also use "fisher-scoring".

same.cens

if true then censoring within clusters are assumed to be the same variable, default is independent censoring.

censoring.probs

if cens.model is "user.weights" these probabilities are used for the bivariate censoring dist.

silent

1 to suppress output about convergence related issues.

...

Not used.

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.

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 $\theta^T z$.

References

Cross odds ratio Modelling of dependence for Multivariate Competing Risks Data, Scheike and Sun (2010), work in progress.

A Semiparametric Random Effects Model for Multivariate Competing Risks Data, Scheike, Zhang, Sun, Jensen (2010), Biometrika.

Examples

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<-comp.risk(Surv(time,cause>0)~+1+cluster(id),data=multcif,causeS=1,
               multcif$cause,n.sim=0,times=times,model="fg",max.clust=NULL)
add2<-comp.risk(Surv(time,cause>0)~+1+cluster(id),data=multcif,causeS=2,
               multcif$cause,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
###########################################################
#functd<-function(theta,t,x) { xt=theta[1]+theta[2]*(t-0.5); return(xt) };
#dfunctd<-function(theta,t,x) { return(c(x[1],(t-0.5))) };

#library(compiler) # using the compiler library to speed up things
#f=cmpfun(functd)
#df=cmpfun(dfunctd)
#out4<-cor.cif(add,data=multcif,multcif$cause,
#parfunc=f,dparfunc=df,
#cause1=1,cause2=1,cens.model="KM",clusters=multcif$id,theta=log(2+1),
#theta.des=theta.des,colnames=c("intercept","slope"))
#summary(out4)

###out4<-cor.cif(add,data=multcif,parfunc=functd,dparfunc=dfunctd,
###             cause1=1,cause2=1,cens.model="KM",theta=log(2+1),
###             theta.des=theta.des,colnames=c("intercept","slope"),dimpar=2)
###summary(out4)
## no indication of timetrend in cross-odds-ratio