Grandom.cif: Additive Random effects model for competing risks data for polygenetic modelling

Description

Fits a random effects model describing the dependence in the cumulative incidence curves for subjects within a cluster. Given the gamma distributed random effects it is assumed that the cumulative incidence curves are indpendent, and that the marginal cumulative incidence curves are on additive form $$ P(T \leq t, cause=1 | x,z) = P_1(t,x,z) = 1- exp( -x^T A(t) - t z^T \beta) $$

Usage

Grandom.cif(
  cif,
  data,
  cause = NULL,
  cif2 = NULL,
  times = NULL,
  cause1 = 1,
  cause2 = 1,
  cens.code = NULL,
  cens.model = "KM",
  Nit = 40,
  detail = 0,
  clusters = NULL,
  theta = NULL,
  theta.des = NULL,
  weights = NULL,
  step = 1,
  sym = 0,
  same.cens = FALSE,
  censoring.weights = NULL,
  silent = 1,
  var.link = 0,
  score.method = "nr",
  entry = NULL,
  estimator = 1,
  trunkp = 1,
  admin.cens = NULL,
  random.design = NULL,
  ...
)

Value

returns an object of type 'random.cif'. With the following arguments:

theta: estimate of parameters of model.
var.theta: variance for gamma.
hess: the derivative of the used score.
score: scores at final stage.
theta.iid: matrix of iid decomposition of parametric effects.

Arguments

cif: a model object from the timereg::comp.risk function with the marginal cumulative incidence of cause2, i.e., the event that is conditioned on, and whose odds the comparision is made with respect to
data: a data.frame with the variables.
cause: specifies the causes related to the death times, the value cens.code is the censoring value.
cif2: specificies model for cause2 if different from cause1.
times: time points
cause1: cause of first coordinate.
cause2: cause of second coordinate.
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.
weights: weights for score equations.
step: specifies the step size for the Newton-Raphson algorith.m
sym: 1 for symmetri and 0 otherwise
same.cens: if true then censoring within clusters are assumed to be the same variable, default is independent censoring.
censoring.weights: Censoring probabilities
silent: debug information
var.link: if var.link=1 then var is on log-scale.
score.method: default uses "nlminb" optimzer, alternatively, use the "nr" algorithm.
entry: entry-age in case of delayed entry. Then two causes must be given.
estimator: estimator
trunkp: gives probability of survival for delayed entry, and related to entry-ages given above.
admin.cens: Administrative censoring
random.design: specifies a regression design of 0/1's for the random effects.
...: extra arguments.

Author

Thomas Scheike

Details

We allow a regression structure for the indenpendent gamma distributed random effects and their variances that may depend on cluster covariates.

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 $\lambda_1/v_1^T \lambda$ and variance $\lambda_1/(v_1^T \lambda)^2$. Note that the random effect $v_1^T (Z_1,...,Z_d)$ has mean 1 and variance $1/(v_1^T \lambda)$.

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 $$ \lambda = pard \theta $$

References

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

Cross odds ratio Modelling of dependence for Multivariate Competing Risks Data, Scheike and Sun (2013), Biostatitistics.

Scheike, Holst, Hjelmborg (2014), LIDA, Estimating heritability for cause specific hazards based on twin data

Examples

Run this code

 ## Reduce Ex.Timings
 d <- simnordic.random(5000,delayed=TRUE,
       cordz=1.0,cormz=2,lam0=0.3,country=TRUE)
 times <- seq(50,90,by=10)
 addm <- timereg::comp.risk(Event(time,cause)~-1+factor(country)+cluster(id),data=d,
 times=times,cause=1,max.clust=NULL)

 ### making group indidcator 
 mm <- model.matrix(~-1+factor(zyg),d)

 out1m<-random.cif(addm,data=d,cause1=1,cause2=1,theta=1,
		   theta.des=mm,same.cens=TRUE)
 summary(out1m)
 
 ## this model can also be formulated as a random effects model 
 ## but with different parameters
 out2m<-Grandom.cif(addm,data=d,cause1=1,cause2=1,
		    theta=c(0.5,1),step=1.0,
		    random.design=mm,same.cens=TRUE)
 summary(out2m)
 1/out2m$theta
 out1m$theta
 
 ####################################################################
 ################### ACE modelling of twin data #####################
 ####################################################################
 ### assume that zygbin gives the zygosity of mono and dizygotic twins
 ### 0 for mono and 1 for dizygotic twins. We now formulate and AC model
 zygbin <- d$zyg=="DZ"

 n <- nrow(d)
 ### random effects for each cluster
 des.rv <- cbind(mm,(zygbin==1)*rep(c(1,0)),(zygbin==1)*rep(c(0,1)),1)
 ### design making parameters half the variance for dizygotic components
 pardes <- rbind(c(1,0), c(0.5,0),c(0.5,0), c(0.5,0), c(0,1))

 outacem <-Grandom.cif(addm,data=d,cause1=1,cause2=1,
		same.cens=TRUE,theta=c(0.35,0.15),
            step=1.0,theta.des=pardes,random.design=des.rv)
 summary(outacem)

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