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 ≤q t, cause=1 | x,z) = P_1(t,x,z) = 1- exp( -x^T A(t) - t z^T β)
*

1 2 3 4 5 6 7 | ```
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, exp.link = 0,
score.method = "fisher.scoring", entry = NULL, estimator = 1,
trunkp = 1, admin.cens = NULL, random.design = NULL, ...)
``` |

`cif` |
a model object from the 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 |

`exp.link` |
if exp.link=1 then var is on log-scale. |

`score.method` |
default uses "nlminb" optimzer, alternatively, use the "fisher-scoring" 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. |

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 *(λ_1,...,λ_d)*. By construction
subjects 1's random effect are Gamma distributed with
mean *λ_1/v_1^T λ*
and variance *λ_1/(v_1^T λ)^2*. Note that the random effect
*v_1^T (Z_1,...,Z_d)* has mean 1 and variance *1/(v_1^T λ)*.

The parameters *(λ_1,...,λ_d)*
are related to the parameters of the model
by a regression construction *pard* (d x k), that links the *d*
*λ* parameters
with the (k) underlying *θ* parameters

*
λ = pard θ
*

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. |

Thomas Scheike

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | ```
## Reduce Ex.Timings
d <- simnordic.random(5000,delayed=TRUE,
cordz=0.5,cormz=2,lam0=0.3,country=TRUE)
times <- seq(50,90,by=10)
addm<-comp.risk(Event(time,cause)~const(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(0.4,4),step=0.5,
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$zyg=="DZ"
n <- nrow(d)
### random effects for each cluster
des.rv <- cbind(mm,(zygbin==1)*rep(c(1,0)),(zygbin==1)*rep(c(0,1)),1)
### design making parameters half the variance for dizygotic components
pardes <- rbind(c(1,0), c(0.5,0),c(0.5,0), c(0.5,0), c(0,1))
outacem <-Grandom.cif(addm,data=d,cause1=1,cause2=1,
same.cens=TRUE,theta=c(0.7,-0.3),
step=1.0,theta.des=pardes,random.design=des.rv)
summary(outacem)
## genetic variance is
exp(outacem$theta[1])/sum(exp(outacem$theta))^2
``` |

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