# U1.Clayton: Estimation of an association parameter via the... In Copula.surv: Analysis of Bivariate Survival Data Based on Copulas

 U1.Clayton R Documentation

## Estimation of an association parameter via the pseudo-likelihood

### Description

Estimate the association parameter of the Clayton copula using bivariate survival data. The estimator was derived by Clayton (1978) and reformulated by Emura, Lin and Wang (2010).

### Usage

```U1.Clayton(x.obs,y.obs,dx,dy,lower=0.001,upper=50,U.plot=TRUE)
```

### Arguments

 `x.obs` censored times for X `y.obs` censored times for Y `dx` censoring indicators for X `dy` censoring indicators for Y `lower` lower bound for the association parameter `upper` upper bound for the association parameter `U.plot` if TRUE, draw the plot of U_1(theta)

### Details

Details are seen from the references.

### Value

 `theta` association parameter `tau` Kendall's tau (=theta/(theta+2))

Takeshi Emura

### References

Clayton DG (1978). A model for association in bivariate life tables and its application to epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65: 141-51.

Emura T, Lin CW, Wang W (2010) A goodness-of-fit test for Archimedean copula models in the presence of right censoring, Compt Stat Data Anal 54: 3033-43

### Examples

```n=200
theta_true=2 ## association parameter ##
r1_true=1 ## hazard for X
r2_true=1 ## hazard for Y

set.seed(1)
V1=runif(n)
V2=runif(n)
X=-1/r1_true*log(1-V1)
W=(1-V1)^(-theta_true)
Y=1/theta_true/r2_true*log(  1-W+W*(1-V2)^(-theta_true/(theta_true+1))  )
C=runif(n,min=0,max=5)

x.obs=pmin(X,C)
y.obs=pmin(Y,C)
dx=X<=C
dy=Y<=C

U1.Clayton(x.obs,y.obs,dx,dy)

```

Copula.surv documentation built on March 18, 2022, 5:24 p.m.