TPmsm (version 1.2.12)

dgpTP: Generates bivariate survival data

Description

Generates bivariate censored gap times from some known copula functions.

Usage

dgpTP(n, corr, dist, dist.par, model.cens, cens.par, state2.prob)

Value

An object of class ‘survTP’.

Arguments

n

Sample size.

corr

Correlation parameter. Possible values for the bivariate exponential distribution are between -1 and 1 (0 for independency). Any value between 0 (not included) and 1 (1 for independency) is accepted for the bivariate Weibull distribution.

dist

Distribution. Possible bivariate distributions are “exponential” and “weibull”.

dist.par

Vector of parameters for the allowed distributions. Two (scale) parameters for the bivariate exponential distribution and four (2 location parameters and 2 scale parameters) for the bivariate Weibull distribution. See details below.

model.cens

Model for censorship. Possible values are “uniform” and “exponential”.

cens.par

Parameter for the censorship distribution. For censure model equal to “exponential” the argument cens.par must be greater than 0. For censure model equal to “uniform” the argument must be greater or equal than 0.

state2.prob

The proportion of individuals that enter state 2.

Author

Artur Araújo, Javier Roca-Pardiñas and Luís Meira-Machado

Details

The bivariate exponential distribution, also known as Farlie-Gumbel-Morgenstern distribution is given by $$F(x,y)=F_1(x)F_2(y)[1+\alpha(1-F_1(x))(1-F_2(y))]$$ for \(x\ge0\) and \(y\ge0\). Where the marginal distribution functions \(F_1\) and \(F_2\) are exponential with scale parameters \(\theta_1\) and \(\theta_2\) and correlation parameter \(\alpha\), \(-1 \le \alpha \le 1\).

The bivariate Weibull distribution with two-parameter marginal distributions. It's survival function is given by $$S(x,y)=P(X>x,Y>y)=e^{-[(\frac{x}{\theta_1})^\frac{\beta_1}{\delta}+(\frac{y}{\theta_2})^\frac{\beta_2}{\delta}]^\delta}$$

Where \(0 < \delta \le 1\) and each marginal distribution has shape parameter \(\beta_i\) and a scale parameter \(\theta_i\), \(i = 1, 2\).

References

Araújo A, Meira-Machado L, Roca-Pardiñas J (2014). TPmsm: Estimation of the Transition Probabilities in 3-State Models. Journal of Statistical Software, 62(4), 1-29. tools:::Rd_expr_doi("10.18637/jss.v062.i04")

Devroye L. (1986). Non-Uniform Random Variate Generation, New York: Springer-Verlag.

Johnson M. E. (1987). Multivariate Statistical Simulation, John Wiley and Sons.

Johnson N., Kotz S. (1972). Distributions in statistics: continuous multivariate distributions, John Wiley and Sons.

Lu J., Bhattacharya G. (1990). Some new constructions of bivariate weibull models. Annals of Institute of Statistical Mathematics, 42(3), 543-559. tools:::Rd_expr_doi("10.1007/BF00049307")

Meira-Machado L., Faria S. (2014). A simulation study comparing modeling approaches in an illness-death multi-state model. Communications in Statistics - Simulation and Computation, 43(5), 929-946. tools:::Rd_expr_doi("10.1080/03610918.2012.718841")

Meira-Machado, L., Sestelo M. (2019). Estimation in the progressive illness-death model: a nonexhaustive review. Biometrical Journal, 61(2), 245–263. tools:::Rd_expr_doi("10.1002/bimj.201700200")

See Also

corrTP.

Examples

# Set the number of threads
nth <- setThreadsTP(2);

# Example for the bivariate Exponential distribution
dgpTP(n=100, corr=1, dist="exponential", dist.par=c(1, 1),
model.cens="uniform", cens.par=3, state2.prob=0.5);

# Example for the bivariate Weibull distribution
dgpTP(n=100, corr=1, dist="weibull", dist.par=c(2, 7, 2, 7),
model.cens="exponential", cens.par = 6, state2.prob=0.6);

# Restore the number of threads
setThreadsTP(nth);