# Generation of Cox Markov data from an illness-death model

### Description

Generation of Cox Markov data from an illness-death model.

### Usage

1 |

### Arguments

`n` |
Sample size. |

`model.cens` |
Model for censorship. Possible values are "uniform" and "exponential". |

`cens.par` |
Parameter for the censorship distribution. Must be greater than 0. |

`beta` |
Vector of three regression parameters for the three transitions: (beta_12,beta_13,beta_23). |

`covar` |
Parameter for generating the time-fixed covariate. An uniform distribution is used. |

`rate` |
Vector of dimension six: (shape1, scale1, shape2, scale2, shape3, scale3). A Weibull baseline hazard function is assumed (with two parameters) for each transition (see details below). |

### Details

The Weibull distribution with shape parameter *λ* and scale parameter *θ* has hazard function given by:

*α(t)=λθ t^{θ-1}*

### Value

An object with two classes, `data.frame`

and `CMM`

.
The data structure used for generating survival data from the Cox Markov Model (CMM) is similar as for the time-dependent Cox model (TDCM).
In this case the data structure has one more variable representing the transition (variable `trans`

).
`trans=1`

denotes the transition from State 1 to State 3 (without observing the intermediate event; State 2);
`trans=2`

denotes the transition from State 1 to State 2; and `trans=3`

denotes the transition from State 2 to State 3 (absorbing).

### Author(s)

Artur Araújo, Luís Meira Machado and Susana Faria

### References

Meira-Machado, L., Cadarso-Suárez, C., De Uña- Álvarez, J., Andersen, P.K. (2009). Multi-state models for the analysis of time to event data. Statistical Methods in Medical Research, 18(2):195-222.

Meira-Machado, L., Roca-Pardiñas, J. (2011). p3state.msm: Analyzing Survival Data from an Illness-Death Model. Journal of Statistical Software, 38(3): 1-18.

Therneau, T.M., Grambsch, P.M. (2000). Modelling survival data: Extending the Cox Model. New York: Springer.

### See Also

`genCPHM`

,
`genTDCM`

,
`genTHMM`

.

### Examples

1 2 3 4 5 6 7 8 9 10 | ```
cmmdata <- genCMM( n=1000, model.cens="uniform", cens.par=2.5, beta=c(2,1,-1),
covar=10, rate=c(1,5,1,5,1,5) )
head(cmmdata, n=20L)
library(survival)
fit_13<-coxph(Surv(start,stop,event)~covariate, data=cmmdata, subset=c(trans==1))
fit_13
fit_12<-coxph(Surv(start,stop,event)~covariate, data=cmmdata, subset=c(trans==2))
fit_12
fit_23<-coxph(Surv(start,stop,event)~covariate, data=cmmdata, subset=c(trans==3))
fit_23
``` |

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