#
Estimates P(TL t0, Z), i.e. given discrete covariate.

### Description

This function calculates the probability that the an individual has the event of interest before t0 + tau given the discrete covariate and given the event has not yet occurred and the individual is still at risk at time t0; this estimated probability does not incorporate any information about the short term event information.

### Usage

1 | ```
Prob.Covariate(t0, tau, data, weight = NULL, short = TRUE, newdata = NULL)
``` |

### Arguments

`t0` |
the landmark time. |

`tau` |
the residual survival time for which probabilities are calculated. Specifically, this function estimates the probability that the an individual has the event of interest before t0 + tau given the event has not yet occurred and the individual is still at risk at time t0. |

`data` |
n by k matrix, where k =3 or k=5. A data matrix where the first column is XL = min(TL, C) where TL is the time of the long term event, C is the censoring time, and the second column is DL =1*(TL<C). If short term event information is included in this dataset then the third column is XS = min(TS, C) where TS is the time of the short term event, C is the censoring time, and the fourth column is DS =1*(TS<C), and the fifth column is the covariate. If short term event information is not included then the third column is the covariates (see "short" parameter). These are the data used to calculate the estimated probabilities. |

`weight` |
an optional weight to be incorporated in all estimation. |

`short` |
logical value indicating whether data includes short term event information. Should be TRUE if short term XS and DS are includes as third and fourth columns of data matrix meaning that the covariates is in the fifth column, FALSE if not meaning that the covariate is in the third column. Default is TRUE. |

`newdata` |
n by k matrix, where k =3 or k=5. A data matrix where the first column is XL = min(TL, C) where TL is the time of the long term event, C is the censoring time, and the second column is DL =1*(TL<C), and the last column (either 3rd or 5th) contains covariate values. Predicted probabilities are estimated for these data. |

### Value

`Prob` |
matrix of estimated probability for each value of the covariate; first column shows all covariate values and second column contains predicted probability at that covariate value |

`data` |
the data matrix with an additional column with the estimated individual probabilities; note that the predicted probability is NA if TL <t0 since it is only defined for individuals with TL> t0 |

`newdata` |
the newdata matrix with an additional column with the estimated individual probabilities; note that the predicted probability is NA if TL <t0 since it is only defined for individuals with TL> t0; if newdata is not supplied then this returns NULL |

### Author(s)

Layla Parast

### References

Parast, Layla, Su-Chun Cheng, and Tianxi Cai. Incorporating short-term outcome information to predict long-term survival with discrete markers. Biometrical Journal 53.2 (2011): 294-307.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
data(data_example_landpred)
t0=2
tau = 8
Prob.Covariate(t0=t0,tau=tau,data=data_example_landpred)
out = Prob.Covariate(t0=t0,tau=tau,data=data_example_landpred)
out$Prob
out$data
newdata = matrix(c(1,1,1, 3,0,1, 4,1,1, 10,1,0, 11,0,1), ncol = 3, byrow=TRUE)
out = Prob.Covariate(t0=t0,tau=tau,data=data_example_landpred,newdata=newdata)
out$Prob
out$newdata
``` |