This function calculates the probability that 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; this estimated probability does not incorporate any information about the covariate or short term event information.

1 |

`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 >=2. 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). These are the data used to calculate the estimated probability. |

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

`newdata` |
an optional n by k matrix, where k >=2. 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). Predicted probabilities are estimated for these data. |

`Prob` |
Estimated 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; this estimated probability does not incorporate any information about the covariate or short term event information. |

`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 |

Layla Parast

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.

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

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