This function calculates the AUC given the data (truth) and corresponding estimated probabilities; uses a continuity correction.

1 | ```
AUC.landmark(t0, tau, data, short = TRUE, weight=NULL)
``` |

`t0` |
the landmark time. |

`tau` |
the residual survival time of interest. |

`data` |
n by k matrix, where k = 4 or 6. 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), the second to last column is the covariate vector (can be NULL) and the last column is the estimated probability P(TL<t0+tau | TL>t0). |

`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, FALSE if not. Default is TRUE. |

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

`AUC.est` |
Estimated AUC |

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 | ```
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
AUC.landmark(t0=t0,tau=tau, data = out$data)
``` |

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