#
Estimates P(TL t0, Z, min(TS, t0), I(TS<=t0)), i.e. given discrete covariate and TS information.

### Description

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

### Usage

1 | ```
Prob.Covariate.ShortEvent(t0, tau, data, weight = NULL, bandwidth = NULL, 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 5 matrix. 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 third column is XS = min(TS, C) where TS is the time of the short term event, C is the censoring time, the fourth column is DS =1*(TS<C), and the fifth column is the covariate. These are the data used to calculate the estimated probability. |

`weight` |
a weight to be incorporated in all estimation. |

`bandwidth` |
an optional bandwidth to be used in kernel smoothing; is not provided then function calculates an appropriate bandwidth using bw.nrd and then undersmoothing with c = .10 (See reference) |

`newdata` |
an optional n by 5 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 third column is XS = min(TS, C) where TS is the time of the short term event, C is the censoring time, the fourth column is DS =1*(TS<C), and the fifth column is the covariate. Predicted probabilities are estimated for these data. |

### 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 14 15 16 17 18 19 20 21 22 | ```
data(data_example_landpred)
t0=2
tau = 8
#note: computationally intensive command below
#Prob.Covariate.ShortEvent(t0=t0,tau=tau,data=data_example_landpred)
#out = Prob.Covariate.ShortEvent(t0=t0,tau=tau,data=data_example_landpred)
#out$data
#data.plot = out$data
#plot(data.plot$XS[data.plot$Z ==1], data.plot$Probability[data.plot$Z ==1],
#pch = 20, xlim = c(0,t0))
#points(data.plot$XS[data.plot$Z ==0], data.plot$Probability[data.plot$Z ==0],
#pch = 20, col = 2)
newdata = matrix(c(1,1,0.5,1,0,
3,0,1,1,1,
4,1,1.5,1,0,
10,1,5,1,0,
11,0,11,0,1), ncol = 5, byrow=TRUE)
#note: computationally intensive command below
#out = Prob.Covariate.ShortEvent(t0=t0,tau=tau,data=data_example_landpred,newdata=newdata)
#out$newdata
``` |