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

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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

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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

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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