PWEALL (version 1.3.0)

fourhr: A utility functon

Description

This will calculate the more complex integration

Usage

fourhr(t=seq(0,5,by=0.5),rate1=c(0,5,0.8),rate2=rate1,
                   rate3=c(0.1,0.2),rate4=rate2,tchange=c(0,3),eps=1.0e-2)

Value

fx

values

Arguments

t

A vector of time points

rate1

piecewise constant event rate

rate2

piecewise constant event rate

rate3

piecewise constant event rate

rate4

additional piecewise constant

tchange

a strictly increasing sequence of time points starting from zero at which event rate changes. The first element of tchange must be zero. The above rates and tchange must have the same length.

eps

tolerance

Author

Xiaodong Luo

Details

Let \(h_1,\ldots,h_4\) correspond to rate1,...,rate4, and \(H_1,\ldots,H_4\) be the corresponding survival functions. We calculate $$\int_0^t h_1(s)H_2(s)h_3(t-s)H_4(t-s)ds.$$

References

Luo et al. (2018) Design and monitoring of survival trials in complex scenarios, Statistics in Medicine <doi: https://doi.org/10.1002/sim.7975>.

See Also

rpwe

Examples

r1<-c(0.6,0.3)
r2<-c(0.6,0.6)
r3<-c(0.1,0.2)
r4<-c(0.5,0.4)
tchange<-c(0,1.75)
fourhrfun<-fourhr(t=seq(0,5,by=0.5),rate1=r1,rate2=r2,rate3=r3,
                 rate4=r4,tchange=c(0,3),eps=1.0e-2)
fourhrfun

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