ovbeta {PWEALL}

calculate the overall log hazard ratio

Description

This will calculate the overall (log) hazard ratio accouting for staggered entry, delayed treatment effect, treatment crossover and loss to follow-up.

Usage

ovbeta(tfix=2.0,taur=5,u=c(1/taur,1/taur),ut=c(taur/2,taur),pi1=0.5,
       rate11=c(1,0.5),rate21=rate11,rate31=c(0.7,0.4),rate41=rate21,
       rate51=rate21,ratec1=c(0.5,0.6),
       rate10=rate11,rate20=rate10,rate30=rate31,rate40=rate20,
       rate50=rate20,ratec0=c(0.4,0.3),
       tchange=c(0,1),type1=1,type0=1,
       rp21=0.5,rp20=0.5,
       eps=1.0e-2,veps=1.0e-2,
       beta0=0,epsbeta=1.0e-4,iterbeta=25)

Arguments

tfix

The time point where the overall log hazard ratio is computed.

taur

Recruitment time

u

Piecewise constant recuitment rate

ut

Recruitment intervals

pi1

Allocation probability for the treatment group

rate11

Hazard before crossover for the treatment group

rate21

Hazard after crossover for the treatment group

rate31

Hazard for time to crossover for the treatment group

rate41

Hazard after crossover for the treatment group for complex case

rate51

Hazard after crossover for the treatment group for complex case

ratec1

Hazard for time to censoring for the treatment group

rate10

Hazard before crossover for the control group

rate20

Hazard after crossover for the control group

rate30

Hazard for time to crossover for the control group

rate40

Hazard after crossover for the control group for complex case

rate50

Hazard after crossover for the control group for complex case

ratec0

Hazard for time to censoring for the control group

tchange

A strictly increasing sequence of time points at which the event rates changes. The first element of tchange must be zero. It must have the same length as rate11, rate21, rate31, etc.

type1

Type of crossover in the treatment group

type0

Type of crossover in the control group

rp21

re-randomization prob in the treatment group

rp20

re-randomization prob in the control group

eps

A small number representing the error tolerance when calculating the utility function

\Phi_l(x)=\frac{\int_0^x s^l e^{-s}ds}{x^{l+1}}

with l=0,1,2.

veps

A small number representing the error tolerance when calculating the Fisher information.

beta0

The starting value of the Newton-Raphson iterative procedure.

epsbeta

Absolute tolerance when calculating the overall log hazard ratio.

iterbeta

Maximum number of iterations when calculating the overall log hazard ratio.

Details

The hazard functions corresponding to rate11,...,rate51,ratec1, rate10,...,rate50,ratec0 are all piecewise constant function taking the form \lambda(t)=\sum_{j=1}^m \lambda_j I(t_{j-1}\le t<t_j), where \lambda_1,\ldots,\lambda_m are the corresponding elements of the rates and t_0,\ldots,t_{m-1} are the corresponding elements of tchange, t_m=\infty. Note that all the rates must have the same tchange.

Value

b1

The overall log hazard ratio

hr

The overall hazard ratio

err

Error at the last iterative step

iter

Number of iterations performed

bhist

The overall log hazard ratio at each step

xnum

The expected score function at each step

xdenom

The Fisher information at each step

atsupp

The grids used to cut the interval [0,tfix] in order to approximate the Fisher information

Note

Version 1.0 (7/19/2016)

Author(s)

Xiaodong Luo

References

Luo, et al. (2017)

See Also

pwe,rpwe,qpwe

Examples

taur<-1.2
u<-c(1/taur,1/taur)
ut<-c(taur/2,taur)
r11<-c(1,0.5)
r21<-c(0.5,0.8)
r31<-c(0.7,0.4)
r41<-r51<-r21
rc1<-c(0.5,0.6)
r10<-c(1,0.7)
r20<-c(0.5,1)
r30<-c(0.3,0.4)
r40<-r50<-r20
rc0<-c(0.2,0.4)
getbeta<-ovbeta(tfix=2.0,taur=taur,u=u,ut=ut,pi1=0.5,
       rate11=r11,rate21=r21,rate31=r31,rate41=r41,rate51=r51,ratec1=rc1,
       rate10=r10,rate20=r20,rate30=r30,rate40=r40,rate50=r50,ratec0=rc0,
       tchange=c(0,1),type1=1,type0=1,eps=1.0e-2,veps=1.0e-2,beta0=0,epsbeta=1.0e-4,iterbeta=25)
getbeta$b1