pssm (version 1.1.1)

pssm: Fits a joint piecewise exponential model for progression and survival

Description

'pssm' fits a proportional hazards model where the underlying hazard of time to progression and subsequent survival are both piecewise constant. The hazard from progression to death is different for each interval for which the hazard of progression is constant. The covariates for progression and death after progression may be different. Time to progression is interval censored while time to death is right censored. Patients who die must have a progression interval with a right endoint that is at or before the death time.

Usage

pssm(progr, survv, dat, intervals = 5, start = NULL, rescale = 1, prior=NULL)

Arguments

progr

a formula object of the form Surv(time0,time1)~covariates for the time to progression, if NULL it fits a piecewise exponential model for survival time only. The progression time is assumed to be interval censored between time0 and time1. If progression does not occur then time1=NA.

survv

a formula object of the form Surv(time,cns)~covariates for time from progression to death, if NULL a model for time to progression is fit. The code for "cns" is 1=dead, 0=alive.

dat

A data frame with the data used in the estimation

intervals

An integer indicating the number of intervals in the time to progression or survival model. If both progr and survv are present than intervals is the number of intervals for the progession model. The survival model will have intervals*(intervals+1)/2 hazard parameters. If the model doesn't converge the number of intervals will be reduced by the program until convergence occurs.

start

starting values for the parameter vector, suppose intervals=m and there are \(n_1\) progression covariates and \(n_2\) survival covariates then the parameter vector will be of length, \(m+m(m+1)/2+n_1+n_2\) the survival covariates are ordered by progression interval i.e the first \(m\), are survival intervals for patients who progressed between time 0 and 1,the next \(m-1\) or for patients who progressed between time 1 and 2,… The first \(m*(m+1)/2\) elements are the log-survival hazard, the next \(m\) the log-progression hazard followed by the progression covariate vector followed by the survival covariate vector. If NULL the starting values are estimated.

rescale

A number that will multiply the survival and progression times before processing. This will be changed by the program if the maximum survival or progression time is greater than \(m r\).

prior

A vector of prior values for the covariates affecting the hazards, set to 0 if NULL.

Value

An S4 pssm.object containing the estimated parameters, their standard errors, their variance covariance matrix, and details of the model that was fit. The generic functions plot, summary and print are defined for the object.

References

Assessing survival benefit when treatment delays disease progression DA Schoenfeld, DM Finkelstein Clinical Trials 13 (3), 352-357

See Also

pssm-class, pssm-package, pssm.generate.data, pssm.object, pssm.simulate, pssm.survivalcurv, plot-methods, pssm.power pssm.noninferiority.boundary

Examples

# NOT RUN {
##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.
#generate data
set.seed(359)
u<-pssm.generate.data(theta1=.5,theta2=0,phaz.progression=rep(log(-log(.3)/4),5),
phaz.survival=rep(log(-log(.2)/4),15),accrual=2,followup=2.9,m=5,n=100,times=c(.8,2.1,3.4))
#estimate based on joint model
ps<-pssm(surv(tprog0,tprog1)~rx,surv(tdeath,cdeath)~rx,u,intervals=3,rescale=1)
summary(ps)
plot(ps,type='survival',cov1=matrix(c(1,0),2,1),cov2=matrix(c(1,0),2,1))
plot(ps)
plot(ps,type='progression',cov1=matrix(c(1,0),2,1),cov2=matrix(c(1,0),2,1))
#estimate time to progression only (tumor free survival)
ps1=pssm(surv(tprog0,tprog1)~rx,NULL,u,intervals=3,rescale=1)
summary(ps1)
plot(ps1)
plot(ps1,type='progression',cov1=matrix(c(1,0),2,1),cov2=matrix(c(1,0),2,1))
#estimate survival only
ps2=pssm(NULL,surv(tdeath,cdeath)~rx,u,intervals=3,rescale=1)
summary(ps2)
plot(ps2)
plot(ps2,type='survival',cov1=matrix(c(1,0),2,1),cov2=matrix(c(1,0),2,1))
# }