simulation.pwexp: Simulate data following piece-wise exponential distribution...
In phe9480/rgs: What the Package Does (One Line, Title Case)

Description Usage Arguments Value Examples

Simulate Randomized two-arm trial data with the following characteristics: (1) randomization time (entry time) is generated according to the specified non-uniform accrual pattern, i.e. the cumulative recruitment at calendar time t is (t/A)^w with weight w and enrollment complete in A months. w = 1 means uniform enrollment, which is usually not realistic due to graduate sites activation process. (2) Survival time follows piece-wise exponential distribution for each arm. (3) N total patients with r:1 randomization ratio (4) Random drop off can be incorporated into the censoring process. (5) Data cutoff dates are determined by specified vector of target events for all analyses. (6) A dataset is generated for each analysis according to the specified number of target events. Multiple analyses can be specified according to the vector of targetEvents, eg, targetEvents = c(100, 200, 300) defines 3 analyses at 100, 200, and 300 events separately.

simulation.pwexp(
  nSim = 100,
  N = 600,
  A = 21,
  w = 1.5,
  r = 1,
  lam0 = log(2)/12,
  lam1 = log(2)/12 * 0.65,
  cuts = NULL,
  drop0 = 0,
  drop1 = 0,
  targetEvents = c(400, 500),
  DCO = NULL
)

`nSim`	Number of trials
`N`	Total number patients in two arms.
`A`	Total accrual period in months
`w`	Weight parameter in cumulative enrollment pattern. The cumulative enrollment at month t is (t / A)^w, eg, at month 6, the enrollment is N*(6/24)^2 = N/16 for 24 months planned accrual period.
`r`	Randomization ratio r:1, where r refers to the experimental arm, eg, r=2 in 2:1 ratio
`lam0`	Hazard rates for control arm of intervals defined by cuts; for exponential(lam0) distribution, lam0 = log(2) / median;
`lam1`	Hazard rates for experimental arm for intervals; for exponential(lam1) distribution, lam1 = log(2) / median; For delayed effect under H1, lam1 is a vector (below).
`cuts`	Timepoints to form intervals for piecewise exponential distribution. For example, experimental arm has hr = 0.6 after delay, then cuts = 6, and lam0 = log(2) / m0 or lam0 = rep(log(2) / m0, 2), lam1 = c(log(2)/m0, log(2)/m0hr). treatment after 24 mo, so its hazard decreases 20%. Then, lam0 = c(log(2)/m0, log(2)/m0, log(2)/m00.8), lam1 = c(log(2)/m0, log(2)/m0hr, log(2)/m0hr), and cuts = c(6, 24), which forms 3 intervals (0, 6), (6, 24), (24, infinity)
`drop0`	Drop Off rate per month, eg, 3% every year for control arm, then drop0=0.03/12
`drop1`	Drop Off rate per month, eg, 1%, for experimental arm
`targetEvents`	A vector of target events is used to determine DCOs. For example, 397 target events are used to determine IA DCO; and 496 events are used to determine the FA cutoff.
`DCO`	A vector of data cut-off time in months, calculated from first subject in. Default NULL. The date cut-off times will be determined by targetEvents. If provided, then the targetEvents will be ignored.

An object with a dataframe for each analysis including the following variables:

sim: sequence number of simulated dataset;
treatment: treatment group with values of "control" and "experimental"
enterTime: Time of randomization in calendar time
calendarTime: the time when event/censoring occurred in calendar time
survTime: Survival time for analysis, = calendarTime - enterTime
cnsr: censor status (0=event; 1=censor) before administrative censoring due to data cut
calendarCutOff: Data CutOff Time (DCO);
survTimeCut: Survival time after cut
cnsrCut: Censor status after cut

#Example (1): Simulate 10 samples from proportional hazards scenario. 
#Total 600 pts, 1:1 randomization, control median OS 12 mo; 
#HR = 0.65, enrollment 24 months, weight 1.5, no drop offs; 
#IA and FA are performed at 400 and 500 events respectively.

sim.ph = simulation.pwexp(nSim=10, N = 600, A = 24, w=1.5, r=1, lam0=log(2)/12, lam1= log(2)/12*0.65, cuts=NULL, drop0= 0, drop1= 0, targetEvents = c(400, 500))
km.IA<-survival::survfit(survival::Surv(survTimeCut,1-cnsrCut)~treatment,data=sim.ph[[1]][sim==1,])
plot(km.IA,xlab="Month Since Randomization",ylab="Survival",lty=1:2,xlim=c(0,36))
km.FA<-survival::survfit(survival::Surv(survTimeCut,1-cnsrCut)~treatment,data=sim.ph[[2]][sim==1,])
plot(km.FA,xlab="Month Since Randomization",ylab="Survival",lty=1:2,xlim=c(0,36))

#Example (2): Simulate 10 samples with delayed effect at month 6;
#Total 600 pts, 1:1 randomization, control median OS 12 mo; 
#HR = 0.65, enrollment 24 months, weight 1.5, no drop offs; 
#IA and FA are performed at 400 and 500 events respectively.

sim.delay6 = simulation.pwexp(nSim=10, N = 600, A = 24, w=1.5, r=1, lam0=log(2)/12, lam1= c(log(2)/12,log(2)/12*0.65), cuts=6, drop0= 0, drop1= 0, targetEvents = c(400, 500))
km.IA<-survival::survfit(survival::Surv(survTimeCut,1-cnsrCut)~treatment,data=sim.delay6[[1]][sim==1,])
plot(km.IA,xlab="Month Since Randomization",ylab="Survival",lty=1:2,xlim=c(0,36))
km.FA<-survival::survfit(survival::Surv(survTimeCut,1-cnsrCut)~treatment,data= sim.delay6[[2]][sim==1,])
plot(km.FA,xlab="Month Since Randomization",ylab="Survival",lty=1:2,xlim=c(0,36))

#Example (3): Simulate 10 samples with delayed effect at month 6 
#Control arm has crossover to subsequent IO after 24 mo, so its hazard decreases 20%.
#control arm has constant hazard (median 11.7 mo) and experimental arm has 
#hr = 1 and 0.65 at intervals (0, 6) and (6, 24) respectively.
#HR = 0.65, enrollment 24 months, weight 1.5, no drop offs; 
#IA and FA are performed at 400 and 500 events respectively.

crossEffect = 0.8 #Hazard ratio in control arm (after crossover vs before crossover)
lam0 = log(2)/12*c(1, 1, crossEffect); lam1 = log(2)/12*c(1, hr, hr)
sim.delay6crs=simulation.pwexp(nSim=10,N=600,A=24,w=1.5,r=1,lam0=lam0, lam1=lam1,cuts=c(6, 24),drop0=0,drop1=0, targetEvents=c(400, 500))
km.IA<-survival::survfit(survival::Surv(survTimeCut,1-cnsrCut)~treatment,data=sim.delay6crs[[1]][sim==1,])
plot(km.IA,xlab="Month Since Randomization",ylab="Survival",lty=1:2,xlim=c(0,36))
km.FA<-survival::survfit(survival::Surv(survTimeCut,1-cnsrCut)~treatment,data= sim.delay6crs[[2]][sim==1,])
plot(km.FA,xlab="Month Since Randomization",ylab="Survival",lty=1:2,xlim=c(0,36))