simulation.mcr.pfs: Simulation of PFS Data Following Mixture Cure Rate...
In phe9480/rgs: What the Package Does (One Line, Title Case)

Description Usage Arguments Details Value Examples

Consider the survival function of mixture cure rate (MCR) distribution: S(t) = p + (1-p)S0(t), where S0(t) is a survival distribution for susceptible subject, i.e., S0(0)=1 and S0(t) -> 0 as t -> Infinity. S0(t) can be any proper survival function. For generality of S0(t), consider the generalized modified Weibull (GMW) distribution with parameters (alpha, beta, gamma, lambda) Martinez et al(2013).

simulation.mcr.pfs(
  nSim = 100,
  N = 600,
  A = 18,
  w = 1.5,
  r = 1,
  p = c(0.1, 0.1),
  alpha = c(log(2)/12, log(2)/12),
  beta = c(1, 1),
  gamma = c(1, 1),
  lambda = c(0, 0),
  tau = c(0, 0),
  psi = c(1, 1),
  drop = c(0, 0),
  targetEvents = c(300, 420),
  DCO = NULL,
  scanfreq0 = c(rep(6, 2), rep(9, 100)) * 7/(365.25/12),
  scanfreq1 = c(rep(6, 2), rep(9, 100)) * 7/(365.25/12)
)

`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
`p`	Cure rate parameter. When p = 0, it reduces to `GMW(alpha, beta, gamma, lambda)` distribution. Each of the following parameters is a vector of 2 components for two treatment groups (control, experimental arm): `p`, `alpha`, `beta`, `gamma`, `lambda`, `tau`, `psi`, `drop`.
`alpha`	Generalized modified Weibull (GMW) distribution parameters. `alpha > 0`
`beta`	Generalized modified Weibull (GMW) distribution parameters. `beta > 0`
`gamma`	Generalized modified Weibull (GMW) distribution parameters. `gamma >= 0` but `gamma` and `lambda` cannot be both 0.
`lambda`	Generalized modified Weibull (GMW) distribution parameters. `lambda >= 0` but `gamma` and 'lambda“ cannot be both 0.
`tau`	Threshold for delayed effect period. `tau = 0` reduces no delayed effect.
`psi`	Hazard ratio after delayed effect. `psi = 1` reduces to the survival function without proportional hazards after delayed period (`tau`).
`drop`	Drop-off rate per unit time. For example, if 3% drop off in 1 year of followup, then `drop = 0.03/12`.
`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.
`scanfreq0`	A vector of scan frequency for control arm, eg, every 6 weeks for 2 scans, then every 9 weeks thereafter. scanfreq = c(rep(6, 2), rep(9, 1000))*7. Applicable for PFS data.
`scanfreq1`	A vector of scan frequency for experimental arm, eg, every 6 weeks for 2 scans, then every 9 weeks thereafter. scanfreq = c(rep(6, 2), rep(9, 1000))*7. Applicable for PFS data.

alpha: scale parameter beta and gamma: shape parameters lambda: acceleration parameter

S0(t) = 1-(1-exp(-alphat^gammaexp(lambda*t)))^beta

Special cases: (1) Weibull dist: lambda = 0, beta = 1. Beware of the parameterization difference. (2) Exponential dist: lambda = 0, beta = 1, gamma = 1. The shape parameter (hazard rate) is alpha. (3) Rayleigh dist: lambda = 0, beta = 1, gamma = 2. (4) Exponentiated Weibull dist (EW): lambda = 0 (5) Exponentiated exponential dist (EE): lambda = 0 and gamma = 1 (6) Generalized Rayleigh dist (GR): lambda = 0, gamma = 2 (7) Modified Weibull dist (MW): beta = 1

Let T be the survival time according to survival function S1(t) below. Denote T's distribution as MCR(p, alpha, beta, gamma, lambda, tau, psi), where tau is the delayed effect and psi is the hazard ratio after delayed effect, ie. proportional hazards to S(t) after delay tau. S(t) = p + (1-p)*S0(t) S1(t) = S(t)I(t<tau) + S(tau)^(1-psi)*S(t)^psi In brief, S0(t) is the proper GMW distribution (alpha, beta, gamma, lambda); S(t) is MCR with additional cure rate parameter p; In reference to S(t), S1(t) is a delayed effect distribution and proportional hazards after delay.

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. Delayed effect 6 months, proportional hazards HR = 0.6
#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.

set.seed(2022)
data = simulation.mcr.pfs(nSim=1, N = 600, A = 18, w=1.5, r=1, p=c(0.1,0.1), 
alpha = c(log(2)/12,log(2)/12), beta=c(1,1), gamma=c(1,1), 
lambda=c(0,0), tau=c(0,6), psi=c(1,0.6), drop=c(0,0),
targetEvents = c(350, 500), DCO = NULL, scanfreq0=c(rep(6, 2), rep(9, 100))*7/(365.25/12), 
scanfreq1=c(rep(6, 2), rep(9, 100))*7/(365.25/12)) 

data.IA = data[[1]][data[[1]]$sim==1,]
data.FA = data[[2]][data[[2]]$sim==1,]
m0 = qmcr(0.5, p=0.1, alpha = log(2)/12, beta=1, gamma=1, lambda=0, tau=0, psi=1)
m1 = qmcr(0.5, p=0.1, alpha = log(2)/12, beta=1, gamma=1, lambda=0, tau=6, psi=0.6)

km.IA<-survival::survfit(survival::Surv(survTimeCut,1-as.numeric(cnsrCut))~treatment, data=data.IA)
plot(km.IA, ylab="Survival", xlim=range(km.FA$time))
abline(h = c(0.1, 0.5), col="gray80", lty=2)
abline(v=c(6, m1, m0), col="gray80", lty=2)
 
km.FA<-survival::survfit(survival::Surv(survTimeCut,1-as.numeric(cnsrCut))~treatment, data=data.FA)
plot(km.FA, ylab="Survival", xlim=range(km.FA$time)) 
abline(h = c(0.1, 0.5), col="gray80", lty=2)
abline(v=c(6, m1, m0), col="gray80", lty=2)

#No consideration of scan intervals
set.seed(2022)
data0 = simulation.mcr.pfs(nSim=1, N = 600, A = 18, w=1.5, r=1, p=c(0.1,0.1), 
alpha = c(log(2)/12,log(2)/12), beta=c(1,1), gamma=c(1,1), 
lambda=c(0,0), tau=c(0,6), psi=c(1,0.6), drop=c(0,0),
targetEvents = c(350, 500), DCO = NULL, scanfreq0=NULL, 
scanfreq1=NULL) 

data0.IA = data0[[1]][data0[[1]]$sim==1,]
data0.FA = data0[[2]][data0[[2]]$sim==1,]
m0 = qmcr(0.5, p=0.1, alpha = log(2)/12, beta=1, gamma=1, lambda=0, tau=0, psi=1)
m1 = qmcr(0.5, p=0.1, alpha = log(2)/12, beta=1, gamma=1, lambda=0, tau=6, psi=0.6)

km.IA0<-survival::survfit(survival::Surv(survTimeCut,1-as.numeric(cnsrCut))~treatment, data=data0.IA)
km.FA0<-survival::survfit(survival::Surv(survTimeCut,1-as.numeric(cnsrCut))~treatment, data=data0.FA)
plot(km.IA0, ylab="Survival", xlim=range(km.FA0$time))
abline(h = c(0.1, 0.5), col="gray80", lty=2)
abline(v=c(6, m1, m0), col="gray80", lty=2)
 
plot(km.FA0, ylab="Survival", xlim=range(km.FA0$time)) 
abline(h = c(0.1, 0.5), col="gray80", lty=2)
abline(v=c(6, m1, m0), col="gray80", lty=2)