simulation.mcr: Simulation of Two-Arm Trial 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(
  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
)

`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`.

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

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           
set.seed(2022)

#(6) Delayed effect 6 months, proportional hazards HR = 0.6
set.seed(2022)
data = simulation.mcr(nSim=10, 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(300, 420), DCO = NULL) 

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")
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") 
abline(h = c(0.1, 0.5), col="gray80", lty=2)
abline(v=c(6, m1, m0), col="gray80", lty=2)