- N
Number of individuals
- fu.min
Minimum length of follow-up.
- fu.max
Maximum length of follow-up. Individuals length of follow-up is
generated from a uniform distribution on
[fu.min, fu.max]. If fu.min=fu.max, then all individuals have a common
follow-up.
- cens.prob
Gives the probability of being censored due to loss to follow-up before
fu.max. For a random set of individuals defined by a B(N,cens.prob)-distribution,
the time to censoring is generated from a uniform
distribution on [0, fu.max]. Default is cens.prob=0, i.e. no censoring
due to loss to follow-up.
- dist.x
Distribution of the covariate(s) \(X\). If there is more than one covariate,
dist.x must be a vector of distributions with one entry for each covariate. Possible
values are "binomial" and "normal", default is dist.x="binomial".
- par.x
Parameters of the covariate distribution(s). For "binomial", par.x is
the probability for \(x=1\). For "normal", par.x=c(\(\mu, \sigma\))
where \(\mu\) is the mean and \(\sigma\) is the standard deviation of a normal distribution.
If one of the covariates is defined to be normally distributed, par.x must be a list,
e.g. dist.x <- c("binomial", "normal") and par.x <- list(0.5, c(1,2)).
Default is par.x=0, i.e. \(x=0\) for all individuals.
- beta.x
Regression coefficient(s) for the covariate(s) \(x\). If there is more than one
covariate, beta.x must be a vector of coefficients with one entry for each covariate.
simrec generates as many covariates as there are entries in beta.x. Default is
beta.x=0, corresponding to no effect of the covariate \(x\).
- dist.z
Distribution of the frailty variable \(Z\) with \(E(Z)=1\) and
\(Var(Z)=\theta\). Possible values are "gamma" for a Gamma distributed frailty
and "lognormal" for a lognormal distributed frailty.
Default is dist.z="gamma".
- par.z
Parameter \(\theta\) for the frailty distribution: this parameter gives
the variance of the frailty variable \(Z\).
Default is par.z=0, which causes \(Z=1\), i.e. no frailty effect.
- dist.rec
Form of the baseline hazard function. Possible values are "weibull" or
"gompertz" or "lognormal" or "step".
- par.rec
Parameters for the distribution of the event data.
If dist.rec="weibull" the hazard function is $$\lambda_0(t)=\lambda*\nu* t^{\nu - 1},$$
where \(\lambda>0\) is the scale and \(\nu>0\) is the shape parameter. Then
par.rec=c(\(\lambda, \nu\)). A special case
of this is the exponential distribution for \(\nu=1\).\
If dist.rec="gompertz", the hazard function is $$\lambda_0(t)=\lambda*exp(\alpha t),$$
where \(\lambda>0\) is the scale and \(\alpha\in(-\infty,+\infty)\) is the shape parameter.
Then par.rec=c(\(\lambda, \alpha\)).\
If dist.rec="lognormal", the hazard function is
$$\lambda_0(t)=[(1/(\sigma t))*\phi((ln(t)-\mu)/\sigma)]/[\Phi((-ln(t)-\mu)/\sigma)],$$
where \(\phi\) is the probability density function and \(\Phi\) is the cumulative
distribution function of the standard normal distribution, \(\mu\in(-\infty,+\infty)\) is a
location parameter and \(\sigma>0\) is a shape parameter. Then par.rec=c(\(\mu,\sigma\)).
Please note, that specifying dist.rec="lognormal" together with some covariates does not
specify the usual lognormal model (with covariates specified as effects on the parameters of the
lognormal distribution resulting in non-proportional hazards), but only defines the baseline
hazard and incorporates covariate effects using the proportional hazard assumption.\
If dist.rec="step" the hazard function is $$\lambda_0(t)=a, t<=t_1, and \lambda_0(t)=b, t>t_1$$.
Then par.rec=c(\(a,b,t_1\)).
- pfree
Probability that after experiencing an event the individual is not at risk
for experiencing further events for a length of dfree time units.
Default is pfree=0.
- dfree
Length of the risk-free interval. Must be in the same time unit as fu.max.
Default is dfree=0, i.e. the individual is continously at risk for experiencing
events until end of follow-up.